122 results on '"Level set methods"'
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2. Optimal design of unimorph-type cantilevered piezoelectric energy harvesters using level set-based topology optimization by considering manufacturability.
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Miyajima, Ken and Yamada, Takayuki
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ENERGY consumption , *LEVEL set methods , *ENERGY levels (Quantum mechanics) , *PIEZOELECTRIC materials - Published
- 2024
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3. Topology optimization of curved thick shells using level set method and non-conforming multi-patch isogeometric analysis.
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Hübner Scherer, Fernando, Zarroug, Malek, Naceur, Hakim, and Constantinescu, Andrei
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LEVEL set methods , *STRUCTURAL optimization , *ISOGEOMETRIC analysis , *STRUCTURAL frames , *TOPOLOGY , *MODEL airplanes - Abstract
We present a novel framework for topological shape optimization of curved non-conforming multi-patch and trimmed thick-shells subjected to external loads. Our method integrates the level set method (LSM) with a diffuse interface, a Hadamard shape derivative, and multi-patch isogeometric analysis (IGA) into a gradient descent algorithm to systematically capture the evolution of the shape. This integration enables us to directly manipulate CAD-compatible geometries and analysis techniques and to obtain the results as a CAD surface. The novelty lies in the utilization of multi-patch IGA models based on NURBS functions, which allows us to simultaneously maximize the stiffness and minimize the volume of the shell by searching for an optimal material distribution within its middle surface. The material is modeled under a small strain assumption in linear elasticity using a Reissner–Mindlin kinematic shell model in plane stress. The effectiveness of our approach is demonstrated on several curved conforming and non-conforming multi-patch geometries in 3D. • We present a novel framework for topological shape optimization of curved thick-shells subjected to external loads. • By using multi-patch isogeometric analysis, we manipulate CAD-compatible geometries and analysis techniques to obtain the results as a CAD surface. • A NURBS-based reinterpretation of the level set method permits to obtain shapes that are directly manufacturable through additive manufacturing techniques. • The design framework offers a structure for enhancing three-dimensional parameterized shells through the utilization of compatible multi-patch Reissner–Mindlin shells. [ABSTRACT FROM AUTHOR]
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- 2024
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4. TOBN[sbnd]CFMV: Hybrid topology optimization-based Newton's method and conjugate finite mean value for RBTO of compliance problems.
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Qiu, Lida, Fan, Linyuan, Tang, Jiade, and Alfouneh, Mahmoud
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LEVEL set methods , *NEWTON-Raphson method , *BENCHMARK problems (Computer science) , *STRUCTURAL optimization , *SEQUENTIAL analysis , *CONJUGATE gradient methods - Abstract
• TOBN CFMV is proposed for RBTO using STORA the continues mechanical structures. • In optimization loop of STORA, TO-based Newton method is presented for optimal probabilistic constraint. • CFMV-based conjugate gradient in reliability loop is applied for MPP search in STORA method. • Sufficient descent condition is applied in formulation of CFMV method for satisfying robustness. • Three TO methods are discussed using the TOBN coupled by the CFMV though several RBTO problems. Uncertainties resulting from geometrical dimensions, external load, and material properties are inevitable in realistic engineering applications. Such uncertainties may result in substantial ineffectiveness in system performance or even unreliability in optimized outcomes which a designer must handle prior to the design and production stages. To address these issues, in this study, a novel hybrid reliability based topology optimization (RBTO) method is extended for considering the probabilistic constraints under uncertainties of compliance TO problems for evaluating the optimum layout. The optimum shapes of continues structures are evaluated based on the various TO approaches combined with the Newton's method and then the probabilistic constraints are approximated based on the performance measure approach (PMA) computed by the conjugate finite step mean value (CFMV). Inverse TO-based Newton' method (TOBN) is implemented for three different topology optimizations including evolutionary structural optimization (ESO), SIMP, and level set method. In TOBN, optimal results included optimal elemental data are yielded through mean volume fraction method TO which later these optimal results are used for RBTO method by hybrid approaches as TOBN for topology design optimum and CFMV for reliability assessment of topology constraints under uncertainties named TOBN CFMV. The CFMV approximates the probabilistic constraints under a conjugate sensitivity vector evaluated based on the finite value of gradient vector and new points i.e. most probable points (MPP). In the CFMV method, decent conditions are guaranteed stability when the objective function in the TO is structural compliance minimization. By having the MPP values the optimized volume fraction and therefore optimized features for RBTO can be achieved. The combination of Newton's method, the highly improved CFMV solution, and TO methods can be regarded as the innovations of the proposed approach. Additionally, the TOBN and dynamical mean value introduce a new sequential TO and reliability analysis method (STORA). The methodologies are demonstrated on benchmark problems which are frequently utilized in different TO approaches considering the uncertainties including material properties and external loads. With the comparison of the derived optimal results and topologies of TO and RBTOs, advantageous results concerning efficiency, validity, and accuracy of RBTO solution are drawn. [ABSTRACT FROM AUTHOR]
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- 2024
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5. Efficient single variable Level Set method for capturing moving interfaces in powder densification processes.
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Torres Cruz, Alberto, de Lange, Dirk Frederik, and Van Paepegem, Wim
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LEVEL set methods , *PARTIAL differential equations , *SPECIFIC gravity , *DEGREES of freedom , *POWDERS , *SET functions - Abstract
Among all the different techniques for modeling moving interfaces, the ones that capture the interfaces with a phase function such as Level Set (LS) methods have a great advantage over surface tracking approaches when managing topological changes. However, the standard LS method and the Conservative Level Set (CLS) method only distinguish between two different stable levels or phases using one level set equation, which is a second-order partial differential equation. When managing three or more levels or phases, the formulation requires additional level set equations. The model presented in this work is a modification of the CLS method by which one single level set variable can manage three stable levels. The level set variable can then be interpreted as the average relative density of a specific material with three stable density levels. The presented model is suitable to represent the deposition and densification of powder material, where three different stable levels (void, powder, and fully dense material) coexist, and therefore can be applied to capture the evolving interfaces, as is of particular interest for processes such as powder based additive manufacturing. The main advantage of the proposed model is the large reduction of the number of degrees of freedom compared to the traditional LS formulation, reducing the required computational resources. Several test cases, including densification cases, are addressed in the present article. [ABSTRACT FROM AUTHOR]
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- 2024
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6. A multivariate level set method for concurrent optimization of graded lattice structures with multiple microstructure prototypes.
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Shu, Zhengtao, Gao, Liang, and Li, Hao
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LEVEL set methods , *TOPOLOGY , *GEOMETRIC connections , *MICROSTRUCTURE , *PROTOTYPES , *SET functions - Abstract
The concurrent optimization design of graded lattice structures (GLSs) considering both the diversity of microstructure prototypes and the geometric continuity has attracted extensive attention. This paper presents a multivariable level set-based topology optimization method for designing GLSs considering the matching of multiple microstructure prototypes. In this method, the basic level set functions (LSFs) of implicit and designable microstructures are constructed using the signed distance function. Multiple sets of LSFs are further developed by introducing weight coefficients to generate GLSs based on the basic LSFs. During optimization, each set of LSFs will generate a sub-GLS corresponding to the pre-defined microstructure prototype. Then, the final GLS containing multiple microstructures is obtained by combining these sub-GLSs through a union operation. Due to the continuity of the multivariable LSF, perfect geometric connections between neighboring graded microstructures are guaranteed without imposing any extra constraints. This work offers a novel strategy to optimize the macroscopic graded pattern of GLSs, resulting in an enlarged design space and performance improvement. Several 2D and 3D examples are presented to demonstrate the effectiveness and applicability of the proposed method. [ABSTRACT FROM AUTHOR]
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- 2024
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7. A novel quasi-smooth tetrahedral numerical manifold method and its application in topology optimization based on parameterized level-set method.
