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Vibration control has significant applications in many engineering areas to achieve designed vibration performances or suppress structural fatigue and failure. This paper presents a velocity field level set method for topology optimization of the piezoelectric layer on a plate with active vibration control. The material distribution of the piezoelectric layer and the topology optimization model for this problem is formulated in the level set framework, which can precisely track the layout (topology/shape) of piezoelectric layers with clear/smooth boundaries. Compared with the density-based method, the level set method can avoid the difficulties in the definition of material distributions and piezoelectric material properties for intermediate densities, which also leads to more accurate vibration control. We employ the constant gain velocity feedback as the vibration control algorithm. The dynamic compliance is set as the objective function and treated as the index representing the plate's vibration level. Using the velocity field level set method can map the original variational boundary shape optimization problem into the finite dimensional space and solve the optimization problem efficiently by general optimizers. We also show that the self-adjoint scheme can be used in the sensitivity analysis, which avoids solving additional adjoint problems. To verify the validity and efficiency of the proposed method, we give three numerical examples, in which the influence of the external frequency and the constant gain coefficient on optimization results are also discussed. [ABSTRACT FROM AUTHOR]

Short-chain fatty acids (SCFAs) butyrate promote the postnatal rumen epithelial development and maturation in ruminants. However, molecular mechanisms of effects of butyrate on the bovine rumen epithelial cells (BRECs) proliferation remain elusive. Therefore, purpose of this study was to investigate the effects of butyrate on the expression of genes and proteins at G0/G1 and S phase of BRECs cycle. Our results showed that BRECs treated with butyrate inhibited (P < 0.05) the proliferation of BRECs, relatively to control. Flow cytometric assays revealed that butyrate triggers the BRECs cycle arrest at the G0/G1 phase. qRT-PCR analyses of mRNA level of genes involved in the G0/G1 phase of cell cycle showed that butyrate significantly upregulated (P < 0.001) the expression of mRNA encoding p21Cip1 compared with control group, but it decreased (P < 0.05) the mRNA levels of cyclin D1 and CDK4 genes at G0/G1 phase checkpoint compared with control. Moreover, Western blot also revealed that butyrate downregulated the expression of cyclin D3, CDK6, p-Rb, and E2F1 proteins involved in the modulation of G0/G1 phase of cell cycle. In conclusion, our results demonstrated that butyrate inhibits the proliferation of BRECs via downregulation of positive regulators at G0/G1 phase checkpoint. [ABSTRACT FROM AUTHOR]

A photothermal nanoconfinement reactor (PNCR) system is proposed and demonstrated by using hollow carbon nanospheres (HCNs) to enhance the performance of the chemical reaction. Under light irradiation, the local temperature of the HCN inner void space was much higher than the bulk solution temperature because the confined space concentrates heat and inhibits heat loss. Using the temperature‐sensitive model reaction, peroxydisulfate (PDS) activation to oxidize micropollutant, it is shown that the degradation rate of sulfamethoxazole in the PNCR system is 7.1 times of that without nanoconfinement. It is further discovered that the high‐quality local heat inside the nanoconfined space shifted the model reaction from an otherwise non‐radical pathway to a radical‐based pathway. This work provides an interesting strategy to produce a locally high temperature, which has a wide range of applications to energy and environmental fields. [ABSTRACT FROM AUTHOR]

A photothermal nanoconfinement reactor (PNCR) system is proposed and demonstrated by using hollow carbon nanospheres (HCNs) to enhance the performance of the chemical reaction. Under light irradiation, the local temperature of the HCN inner void space was much higher than the bulk solution temperature because the confined space concentrates heat and inhibits heat loss. Using the temperature‐sensitive model reaction, peroxydisulfate (PDS) activation to oxidize micropollutant, it is shown that the degradation rate of sulfamethoxazole in the PNCR system is 7.1 times of that without nanoconfinement. It is further discovered that the high‐quality local heat inside the nanoconfined space shifted the model reaction from an otherwise non‐radical pathway to a radical‐based pathway. This work provides an interesting strategy to produce a locally high temperature, which has a wide range of applications to energy and environmental fields. [ABSTRACT FROM AUTHOR]