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Deng, Shanyao, Wang, Pan, Wen, Weibin, and Liang, Jun
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LEVEL set methods , *TOPOLOGY , *STRUCTURAL optimization - Abstract
In this paper, a novel quasi-smooth tetrahedral numerical manifold method (NMM) and its two-dimensional (2D) counterpart are proposed. A new topology optimization method is established by combining the quasi-smooth manifold element (QSME) with the parameterized level set method (PLSM). The QSME introduces an innovative displacement function characterized by high accuracy and high-order continuity, effectively addressing the "linear dependence" (LD) issue inherent in traditional high-order NMM. To integrate QSME and PLSM, the corresponding optimization formulations and sensitivity analyses are provided. In order to fully utilize advantages of this novel quasi-smooth NMM and the PLSM, an element subdivision technique based on model recognition is proposed to accurately capture the physical boundaries. Additionally, a volume fraction update method based on element refinement is proposed. Taking advantage of the characteristics of the PLSM, a structure visualization method based on the sign distance function is developed to accurately describe curve boundary. This method allows for precise visualization of optimized structures. This study verifies high efficiency of the QSME-based PLSM for minimum compliance topology optimization problems in both 2D and 3D structures. Some representative structural optimization examples are tested to demonstrate effectiveness of the proposed method in both 2D and 3D problems, especially in complex design domain. [ABSTRACT FROM AUTHOR]
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- 2024
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8. Multi-scale topological design of asymmetric porous sandwich structures with unidentical face sheets and composite core.
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Ding, Zhe, Zou, Zhimiao, Zhang, Lei, Li, Xiaobai, and Zhang, Yan
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SANDWICH construction (Materials) , *LEVEL set methods , *MOUTH protectors - Abstract
• A novel multiscale topology optimization method is proposed for designing asymmetric porous sandwich structures. • Multi-material sandwich structures are topologically optimized using the proposed method. • The thickness and material of two face sheets and the configuration of composite cores are simultaneously optimized. • Parametric level set method and alternating active-phase method are adopted. • Several 2D and 3D numerical examples are investigated and compared. Compared with conventional symmetric sandwich structure with identical face sheets and single-material core, asymmetric porous sandwich structures (APSSs), which are composed of unidentical face sheets and composite core, usually take better advantage of all materials and provide superior bending stiffness. However, current studies regarding the APSSs are mainly analytical- and experimental-based methods with predefined face sheet thicknesses and core configurations, which greatly confines the potential loading capacity of sandwich structures. This paper develops a multiscale topology optimization method for the multi-material APSSs, which can realize the designs of the thickness and material of two face sheets at macroscale as well as the configuration of composite cores at microscale for minimizing structural compliance. Firstly, at macroscale, a multi-material variable thickness sheet method integrated with an alternating active-phase algorithm are employed to optimize the thickness and material of two solid face sheets. Then, at microscale, a difference-set-based multi-material level set (DS-MMLS) model is applied to represent the topology of each material phase within sandwich core, and their topological evolution can be readily achieved by using a parametric level set method also combined with the alternating active phase algorithm. Several 2D and 3D numerical examples are provided to show the effectiveness and advantages of the proposed method. The results indicate that compliances of the optimized APSSs show superior advantages over some conventional sandwich structures with predefined design features. [ABSTRACT FROM AUTHOR]
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- 2024
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9. An interface-enriched generalized finite element method for the analysis and topology optimization of 2-D electromagnetic problems.
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van Bergen, Steven, Norte, Richard A., and Aragón, Alejandro M.
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FINITE element method , *BAND gaps , *TOPOLOGY , *ELECTROMAGNETIC interactions , *ELECTROMAGNETIC wave scattering , *LEVEL set methods , *ELECTROMAGNETIC waves - Abstract
The computational analysis of nanophotonic devices is usually carried out via the standard finite element method (FEM). However, FEM requires meshes that are fitted to the devices' boundaries, so making changes to the geometry (and thus the mesh) results in an inefficient process at best. Such an approach is therefore at odds when conducting design, which requires the analysis of multiple device geometries until reaching a satisfactory solution. Computational design tools such as topology optimization are often used, but the use of density-based representations of geometry inevitably leads to other issues—e.g., pixelized fuzzy boundaries with "gray material" (that does not correspond to dielectric nor vacuum) have an adverse effect on the devices' interaction with electromagnetic waves. In this paper we propose an interface-enriched generalized finite element method (IGFEM) for the analysis of two-dimensional electromagnetic scattering and eigenvalue problems. IGFEM enables the use of finite element meshes that are completely decoupled from the problem's geometry. The analysis procedure is further coupled to a level set description of topology, resulting in a versatile enriched approach to topology optimization; this level set-based interface-enriched topology optimization procedure is devoid of the issues mentioned above regarding density-based methods, and yields crisp "black-and-white" designs that are devoid of jagged fuzzy edges. We first demonstrate that the analysis procedure achieves the same convergence rate as that of standard FEM using geometry-fitted meshes. We then compare the convergence properties of IGFEM with Nitsche's method on a problem containing an embedded straight interface. Finally, we conduct topology optimization for designing both a 2-D metalens and a 2-D reflector, maximizing their ability to focus light onto a target point. [Display omitted] • Interface-enriched GFEM with nodal elements allows to decouple mesh from geometry. • Nodal enrichments allow for straightforward implementation in displacement-based FEM codes. • IGFEM-based analysis has optimal error convergence in L 2 norm for smooth problems. • Photonic crystal band structures can be computed accurately with IGFEM-based analysis. • Enriched level set-based topology optimization yields black-and-white smooth designs. [ABSTRACT FROM AUTHOR]
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- 2024
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10. A new multiscale topology optimization method for multiphase composite structures of frequency response with level sets.
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Li, Hao, Luo, Zhen, Xiao, Mi, Gao, Liang, and Gao, Jie
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COMPOSITE structures , *COMPOSITE materials , *LEVEL set methods , *SET functions , *TOPOLOGY , *FINITE element method - Abstract
This paper proposes a new multiscale topology optimization method for the concurrent design of multiphase composite structures under a certain range of excitation frequencies. Distinguished from the existed studies, a general concurrent design formulation for the dynamic composite structures with more than two material phases is developed. The macrostructureand its microstructures with multiple material phases are optimized simultaneously. The integral of the dynamic compliances over an interval of frequencies is formulated as the optimization objective, so as to minimize the frequency response within the concerned excitation range. The effective properties of the multiphase microstructures are evaluated by using the numerical homogenization method, which actually serves as a link to bridge the macro and micro finite element analyses. Furthermore, to describe the boundaries of multiple material phases for the microstructure, a parametric color level set method (PCLSM) is developed by using an efficient interpolation scheme. In this way, L level set functions can represent at most 2 L material phases without any overlaps. Moreover, these "color" level sets are updated by directly using the well-established gradient-based algorithm, which can greatly facilitate the proposed method to solve the multi-material optimizations with multiple design constraints. Several 2D and 3D numerical examples are used to demonstrate the effectiveness of the proposed method in the concurrent design of the dynamic composite structures under the excitation frequency ranges. • A general concurrent design formulation for composite structures with more than two material phases. • Multiscale optimization of macrostructure and its multiphase microstructure under excitation ranges. • A parametric color level set method for multi-material optimizations. • Multiple volume constraints at different scales can be conveniently handled. • Clear and distinctive interfaces of different material phases for both macrostructure and microstructure. [ABSTRACT FROM AUTHOR]
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- 2019
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11. Variational approach to relaxed topological optimization: Closed form solutions for structural problems in a sequential pseudo-time framework.
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Oliver, J., Yago, D., Cante, J., and Lloberas-Valls, O.
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LEVEL set methods , *TOPOLOGICAL derivatives , *STRUCTURAL optimization , *TOPOLOGICAL fields , *CHARACTERISTIC functions , *ANALYTICAL solutions , *COST functions - Abstract
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a non-smoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function , which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint , at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method , are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closed-form solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the work. [ABSTRACT FROM AUTHOR]
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- 2019
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12. Generalized hole nucleation through BESO for the level set based topology optimization of multi-material structures.
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Xia, Qi and Shi, Tielin
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LEVEL set methods , *NUCLEATION , *TOPOLOGICAL derivatives - Abstract
When a multi-material structure is optimized by using the level set method, besides the topological changes that are familiar to people (i.e., vanishing of a hole, nucleation of a hole, merging of holes, and breaking apart of a region), another topological change, i.e., the conversion between a pair of materials, is also possible to happen but receives little attention. In this case, a hole is no longer a region of void but becomes occupied by a different solid material. In our present study, such a topological change is called the generalized hole nucleation, and the material conversion scheme of the BESO is integrated into the level set based framework to deal with it. A strategy determining where and when to conduct generalized hole nucleation is presented. In addition, the shape derivatives of the structure's traction free boundary and the interfaces between material regions are carefully analyzed. The results of several numerical examples prove that the proposed method is effective and efficient. • The optimization framework combining level set and BESO is introduced. • Material conversion scheme of BESO is used for generalized nucleate holes. • A strategy determining where and when to conduct generalized hole nucleation is presented. • The shape derivatives of boundary and the interfaces between material regions are carefully analyzed. [ABSTRACT FROM AUTHOR]
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- 2019
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13. VCUT level set method for topology optimization of functionally graded cellular structures.
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Zong, Hongming, Liu, Hui, Ma, Qingping, Tian, Ye, Zhou, Mingdong, and Wang, Michael Yu
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LEVEL set methods , *CELL anatomy , *GEOMETRIC connections , *NONLINEAR analysis , *TOPOLOGY , *SET functions , *CONTINUOUS functions - Abstract
This paper presents a variable cutting (VCUT) level set based topology optimization method to design functionally graded cellular structures (FGCS). A variable and continuous cutting function by interpolating with a set of height variables is proposed to generate functionally graded cellular structures, which offers a novel tool to optimize the macroscopic graded pattern. Due to the continuity of the cutting function, perfect geometric connections between adjacent cells are guaranteed without imposing extra constraints in the optimization. In addition, a solid covering skin can be easily attached to the FGCS by means of the variable cutting function. Three FGCS design problems, including graded density control, compliance minimization and layered cellular structure design, are presented to demonstrate the effectiveness and applicability of the proposed method. The optimized 2D and 3D macroscopic FGCS designs exhibit well-performing structural layout with fully connected micro-scale geometries. [ABSTRACT FROM AUTHOR]
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- 2019
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14. A contact algorithm for voxel-based meshes using an implicit boundary representation.
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Leichner, Alexander, Andrä, Heiko, and Simeon, Bernd
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SURFACE dynamics , *LEVEL set methods - Abstract
Numerical methods operating on structured grids have become popular since they offer good run time performance and are able to process directly voxel-based digital data from image recordings. Hence, the general framework of these fast solvers presupposes an unfitted boundary approximation avoiding complicated meshing of bodies. This allows an efficient handling with geometrical issues. Nevertheless, contacts between deformable solids are hard to deal with in the presence of this boundary representation. For this difficulty we suggest the usage of an implicit boundary representation combined with a modified saddle point formulation, resembling Nitsche's approach. Both ideas give an elegant approach for discretizing the contact terms and enable a simple contact detection. Moreover, we suggest an intermediate surface as new reference contact area which fits well into our proposed method. In the end we present numerical results and analyze the accuracy and convergence rate. Furthermore, we demonstrate the current application range of our approach for problems with multiple contacts. In this paper we focus only on frictionless contact with small deformations. • A numerical method on structured meshes for contact in 2D and 3D is presented • The concept of intermediate surfaces as contact surfaces is considered. • Implicit surface dynamics is used for contact detection and kinematics. • A modified Nitsche's approach enforces the contact constraints. • Geometrical approximations are based on implicit surface representations. [ABSTRACT FROM AUTHOR]
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- 2019
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15. Piecewise length scale control for topology optimization with an irregular design domain.
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Liu, Jikai
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TOPOLOGY , *LEVEL set methods , *CONSTRAINED optimization , *IMAGE processing - Abstract
This paper presents a piecewise length scale control method for level set topology optimization. Different from the existing methods, where a unique lower limit or upper limit was applied to the entire design domain, this new method decomposes the topological design into pieces of strip-like components based on the connectivity condition, and then, the lower or upper limit for length scale control could be piecewise and dynamically defined based on each component's real-time status (such as position, orientation, or dimension). Specifically, a sub-algorithm of structural skeleton identification and segmentation is developed to decompose the structure and its skeleton. Then, a skeleton segment-based length scale control method is developed to achieve the piecewise length scale control effect. In addition, a special type of length scale constrained topology optimization problem that involves an irregular design domain will be addressed, wherein the complex design domain plus the length scale constraint may make the conventional length scale control methods fail to work. Effectiveness of the proposed method will be proved through a few numerical examples. • Realize the piecewise length scale control for level set topology optimization. • Dynamically and separately define the length scale target based on each component's real-time status. • Use image processing techniques for structural skeleton identification and segmentation. • Address the length scale constrained topology optimization problem that involves an irregular design domain. [ABSTRACT FROM AUTHOR]
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- 2019
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16. Cellular level set in B-splines (CLIBS): A method for modeling and topology optimization of cellular structures.
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Wang, Michael Yu, Zong, Hongming, Ma, Qingping, Tian, Ye, and Zhou, Mingdong
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CELL anatomy , *THREE-dimensional modeling , *GEOMETRIC connections , *TOPOLOGY , *LEVEL set methods , *COMPUTING platforms - Abstract
Abstract In this work, we develop a level set modeling technique for designing and optimization of solid/cellular structures, called cellular level set in B-splines (CLIBS). In this technique, the entire design domain for the solid/cellular structure in question is subdivided into a set of connected volumetric cells in three dimensions. In the level set scheme for representing the structural geometry, an implicit trivariate B-spline function is defined on each subdomain cell. This parameterization scheme allows us to impose constraints on the relevant B-spline coefficients for naturally maintaining geometric continuities at the connection faces between neighboring cells. Benefiting from the intrinsic properties of the trivariate B-spline functions, the method offers several useful properties and powerful functionalities to build and modify a solid/cellular structure in the modeling process and to conduct topology optimization. These processes are directly dealt with in terms of the B-spline coefficients with great numerical efficiency. While the model construction can be carried out in a use of the fast B-spline interpolation, the topology optimization may involve a sequence of discrete B-spline convolutions. Several 3D modeling and optimization examples are presented, including single-scale solid structures, periodic cellular structures and layered cellular structures. The proposed method is highly scalable, potentially leading to high definition modeling and optimization applications on a large-scale computing platform. Highlights • A CLIBS method is developed for modeling and optimization of cellular structures. • The method is highly scalable by defining B-spline functions on subdivided cells. • Powerful functionalities for building and modifying cellular structures are provided. • Geometric continuities can be achieved by constraints on the B-spline coefficients. [ABSTRACT FROM AUTHOR]
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- 2019
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17. Kriging-assisted topology optimization of crash structures.
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Raponi, Elena, Bujny, Mariusz, Olhofer, Markus, Aulig, Nikola, Boria, Simonetta, and Duddeck, Fabian
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KRIGING , *LEVEL set methods , *TOPOLOGY , *SURROGATE-based optimization , *MATHEMATICAL optimization , *COVARIANCE matrices - Abstract
Abstract Over the recent decades, Topology Optimization (TO) has become an important tool in the design and analysis of mechanical structures. Although structural TO is already used in many industrial applications, it needs much more investigation in the context of vehicle crashworthiness. Indeed, crashworthiness optimization problems present strong nonlinearities and discontinuities, and gradient-based methods are of limited use. The aim of this work is to present an in-depth analysis of the novel Kriging-Assisted Level Set Method (KG-LSM) for TO. It is based on an adaptive optimization strategy using the Kriging surrogate model and a modified version of the Expected Improvement (EI) as the update criterion, which allows for embedding opportune constraints. The adopted representation using Moving Morphable Components (MMCs) significantly reduces the dimensionality of the problem, enabling an efficient use of surrogate-based optimization techniques. A minimum compliance cantilever beam test case of different dimensionalities is used to validate the presented strategy, as well as identify its potential and limits. The method is then applied to a 2D crash test case, involving a cylindrical pole impact on a rectangular beam fixed at both ends. Compared to the state-of-the-art Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the KG-LSM optimization algorithm demonstrates to be efficient in terms of convergence speed and performance of the optimized designs. [ABSTRACT FROM AUTHOR]
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- 2019
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18. An algorithm for adaptive introduction and arrangement of velocity discontinuities within 3D finite-element-based upper bound limit analysis approaches.
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Li, M., Füssl, J., Lukacevic, M., Eberhardsteiner, J., and Martin, C.M.