Topology optimization of transient dynamics is of great importance in engineering. However, the computational cost required by the repeated dynamic response and design sensitivity analysis during design iterations is often extremely high for large-scale problems, which significantly limits its practical application. To address this issue, we propose a new method based on successive iteration of analysis and design in conjunction with a quasi-static response-enhanced mode displacement method. The conventional mode displacement method requires an inner-loop iteration in addition to the outer-loop design updating, for finding the eigenmodes of the undamped system. In order to avoid the high computational burden caused by the nested double-loop solution, we employ the concept of successive iteration of analysis and design, which integrates approximate eigenvalue analysis and design variable updating into a single iteration loop. By this means, the eigenmodes are sequentially improved through a one-step inverse iteration in each design iteration, and simultaneous convergence of the eigenmodes and the design is sought during the optimization process. These approximate eigenmodes and the quasi-static response are used as the model reduction basis for each intermediate design, and the direct time integration of the reduced-dimensional system is then performed to calculate the structural responses of interest and their derivatives with respect to the design variables. Several numerical examples are presented to demonstrate the efficiency of the proposed method. It is shown that the method can be used to solve transient dynamic topology optimization problems up to 15 million degrees of freedom on a desktop computer at affordable time cost. [ABSTRACT FROM AUTHOR]

This paper presents MATLAB implementations of the velocity field level set method for topology optimization. An 80-line code and a 100-line code are provided for 2D and 3D static compliance minimization problems, respectively. The velocity field level set method inherits the implicit topology and shape representation of the standard level set method but advances the design boundaries with a velocity field constructed from the velocity design variables and basis functions. Therefore, it can achieve structural designs with relatively clear and smooth material boundaries. Moreover, it allows general mathematical programming algorithms to be conveniently employed to handle more constraints when solving the optimization problem. In the presented codes, the method of moving asymptotes is used as the optimizer. For simplification, the presented MATLAB code is in a basic version. Some modifications and extensions are given in the examples to show the validity and efficiency of the codes. Further adaption of the current codes can also be made to fulfill various requirements. [ABSTRACT FROM AUTHOR]

Topology optimization has become a useful tool for designing Phononic Crystals (PnCs) to achieve desired elastic wave propagation properties. However, topological design of three-dimensional (3D) PnCs remains a significant challenge due to extremely high computational cost required for the repeated solution of the nested double-loop problem of design optimization and eigenvalue analysis to determine the band structure during the optimization iteration process. This paper presents a more efficient topology optimization method based on the concept of successive iteration of analysis and design. The method employs a sequential approximation of the eigenpairs through an inverse iteration-like procedure to avoid solving the expensive eigenvalue problems in each design iteration. To further improve the efficiency of the design iteration, the eigenmodes of the intermediate PnCs designs are first computed on a relatively coarse finite element mesh. Then they are mapped onto the fine mesh and used as the initial trial eigenmodes in the eigenpair analysis and design sensitivity analysis. The high efficiency of the proposed method, as compared with conventional nested double-loop optimization approaches, is demonstrated by 3D numerical examples with over one million degrees of freedom. It is shown that this approach can achieve simultaneous convergence of the eigenvectors along with the design evolution of the unit cell, therefore substantially reduces the computational burden for high-resolution topological design of 3D PnCs. [ABSTRACT FROM AUTHOR]

Abstract This paper studies concurrent two-scale design optimization of composite structures filled with multiple microstructural unit cells. The task of the design problem is to simultaneously optimize microstructural configurations of the unit cells and their spatial distribution in the macroscale. To this end, a new topology optimization framework based on combined topology representation of the density model and the level set model is proposed. The homogenization method is used to link the material microstructural design and the macroscale design by evaluating the effective properties of the microstructures. In the microscale, topology optimization of multiple microstructural unit cells is performed with the density-based method. In the macroscale design, the distribution of multiple microstructural unit cells is optimized by the velocity field level set method, which inherits advantages of the implicit geometrical representation of the conventional level set model (relatively clear and smooth material boundaries/interfaces, more natural description of topological evolution). Moreover, the velocity field level set method maps the variational boundary shape optimization problem into a finite-dimensional design space, thus making it relatively easy and efficient to employ general mathematical programming algorithms to handle the multiple constraints and two types of design variables in the concurrent two-scale design problem. Numerical examples show that the present concurrent two-scale design method can generate meaningful designs of hierarchical cellular structures with well-defined boundaries and material interfaces. Highlights • A concurrent two-scale design of multiple unit cells and structure is presented. • VFLS and SIMP method are respectively used in macroscale and microscale designs. • Level set model gives a rigorous interpretation of microstructure distribution. • VFLS method can efficiently handle multiple constraints in multiscale design. • Using multiple unit cells can obtain higher structural stiffness than uniform ones. [ABSTRACT FROM AUTHOR]