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LEVEL set methods , *VELOCITY , *DEGREES of freedom , *FAILURE mode & effects analysis , *FINITE element method - Abstract
Abstract This paper presents a new adaptive strategy to efficiently exploit velocity discontinuities in 3D finite-element-based upper bound limit analysis formulations. Based on an initial upper bound result, obtained with a conventional approach without velocity discontinuities, possible planes of plastic flow localisation are determined at each strain-rate evaluation node and, subsequently, this information is used to sequentially introduce discontinuities into the considered discretised structure. During a few iterations, by means of introducing new and adjusting existing discontinuities, an optimal velocity discontinuity layout is obtained. For the general 3D case, the geometry of this layout is defined by the well-known level set method, standardly used to define the geometry of cracks in the extended finite element method. To make this method also applicable for orthotropic strength behaviours, traction-based yield functions defining the plastic flow across discontinuities are derived from their stress-based counterparts. This procedure is outlined in detail and the obtained traction-based yield functions are verified numerically, to guarantee a consistent strength behaviour throughout the whole discretised structure. By means of three different examples, including isotropic as well as orthotropic yield functions, the performance of the proposed strategy is investigated and upper bound results as well as failure modes are compared to reference solutions. The proposed approach delivers reliable upper bounds for each example and the majority of plastic flow takes place across the sensibly-arranged discontinuities. For this reason, very good upper bounds can be obtained with a quite coarse finite element mesh and only few introduced velocity discontinuities. This represents an attractive alternative to commonly-used adaptive mesh refinement strategies, where often a huge number of degrees of freedom need to be added to capture localised failure. Highlights • Implementing velocity discontinuities into numerical upper bound formulations. • Developing an adaptive strategy to implement discontinuities in the optimal layout. • Using traction-based yield functions for strength behaviours across discontinuities. • Deriving a projection algorithm to guarantee consistent strength behaviours. [ABSTRACT FROM AUTHOR]
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- 2019
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19. Analysis of landslides employing a space–time single-phase level-set method.
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Reinstädler, S., Kowalsky, U., and Dinkler, D.
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SPACETIME , *PHASE transitions , *FLUID-structure interaction , *LEVEL set methods , *DISCRETIZATION methods - Abstract
Abstract Landslide dynamics are characterized by a phase transition from a solid like behavior to a fluid one. Since the material is moving through space special discretization techniques are required. Four-dimensional space–time finite elements for fluid–structure interactions are applied together with the single-phase level-set method to investigate the dynamics of 3D landslides interacting with flexible walls. The wall is modeled as a geometric nonlinear solid with elastic–viscoplastic material behavior, whereas the liquefied soil is described with the Navier–Stokes equations for incompressible Bingham fluids. Between fluid and solid advanced coupling conditions are taken into account incorporating friction. In order to solve the governing equations of the multi-field problem, the weighted-residuals method is applied, which is discretized by time-discontinuous space–time elements. Within the monolithic solution procedure for the coupled problem, the kinematics of both solid and fluid are described using velocities as primary variables. A pseudo-structure adapts the coordinates of the fluid mesh to the deformations of adjacent structures. The single-phase level-set method describes the motion of the free surface of the sliding material. To accurately transport the free surface a pde-based extrapolation is used for the velocities. Various effects in 3D landslide dynamics are investigated. [ABSTRACT FROM AUTHOR]
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- 2019
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20. Complex uncertainty-oriented robust topology optimization for multiple mechanical metamaterials based on double-layer mesh.
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Li, Zeshang, Wang, Lei, Geng, Xinyu, Chen, Weimin, and Han, Bing
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ROBUST optimization , *POISSON'S ratio , *METAMATERIALS , *MECHANICAL engineering , *LEVEL set methods - Abstract
With the continuous improvement of structural performance requirements of advanced equipment, the multiscale design of materials and structures is increasingly developing towards refinement and multi-function. Metamaterials have broad application prospects due to their superior mechanical properties. In this paper, a robust topology optimization design strategy for mechanical metamaterials with multiple properties including modulus and Poisson's ratio is proposed. This method considers the manufacturing size uncertainty on properties of metamaterials and adopts a double-layer mesh technology to improve the efficiency of topology optimization. In addition, a topology optimization model for metamaterials with different mechanical properties is established, and mechanical metamaterials with various properties and configurations have been designed and validated. These can provide technical support and design references for the engineering application of mechanical metamaterials. [ABSTRACT FROM AUTHOR]
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- 2024
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21. A level set reliability-based topology optimization (LS-RBTO) method considering sensitivity mapping and multi-source interval uncertainties.
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Li, Zeshang, Wang, Lei, and Xinyu, Geng
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LEVEL set methods , *OPTIMIZATION algorithms , *TOPOLOGY , *STRUCTURAL engineering , *STRUCTURAL design - Abstract
With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, structural design methods are facing more and more factors to be considered. It is necessary to develop advanced design technology. In this paper, a sensitivity mapping technique is proposed to improve the effect of topology optimization based on a gradient optimization algorithm. The applicability of this technology is analyzed. In addition, considering the influence of multi-source uncertainties in the whole life cycle of the structure, a reliability-based topology optimization strategy based on the level set method is proposed. The sensitivity of displacement constraint and reliability constraint with pseudo time is derived. Numerical examples and Monte Carlo verification results fully illustrate the applicability, effectiveness, and efficiency of the proposed method. This method has been successfully applied to the topology optimization design of the rocket skid structure. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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- View/download PDF
22. Orientation optimization via topological derivatives in combination with multi-material topology optimization based on extended level set method.
- Author
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Noda, Masaki, Matsushima, Kei, and Yamada, Takayuki
- Subjects
- *
TOPOLOGICAL derivatives , *LEVEL set methods , *TOPOLOGY , *OPTIMIZATION algorithms , *FIBROUS composites - Abstract
This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the sensitivity of an objective function with respect to a topological change of anisotropic materials. The sensitivity is incorporated into a new gradient-based optimization algorithm. This method improves our ability to obtain better optimal candidates. We provide some numerical examples and verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Strength design of porous materials using B-spline based level set method.
- Author
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Wang, Cong, Xie, Yi Min, Zhuang, Zicheng, Zhang, Xuyu, and Zhou, Shiwei
- Subjects
- *
LEVEL set methods , *POROUS materials , *ASYMPTOTIC homogenization , *FINITE element method , *SURFACE roughness , *STRENGTH of materials - Abstract
The inverse homogenization method can tailor some mechanical and physical effective properties by laying out materials in a periodic representative volume element. However, studies on strength design are yet to be developed because of the difficulties in numerically retrieving its value. Unlike traditional asymptotic homogenization, the fast Fourier transform-based homogenization method based on the augmented Lagrangian approach uses a Green operator in the frequency domain to replace time-consuming finite element analysis and inherently meet the periodic boundary conditions. Thus, it is developed in this work to retrieve material strength in terms of the von Mises yield criterion. The zero-level contour of a linear combination of cubic B-spline basis functions with repeated knots is used to represent the microstructure profile in the design of material strength. The effective strength or its squared difference with a prescribed target is minimized within the framework of the reaction diffusion-based B-spline level set method. The filtered, non-consistent discrete Green operator is adopted to avoid slow convergence of porous material. Examples of porous material demonstrate that the proposed method guarantees surface smoothness, optimization flexibility, and structural periodicity in strength design. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Surface tension effect on flexoelectric energy harvesting based on extended isogeometric analysis.
- Author
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Li, Kaichun and Du, Chengbin
- Subjects
- *
ISOGEOMETRIC analysis , *SURFACE tension , *ENERGY harvesting , *POISSON'S ratio , *FLUID inclusions , *LEVEL set methods - Abstract
This study presents a numerical framework to model the effect of surface tension on a flexoelectric energy harvesting system with liquid inclusions. The equivalent Young's modulus and Poisson's ratio of the liquid inclusions embedded in flexoelectric composites considering the surface tension are derived for the first time. An extended isogeometric analysis (XIGA) based on non-uniform rational B-splines (NURBS) is developed to model and solve the electromechanical response of weak discontinuities in flexoelectric composites. The interface between liquid and solid materials is implicitly represented by the level set method. Several numerical examples are presented as linear dielectric solids embedded with liquid inclusions under mechanical compression and different electric circuit configurations, including square matrixes and truncated pyramids. The simulation results indicate that a significant enhancement in the electromechanical coupling coefficient can be obtained by considering the effect of surface tension in open- and closed-circuit configurations. The maximum electric potential and energy conversion are higher in the open-circuit configuration. In addition, the XIGA simulation shows that the energy conversion of the flexoelectric devices increases as the size of the structural system and Young's modulus of the flexoelectric material decrease. The maximum energy conversion capability of the flexoelectric composite, including the effect of surface tension, is enhanced by 32.4% with a central inclusion and 57% or higher with random inclusions. Finally, the influence of the length scale on the flexoelectricity is analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. A novel numerical manifold method and its application in parameterized LSM-based structural topology optimization.
- Author
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Deng, Shanyao, Duan, Shengyu, Wang, Pan, and Wen, Weibin
- Subjects
- *
STRUCTURAL optimization , *SUBDIVISION surfaces (Geometry) , *LEVEL set methods , *NUMERICAL integration , *COUPLING schemes - Abstract
In this paper, a high-efficiency structural topology optimization framework based on combination of numerical manifold method (NMM) and parameterized level set method (PLSM) is established. The NMM uses two cover systems to discretize the model, which can accurately represent the complex boundary of the design domain. A new numerical manifold element has been derived for the application of NMM in PLSM-based optimization. To obtain enhanced accuracy for structural analysis, a multilevel subdivision technique for numerical manifold element generation is presented, and the related numerical integration scheme coupled with the interpolation point selection strategy is provided. For the proposed topology optimization, the new update method of element stiffness matrix is exclusively formulated as well as the calculation method of volume fraction. Some representative structural optimization problems demonstrate that the proposed structural topology optimization method is very effective for two-dimensional (2D) and three-dimensional (3D) structural topology optimization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. Topology optimization for multiscale design of porous composites with multi-domain microstructures.
- Author
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Gao, Jie, Luo, Zhen, Li, Hao, and Gao, Liang
- Subjects
- *
STRUCTURAL optimization , *POROUS materials , *MICROSTRUCTURE , *ASYMPTOTIC homogenization , *LEVEL set methods - Abstract
Abstract This paper proposes a new multiscale topology optimization method for the design of porous composites composed of the multi-domain material microstructures considering three design elements: the topology of the macrostructure, the topologies of multiple material microstructures and their overall distribution in the macrostructure. The multiscale design involves two optimization stages: the free material distribution optimization and the concurrent topology optimization. Firstly, the variable thickness sheet (VTS) method with the regularization mechanism is used to generate multiple element density distributions in the macro design domain. Hence, different groups of elements with the identical densities can be uniformly arranged in their corresponding domains, and each domain in the space will be periodically configured by a unique representative microstructure. Secondly, with the discrete material distributions achieved in the macro domain, the topology of the macrostructure and topologies of multiple representative microstructures are concurrently optimized by a parametric level set method combined with the numerical homogenization method. Finally. Several 2D and 3D numerical examples are provided to demonstrate the effectiveness of the proposed multiscale topology optimization method. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
27. Stress-constrained level set topology optimization for design-dependent pressure load problems.
- Author
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Emmendoerfer, Hélio, Silva, Emílio Carlos Nelli, and Fancello, Eduardo Alberto
- Subjects
- *
STRAINS & stresses (Mechanics) , *LEVEL set methods , *STRUCTURAL optimization , *STRESS concentration , *HAMILTON-Jacobi equations - Abstract
Abstract This work presents a level set framework to solve topology optimization problems subject to local stress constraints considering design-dependent pressure loads. Two technical difficulties are related to this problem. The first one is the local nature of stresses. To deal with this issue, stress constraints are included to the problem by means of an Augmented Lagrangian scheme. The second is the adequate association between the moving boundary and the pressure acting on it. This difficulty is easily overcome by the level set method that allows for a clear tracking of the boundary along the optimization process. In the present approach, a reaction–diffusion equation substitutes the classical Hamilton–Jacobi equation to control the level set evolution. This choice has the advantage of allowing the nucleation of holes inside the domain and the elimination of the undesirable level set reinitializations. In addition, the optimization algorithm allows the rupture of loading boundaries, that is, the crossing of the pressured (wet) boundary with the traction free boundary is not avoided. This gives more freedom to the algorithm for topological changes. In order to validate the proposed scheme against stress concentrations, all numerical examples are performed on constrained domains containing singularities. Moreover, optimized designs obtained from stress-constrained and compliance problems are compared. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
28. Topology optimization of conformal structures on manifolds using extended level set methods (X-LSM) and conformal geometry theory.
- Author
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Ye, Qian, Guo, Yang, Chen, Shikui, Lei, Na, and Gu, Xianfeng David
- Subjects
- *
MANIFOLDS (Engineering) , *LEVEL set methods , *CONFORMAL geometry , *CONFORMAL mapping , *FAST marching method (Mathematics) - Abstract
Abstract In this paper, we propose a new method to systematically address the issue of structural shape and topology optimization on free-form surfaces. A free-form surface, also termed manifold, is conformally mapped onto a 2D rectangle domain where the level set function is defined. With the conformal mapping, the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar. Keeping this intrinsic relation in mind, we derive the Euclidean form for the Riemannian Hamilton–Jacobi equation governing the boundary evolution on the manifold, which can be solved on a 2D plane using classical level set methods, such as the upwind finite difference or fast marching method. By reducing the dimension of the problem, the topology optimization problem on the manifold embedded in the 3D space can be recast as a 2D topology optimization problem in the Euclidean space. Compared with other approaches which need project the Euclidean differential operators to the manifold, the proposed method can not only reduce the computational cost but also preserve all the advantages of conventional level set methods. The proposed method reveals the fundamental relation between topology optimization on manifolds and Euclidean planes. It provides a unified level-set-based computational framework for the generative design of conformal structures with increasing applications in different fields of interests. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
29. Structural optimization based on meshless element free Galerkin and level set methods.
- Author
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Khan, Wajid, Siraj-ul-Islam, and Ullah, Baseer
- Subjects
- *
STRUCTURAL optimization , *GALERKIN methods , *LEVEL set methods , *ALGORITHMS , *SENSITIVITY analysis - Abstract
Abstract This paper is concentrated on the shape and topology optimization of 2D linear elastic problems using meshless element free Galerkin (EFG) method combined with the level set method (LSM). In this procedure, a level set function (LSF) is used for the implicit representation of the structural geometry, and thus ensuring appropriate essential topological changes to obtain optimized structures. Both the methods (EFG and LSM) use the same Cartesian grid points. Shape and topological sensitivities are evaluated by the EFG method and the structural geometry is updated through LSM. The algorithm is tested on five different standardized structural topology optimization problems for minimum compliance, subject to the application of load at single and multiple points. The results obtained with the proposed method suggest efficiency, convergence, accuracy and good agreement of the simulated results with the optimal topologies reported in the literature. Highlights • Structural optimization is performed using meshless procedure coupled with level set method. • Hamilton–Jacobi equation with topological derivative term is used to update the structure geometry. • Sensitivity analysis of the structural optimization problem is undertaken. • Simulation results are obtained for benchmark structural optimization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
30. Stable hole nucleation in level set based topology optimization by using the material removal scheme of BESO.
- Author
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Xia, Qi, Shi, Tielin, and Xia, Liang
- Subjects
- *
LEVEL set methods , *EVOLUTIONARY algorithms , *HAMILTON-Jacobi equations , *STRUCTURAL optimization , *TOPOLOGY - Abstract
Abstract A method is proposed to nucleate holes during the level based topology optimization by using the material removal scheme of the bi-directional evolutionary optimization (BESO). The key idea is that when a very small amount of inefficient material is removed according to the BESO from the interior of a structure, the effect is essentially the same as that of using the topological derivative to nucleate a hole. For removing material, a threshold of sensitivity number is determined. It is the minimum of two tentative thresholds. The first tentative threshold is determined according to the percentage of material to be removed in each iteration of optimization. The second tentative threshold is determined according to the average sensitivity number along the boundary to be optimized, and it is helpful to stabilize hole nucleation. Details of the optimization procedure are described. The results of several numerical examples prove that the proposed hole nucleation method is effective and efficient. Highlights • Material removal scheme of BESO is used to nucleate holes. • When material in structure is removed, the effect is the same as topological derivative. • For hole insertion, a threshold of sensitivity number is determined. • A tentative threshold is based on average sensitivity number along the boundary. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
31. Level set-based topology optimization with overhang constraint: Towards support-free additive manufacturing.
- Author
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Wang, Yaguang, Gao, Jincheng, and Kang, Zhan
- Subjects
- *
THREE-dimensional printing , *TOPOLOGY , *LEVEL set methods , *GEOMETRIC modeling , *CANTILEVERS , *MATHEMATICAL optimization - Abstract
This paper presents a level set-based topology optimization method considering the overhang constraint in additive manufacturing (AM) processes. Though the combination of the topology optimization and AM shows a promising potential and high design flexibility, there are still certain limitations. The overhang constraint is one of the major issues that need to be considered in the design stage. It requires the inclination angles of structural downward-facing surfaces to be larger than a given lower bound, so as to prevent the structure from warping or collapsing during the AM process. We propose a new form of overhang constraint in the level set framework, which is expressed as a single domain integral instead of point-wise constraints. This domain integral form facilitates the detection of overhang constraint violation. The shape derivative of the overhang constraint is derived by using the signed distance property of the level set function. The proposed method is capable of dealing with constraints with different minimum overhang angles. Theoretically, it allows the optimization to proceed from an arbitrary structural layout, without the need to satisfy the overhang constraint in the initial design. Several numerical examples are given to show the validity and effectiveness of the proposed method. It is seen in these examples that the overhang constraint is satisfied mainly by adjusting the local shape of structural members violating the overhang constraint during the optimization process. Thus, the overhang angle constrained optimization can generate similar load paths as in conventional optimal designs in most cases, without significantly worsening the structural stiffness. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. A multi-material level set-based topology optimization of flexoelectric composites.
- Author
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Ghasemi, Hamid, Park, Harold S., and Rabczuk, Timon
- Subjects
- *
FLEXOELECTRICITY , *TOPOLOGY , *LEVEL set methods , *BOUNDARY element methods , *STRUCTURAL optimization - Abstract
We present a computational design methodology for topology optimization of multi-material-based flexoelectric composites. The methodology extends our recently proposed design methodology for a single flexoelectric material. We adopt the multi-phase vector level set (LS) model which easily copes with various numbers of phases, efficiently satisfies multiple constraints and intrinsically avoids overlap or vacuum among different phases. We extend the point wise density mapping technique for multi-material design and use the B-spline elements to discretize the partial differential equations (PDEs) of flexoelectricity. The dependence of the objective function on the design variables is incorporated using the adjoint technique. The obtained design sensitivities are used in the Hamilton–Jacobi (H–J) equation to update the LS function. We provide numerical examples for two, three and four phase flexoelectric composites to demonstrate the flexibility of the model as well as the significant enhancement in electromechanical coupling coefficient that can be obtained using multi-material topology optimization for flexoelectric composites. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
33. CMA-ES-based structural topology optimization using a level set boundary expression—Application to optical and carpet cloaks.
- Author
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Fujii, Garuda, Takahashi, Masayuki, and Akimoto, Youhei
- Subjects
- *
TOPOLOGY , *LEVEL set methods , *MUTATION testing of computer software , *STRUCTURAL optimization , *DIELECTRIC properties - Abstract
In this paper, we propose a topology optimization method based on the covariance matrix adaptation evolution strategy (CMA-ES) as a method for solving multimodal structural optimization problems. CMA-ES optimizes level set functions as design variables to minimize the fitness value that is regularized to avoid the ill-posedness of topology optimization using a perimeter constraint. Explicit boundaries between the material and void are obtained using the iso-surface of linearly interpolated level set functions. To show the effectiveness of the proposed method for multimodal structural optimization problems, topology optimization for optical and carpet cloaks is numerically demonstrated. The proposed computational strategy is robust to the settings of the initial configurations, even if the topology optimization problems have multimodal distributions of solutions that include many local minima with insufficient performance, and stably improves the regularized fitness value. The obtained optimal configurations have good performance, and we can obtain them without the trial and error of seeking appropriate initial configurations and adapting strategy parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
34. Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design.
- Author
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Cheng, Lin, Liu, Jikai, Liang, Xuan, and To, Albert C.
- Subjects
- *
LATTICE theory , *TOPOLOGY , *THREE-dimensional printing , *HEAT conduction , *LEVEL set methods - Abstract
Significant advance in additive manufacturing (AM) is leading to a paradigm shift in design-for-manufacturing. The manufacturability concern over geometry complexity has largely been removed by AM, which will greatly promote design creativity. A representative paradigm shift is the increasing focus on lattice structures which can be efficiently manufactured by AM. Specifically, lattice structures have been used to replace conventional solid materials to reduce weight and enhance multi-functional properties. Hence, lattice structure topology optimization (LSTO) has drawn remarkable interest for being an optimal lattice infill design tool. Despite the extensive investigation on LSTO, this paper addresses a novel aspect in the concurrent optimization of lattice infill and design-dependent movable features, on which boundary conditions are prescribed. This type of problem has practical importance, such as cooling channel system (forced convective boundary) design used in different thermal management applications, which is challenging to solve numerically due to the increased complexity in sensitivity calculation. In the proposed method, parametric level set function is used to represent the movable feature geometry and accordingly, the thermal boundary conditions are implicitly applied. A detailed sensitivity analysis is performed to provide the effective sensitivity information for design update. Several numerical examples are provided to prove the effectiveness of the proposed method. In particular, the proposed methodology is applied to the concurrent optimization of cooling channels and the optimized design is printed out to demonstrate the manufacturability. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
35. Topology optimization for concurrent design of structures with multi-patch microstructures by level sets.
- Author
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Li, Hao, Luo, Zhen, Gao, Liang, and Qin, Qinghua
- Subjects
- *
TOPOLOGY , *MICROSTRUCTURE , *STRUCTURAL optimization , *MULTISCALE modeling , *LEVEL set methods - Abstract
This paper focuses on the novel concurrent design for cellular structures consisting of multiple patches of material microstructures using a level set-based topological shape optimization method. The macro structure is featured with the configuration of a cluster of non-uniformly distributed patches, while each patch hosts a number of identical material microstructures. At macro scale, a discrete element density based approach is presented to generate an overall structural layout involving different groups of discrete element densities. At micro scale, each macro element is regarded as an individual microstructure with a discrete intermediate density. Hence, all the macro elements with the same discrete densities (volume fractions) are represented by a unique microstructure. The representative microstructures corresponding to different density groups are topologically optimized by incorporating the numerical homogenization approach into a parametric level set method. The multiscale concurrent designs are integrated into a uniform optimization procedure, so as to optimize both topologies for the macrostructure and its microstructures, as well as locations of the microstructures in the design space. Numerical examples demonstrate that the proposed method can substantially improve the structural performance with an affordable computation and manufacturing cost. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
36. Dynamic response-oriented multiscale topology optimization for geometrically asymmetric sandwich structures with graded cellular cores.
- Author
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Zhang, Yan, Xiao, Mi, Ding, Zhe, Xu, Manman, Jiang, Guozhang, and Gao, Liang
- Subjects
- *
SANDWICH construction (Materials) , *LEVEL set methods , *CELL anatomy , *TOPOLOGY , *DRILL core analysis - Abstract
Compared with conventional symmetric sandwich structures with two identical face-sheets and uniform core, geometrically asymmetric sandwich structures (GASSs) enable better dynamic performance due to the expanded design space provided by two unidentical face-sheets and graded cellular cores (GCCs). This paper proposes a dynamic response-oriented multiscale topology optimization method for the GASSs, which is capable of designing the thicknesses of two solid face-sheets, graded distribution of GCCs and their topological configurations to minimize dynamic compliance. Specifically, at macroscale, a variable thickness sheet method is employed to optimize the thicknesses of two solid face-sheets and then generate an overall free distribution of cellular cores within sandwich layers. At microscale, a parametric level set method combining with a numerical homogenization approach is adopted to progressively optimize multiple representative cellular cores (RCCs), achieving their similar topological configurations. Benefitting from the level set-based topology description of RCCs, a shape interpolation technology is conveniently applied to interpolate the shapes of these RCCs to generate the configurations of GCCs. Moreover, a Kriging metamodel constructed by some cellular cores as sample points is adopted to predict the effective properties of each cellular core within sandwich layers, significantly reducing the computational burden. Several 2D and 3D numerical examples are illustrated to show the validity of the proposed method. The results indicate that the optimized GASSs show superior dynamic performances over the conventional sandwich structures designed by microscale and macroscale topology optimization, as well as filled with the commonly applied lattice and honeycomb cores. • Multiscale topology optimization for geometrically asymmetric sandwich structures. • The multiscale topological design is to minimize dynamic compliance. • Both Solid face-sheets thickness and graded cellular cores are optimized. • A progressive optimization scheme is combined with a shape interpolation method. • Several 2D and 3D numerical examples are investigated and compared. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. A level set method for shape and topology optimization of coated structures.
- Author
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Wang, Yaguang and Kang, Zhan
- Subjects
- *
SURFACE coatings , *THICKNESS measurement , *LEVEL set methods , *TOPOLOGY , *STRUCTURAL analysis (Engineering) - Abstract
Coated structures are commonly used in engineering. The coating material covers the surface of the substrate for protection or to improve certain functionalities. The rising of novel manufacture techniques enables higher design flexibility for such coated structures. This paper presents a level set-based topology optimization method for the design of structures with coating layers. Though a coated structure is composed of two-phase materials, only one level set function is needed in the special case of coating with uniform thickness to describe the distribution of the substrate and the coating layer, thanks to its signed distance property. Without using any intermediate design variables, the proposed method provides a direct interface description between different material phases and geometrical information regarding the coating layer thickness, thus facilitating the sensitivity analysis and numerical implementation. Numerical examples show that the method can be applied to both 2D and 3D problems. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
38. Stress-based shape and topology optimization with the level set method.
- Author
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Picelli, R., Townsend, S., Brampton, C., Norato, J., and Kim, H.A.
- Subjects
- *
STRAINS & stresses (Mechanics) , *TOPOLOGY , *LEVEL set methods , *BOUNDARY value problems , *MATHEMATICAL optimization - Abstract
This paper proposes a level set method to solve minimum stress and stress-constrained shape and topology optimization problems. The method solves a sub-optimization problem every iteration to obtain optimal boundary velocities. A p -norm stress functional is used to aggregate stresses in a single constraint. The shape sensitivity function is derived and a computational procedure based on a least squares interpolation approach is devised in order to compute sensitivities at the boundaries. Adaptive constraint scaling is used to enforce exact control of stress limits. Numerical results show that the method is able to solve the problem efficiently for single and multiple load cases obtaining solutions with smooth boundaries. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
39. A new multi-material level set topology optimization method with the length scale control capability.
- Author
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Liu, Jikai and Ma, Yongsheng
- Subjects
- *
LEVEL set methods , *TOPOLOGY , *THICKNESS measurement , *MATHEMATICAL optimization , *STRUCTURAL analysis (Engineering) - Abstract
Multi-material level set topology optimization methods conventionally rely on the overlap of multiple level set functions to realize the multi-material structural representation. However, this representation may produce redundant material phases and the signed distance information is no longer available within the individual material regions. To fix these issues, a new multi-material level set topology optimization method is proposed in this paper, where m level set functions represent m material phases plus the void, and the signed distance information is straightforwardly available in each material phase. To be specific, each level set function corresponds to a material phase and the overlapping areas are filled with an artificial material type, the property of which is weaker than any of the involved material types. This artificial material plays the role of penalizing the overlap areas to vanish, which is different from the close-to-zero property material type for the void. Hence, the optimization process starts with any multi-level set interpolated input and the overlapping areas will gradually vanish. Based on this new method, we have successfully realized the component length scale control on multi-material structures and innovatively, an approach has been proposed to realize the uniform component thickness control without need of pre-specifying the thickness target. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
40. Topology optimization for functionally graded cellular composites with metamaterials by level sets.
- Author
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Gao, Liang, Li, Hao, Luo, Zhen, and Walker, Paul
- Subjects
- *
METAMATERIALS , *LEVEL set methods , *AUXETIC materials , *MICROSTRUCTURE , *FUNCTIONALLY gradient materials - Abstract
The application of auxetic composites in practice often relies on a compromise between properties as auxetics are mostly too porous (not dense enough or not stiff enough) to bear structural loads. Hence, the focus of this paper is topological design optimization of new functionally graded cellular composites with auxetics using a level set method. Firstly, a new hierarchical multi-scale formulation is developed to account for both the auxetic behavior of the microstructure and the stiffness of the macrostructure. The composite, comprising multiple layers of periodic microstructures, is tailored to have functionally graded properties for stiffness and auxetic behaviors, subject to volumetric gradient constraints. Secondly, the microstructures underpinning composite layers are topologically designed under the consideration of boundary and loading conditions of the macrostructure. Finally, a level set method is applied to evolve the shape and topology of the microstructure for each layer, with the numerical homogenization method to evaluate the effective properties of the microstructures. Several numerical examples are used to demonstrate the effectiveness of the proposed method. It can be seen that such composites systematically gear together the features of the functionally graded materials, cellular composites, and metamaterials towards a new kind of man-made composites. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
41. Computational design and additive manufacturing of periodic conformal metasurfaces by synthesizing topology optimization with conformal mapping.
- Author
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Vogiatzis, Panagiotis, Chen, Shikui, Ma, Ming, and Gu, Xianfeng David
- Subjects
- *
THREE-dimensional printing , *CONFORMAL mapping , *COMPUTER-aided design , *LEVEL set methods , *FINITE element method - Abstract
In this paper, we present a computational framework for computational design and additive manufacturing of free-form periodic metasurfaces. The proposed scheme rests on the level-set-based topology approach and the conformal mapping theory. A metamaterial with pre-specified performance is created using a level-set-based topology optimization method. The achieved unit cell is further mapped to the 3D quad meshes on a free-form surface by applying the conformal mapping method which can preserve the local shape and angle during the mapping. With embedded geometric information, the proposed level-set-based optimization methods not only can act as a motivator for design synthesis, but also can be seamlessly hooked with additive manufacturing without the need of CAD reconstructions. The current computational framework provides a solution to increasing applications involving innovative metamaterial designs on free-form surfaces for different fields of interests. The performance of the proposed scheme is illustrated through two benchmark examples where a negative-Poisson’s-ratio unit cell pattern, and a stiff and light inner structure are mapped to 3D free-form surfaces and fabricated through additive manufacturing. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
42. CBS-based topology optimization including design-dependent body loads.
- Author
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Zhang, Weihong, Zhao, Linying, and Gao, Tong
- Subjects
- *
TOPOLOGY , *STRUCTURAL optimization , *MECHANICAL loads , *PARAMETER estimation , *LEVEL set methods - Abstract
In this paper, the inherent problem of the so-called parasitic effect of low density region caused by design-dependent loads is investigated for topology optimization. A CBS (closed B-splines)-based method is developed to solve efficiently the problem in the way of shape optimization. Compared to the standard density method, design variables are unattached to the finite element model and defined by control parameters dominating the parametric equation of the CBS. As a result, design-dependent loads associated with the material layout of a structure are made change indirectly by the boundary variation of the structure. To favour structural reanalyses and sensitivity analysis, the implicit form of the CBS, i.e., level-set function (LSF) is used in conjunction with the fixed computing grid of finite cell method (FCM). A variety of design-dependent body loads is considered for the mathematical formulation of the CBS-based method. Typical examples are given to illustrate that the CBS-based method is free of low density regions in the optimized topology owing to the proper definitions of design variables. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
43. Parametric structural shape & topology optimization with a variational distance-regularized level set method.
- Author
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Jiang, Long and Chen, Shikui
- Subjects
- *
MATHEMATICAL optimization , *LEVEL set methods , *STABILITY theory , *INTERPOLATION , *PARTIAL differential equations - Abstract
The signed distance function (SDF) gives the shortest distance from a given point to the boundary, and the sign indicates whether this point is inside or outside the closed boundary or enclosed region. The SDF property is highly preferred in classical level set methods to maintain the numerical stability during the topology optimization process and provide a metric for the distance-based interpolation of different material properties. In conventional level set methods, a common way of achieving a level set function with the signed distance property is to periodically implement the so-called reinitialization scheme by solving an additional Hamilton–Jacobi partial differential equation. However, such reinitialization scheme is implemented outside the optimization loop with the optimization process suspended, which may shift the optimization result and bring convergence issues. In this paper, a double-well potential functional is employed for distance regularization inside the topology optimization loop, which can enforce the signed distance property of the level set function in a narrow band along the design boundaries while keeping the level set function flat in the rest area of the computational domain. The radial basis function (RBF) based parameterization technique is combined with mathematical programming to improve the performance of the proposed distance-regularized topology optimization method in handling problems with non-convex objective functions and multiple constraints. The flatness of the level set function in the material region also enables easy creation of new holes to the design in the topology optimization process. Both 2D and 3D benchmark examples are employed to demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
44. An isogeometrical approach to structural level set topology optimization.
- Author
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Jahangiry, Hassan A. and Tavakkoli, S. Mehdi
- Subjects
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ISOGEOMETRIC analysis , *LEVEL set methods , *TOPOLOGY , *MATHEMATICAL optimization , *SPLINE theory - Abstract
This paper aims to utilize the Isogeometric Analysis (IGA) for the level set structural topology optimization. The level set function is parametrized using the Non-Uniform Rational B-Spline (NURBS) basis functions in a higher dimension. The same basis functions are employed for approximating the unknown deformations, geometry modeling of the design domain and the level set function. In this research, three optimization problems including minimization of the mean compliance considering a certain amount of material, minimization of weight with avoiding local stress concentration as well as minimization of weight and strain energy under local stress constraints are dealt with. The sensitivity analyses for the optimization problems are carried out to obtain velocity functions on the boundaries. In order to move the boundaries towards optimum the Hamilton–Jacobi (H–J) equation is solved using the forward Euler scheme. In order to illustrate the performance of the method to obtain reasonable results with smooth boundaries, several numerical examples are presented and compared with well-known problems in literature. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
45. Level-set topology optimization for mechanical metamaterials under hybrid uncertainties.
- Author
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Wu, Jinglai, Luo, Zhen, Li, Hao, and Zhang, Nong
- Subjects
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METAMATERIALS , *MECHANICAL behavior of materials , *LEVEL set methods , *TOPOLOGY , *MATHEMATICAL optimization , *AUXETIC materials - Abstract
This paper proposes a level set-based robust topology optimization (RTO) method for computational design of metamaterials under hybrid uncertainties, e.g. auxetics with negative Poisson’s ratio, where the Young’s modulus of the solid is described as a random variable while the Poisson’s ratio is regarded as an interval variable. Firstly, the robust objective function is formulated by a combination of interval mean and interval variance of the deterministic objective function. Secondly, the interval mean and interval variance are computed by a hybrid uncertain analysis approach, termed as Polynomial Chaos-Chebyshev Interval (PCCI) method. Thirdly, the design sensitivities of the robust objective function are obtained after the implementation of the PCCI method. Finally, a powerful parametric level set method (PLSM) in conjunction with the numerical homogenization method is applied to achieve the robust topological design for the auxetic microstructure. Several numerical cases are used to demonstrate the effectiveness of the proposed method for the robust topology optimization problems. This method is non-intrusive and general, and can be easily extended to a range of design problems of micro-structured metamaterials. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
46. A level-set-based topology optimisation for acoustic–elastic coupled problems with a fast BEM–FEM solver.
- Author
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Isakari, Hiroshi, Kondo, Toyohiro, Takahashi, Toru, and Matsumoto, Toshiro
- Subjects
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TOPOLOGY , *ELASTICITY , *LEVEL set methods , *FINITE element method , *DECIBEL meters , *TOPOLOGICAL derivatives - Abstract
This paper presents a structural optimisation method in three-dimensional acoustic–elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic–elastic coupled problems. In this paper, the acoustic–elastic coupled problems are solved by a BEM–FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM–FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
47. Improved XFEM for multiple crack analysis: Accurate and efficient implementations for stress intensity factors.
- Author
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Wen, Long-Fei, Tian, Rong, Wang, Li-Xiang, and Feng, Chun
- Subjects
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LEVEL set methods , *LINEAR elastic fracture mechanics , *FINITE element method , *SUBDIVISION surfaces (Geometry) - Abstract
The extended finite element method (XFEM) has achieved unprecedented success in crack analysis. However, challenges still remain for a multiple crack simulation. One issue is the difficulty of level set construction, where cracks are generally represented by combinations of different level set functions. Another issue is the rapidly increasing condition number of the global stiffness matrix, which is even more severe than the single crack case. In order to overcome these issues, we make two improvements as follows. On the one hand, inspired by the discontinuous description via cover cutting in Numerical Manifold Method (and later phantom node method in XFEM), we propose a level set templated cover cutting method, which makes use of level set values to cut a nodal patch and then to add virtual nodes. This method, which combines the advantages of both the level set method and the cover cutting technique, is simple and straightforward to implement. The method also plays a role in templated subdivision of discontinuous elements and hence presents an efficient and robust integration scheme. On the other hand, we extend the Improved XFEM (IXFEM), previously proposed by our research group, to the scenario of multiple crack problems. The method fundamentally eliminates the daunting issues of linear dependence and ill-conditioning of the standard XFEM, because it uses an extra-dof-free singularity enrichment around the crack tip. Numerical studies on multiple crack problems show that the developed approach offers various advantages: (1) Highly accurate SIF evaluation over the standard XFEM; (2) Well-conditioning of the global stiffness matrix independent of the number of cracks — condition number being of the same order as the standard FEM; (3) Efficient and robust linear system solving and geometric computations. Thus the developed approach is well capable of modeling arbitrary multiple crack problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. Topology optimization method with nonlinear diffusion.
- Author
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Oka, Tomoyuki and Yamada, Takayuki
- Subjects
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BURGERS' equation , *LEVEL set methods , *TOPOLOGICAL derivatives , *TOPOLOGY , *DIFFUSION coefficients - Abstract
This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible to determine optimal configurations that minimize objective functionals by updating level set functions. In this paper, as an update equation for level set functions, (doubly) nonlinear diffusion equations with reaction terms are derived, and then the singularity and degeneracy of the diffusion coefficient are applied to obtain fast convergence of configurations and damping oscillation on boundary structures. In particular, the reaction terms in the proposed method do not depend on the topological derivatives, and therefore, sensitivity analysis to determine a descent direction for objective functionals is relaxed. Furthermore, a numerical algorithm for the proposed method is constructed and applied to typical minimization problems to show numerical validity. This paper is a justification and generalization of the method using reaction–diffusion equations developed by one of the authors in Yamada et al. (2010). • This study proposes a level set–based topology optimization method using (doubly) nonlinear diffusion. • The singularity of diffusion coefficients yields fast convergence. • The degeneracy of diffusion coefficients provides numerical stability by damping oscillation. • The proposed method is a generalization of the level set–based topology optimization method using reaction–diffusion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. A multiscale Implicit Level Set Algorithm (ILSA) to model hydraulic fracture propagation incorporating combined viscous, toughness, and leak-off asymptotics.
- Author
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Dontsov, E.V. and Peirce, A.P.
- Subjects
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FRACTURE mechanics , *HYDRAULIC fracturing , *STRAINS & stresses (Mechanics) , *FINITE element method , *ALGORITHMS - Abstract
This study uses an Implicit Level Set Algorithm (ILSA) to model the propagation of planar hydraulic fractures in situations when their progress is determined by an interplay of fluid viscosity, rock fracture toughness, and fluid leak-off into the formation. One of the key features of our approach is the use of the three-process tip asymptotic solution both as a propagation condition and to capture the multiscale behavior in a weak sense. Using this special tip asymptote is necessary because the validity region of the classical square root fracture opening solution (stemming from linear elastic fracture mechanics) is often limited to a small zone near the fracture tip, which can only be captured by a very fine mesh. In addition, this validity zone depends on the velocity of fracture propagation, so that slow and fast portions of the fracture front may experience different near-tip behavior. The multiscale tip asymptotic solution, on the other hand, has an increased validity region, which makes it possible to capture the near-tip multiscale behavior on a coarse mesh and yields a computationally efficient algorithm. The presence of leak-off also complicates the model considerably as it involves a delay term containing the trigger time history, which depends on the earlier fracture front positions. Moreover, the leak-off from tip elements in which the fracture front speed changes significantly requires special treatment. This three-process asymptotic solution is used to solve the fully coupled integro-delay-PDE model for a propagating planar hydraulic fracture by using a level set algorithm in conjunction with the tip asymptotic solution to locate the moving fracture front and to capture multiscale behavior. Firstly, the developed algorithm is validated against a reference solution for an axisymmetric hydraulic fracture. Secondly, a set of numerical examples involving three stress layers is presented to illustrate the variation of the multiscale near-tip behavior along the fracture perimeter and the need to use the multiscale asymptotic solution in a hydraulic fracturing simulator. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
50. Integrated design of cellular composites using a level-set topology optimization method.
- Author
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Li, Hao, Luo, Zhen, Zhang, Nong, Gao, Liang, and Brown, Terry
- Subjects
- *
LEVEL set methods , *MATHEMATICAL optimization , *FUNCTIONALLY gradient materials , *COMPOSITE materials , *MULTISCALE modeling - Abstract
This paper proposes a hierarchical multi-scale topology optimization method for the design of integrated materials and structures by taking advantage of both cellular composites and functionally graded materials. The topology optimization involves two scales: firstly, macrostructural design using SIMP to generate an overall multilayered layout with free material distribution involving intermediate densities; and secondly, microstructural design to produce periodic cellular composite for each layer, by integrating the numerical homogenization into a level set approach. Thus, the cellular composites will be characterized by variation in microstructures and the corresponding changes of properties over layers. The proposed method can generate new artificial composites similar to functionally graded materials but layer-based, to achieve multifunctional properties for energy absorption, anti-impact, thermal isolation, etc. Several numerical examples are used to demonstrate the effectiveness of this method. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
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