Abstract Material interface-related uncertainties induced by inter-diffusion or reactions between two different materials may deteriorate the actual performance of a structural design achieved by topology optimization. Thus a rational methodology is needed to address this issue in the design of hybrid-material engineering products implemented by some novel fabrication techniques such as additive manufacturing. This paper presents a robust shape and topology optimization method accounting for uncertain graded interface properties of multi-material structures. A level set function is used to track the evolving material interfaces during the optimization process, and the material interface uncertainties is modeled by introducing an intermediate zone with graded properties represented by a random field. On the basis of discretizing the input random field by means of the Expansion Optimal Linear Estimation (EOLE) method, the uncertain propagation analysis is implemented with the Polynomial Chaos expansion (PCE) to predict the stochastic response. Then the robust shape and topology optimization problem is stated as a multi-criteria optimization problem, in which the expected value and the standard deviation of the performance function of interest are to be minimized under a given material volume constraint. The shape derivative of the stochastic response is derived in the context of Eulerian description, and then used to advance the evolution of the level set function through the Hamilton-Jacobi equation. In the numerical examples, the proposed robust design method is exemplified by the mean compliance minimization problems. [ABSTRACT FROM AUTHOR]

It is often highly desirable to simultaneously optimize the layout of embedded functional components and the topology of the host structure supporting these components to achieve the best overall performance while still ensuring the structural integrity. We propose a topology optimization framework to account for connecting interface behaviors between the components and the host structure. Here we treat the connecting interfaces with the cohesive zone model to reflect the adhesively bonded interface behaviors. A conforming mesh in conjunction with interface elements is employed to discretize the evolving structure while accounting for the strong discontinuity of displacement field across the material interfaces. To give a clear representation of structural boundaries and the connecting interfaces, we also suggest a multi-material interpolation model in the level set framework, which can conveniently define the connecting interface locations and describe multi-material distribution without redundant phase in the design domain. The objective function is defined as the sum of the strain energy and the work done by the traction on the connecting interface, and the evolution velocities of the level set and the embedded components are treated as design variables. These design variables are updated with the MMA optimizer on the basis of adjoint-variable sensitivity analysis. This optimization formulation allows multiple constraints and mixed design variables ( i.e level set design variables and components’ design variables) to be easily handled in level set based optimization. The design is advanced by the Hamilton–Jacobi equation with the velocity design variables as input. Numerical examples demonstrate the validity and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

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]

This paper presents a study on topology optimization of novel material microstructural configurations to achieve directional elastic wave propagation through maximization of partial band gaps. A waveguide incorporating a periodic-microstructure material may exhibit different propagation properties for the plane elastic waves incident from different inlets. A topology optimization problem is formulated to enhance such a property with a gradient-based mathematical programming algorithm. For alleviating the issue of local optimum traps, the random morphology description functions (RMDFs) are introduced to generate random initial designs for the optimization process. The optimized designs finally converge to the orderly material distribution and numerical validation shows improved directional propagation property as expected. The utilization of linear two-dimension phononic crystal with efficient partial band gap is suitable for directional propagation with a broad frequency range. [ABSTRACT FROM AUTHOR]

As a typical form of material imperfection, cracks generally cannot be avoided and are critical for load bearing capability and integrity of engineering structures. This paper presents a topology optimization method for generating structural layouts that are insensitive/sensitive as required to initial cracks at specified locations. Based on the linear elastic fracture mechanics model (LEFM), the stress intensity of initial cracks in the structure is analyzed by using singularity finite elements positioned at the crack tip to describe the near-tip stress field. In the topology optimization formulation, the J integral, as a criterion for predicting crack opening under certain loading and boundary conditions, is introduced into the objective function to be minimized or maximized. In this context, the adjoint variable sensitivity analysis scheme is derived, which enables the optimization problem to be solved with a gradient-based algorithm. Numerical examples are given to demonstrate effectiveness of the proposed method on generating structures with desired overall stiffness and fracture strength property. This method provides an applicable framework incorporating linear fracture mechanics criteria into topology optimization for conceptual design of crack insensitive or easily detachable structures for particular applications. [ABSTRACT FROM AUTHOR]

Variability of load magnitude/direction is a most significant source of uncertainties in practical engineering. This paper investigates robust topology optimization of structures subjected to uncertain dynamic excitations. The unknown-but-bounded dynamic loads/accelerations are described with the non-probabilistic ellipsoid convex model. The aim of the optimization problem is to minimize the absolute dynamic compliance for the worst-case loading condition. For this purpose, a generalized compliance matrix is defined to construct the objective function. To find the optimal structural layout under uncertain dynamic excitations, we first formulate the robust topology optimization problem into a nested double-loop one. Here, the inner-loop aims to seek the worst-case combination of the excitations (which depends on the current design, and is usually to be found by a global optimization algorithm), and the outer-loop optimizes the structural topology under the found worst-case excitation. To tackle the inherent difficulties associated with such an originally nested formulation, we convert the inner-loop into an inhomogeneous eigenvalue problem using the optimality condition. Thus the double-loop problem is reformulated into an equivalent single-loop one. This formulation ensures that the strict-sense worst-case combination of the uncertain excitations for each intermediate design be located without resorting to a time-consuming global search algorithm. The sensitivity analysis of the worst-case objective function value is derived with the adjoint variable method, and then the optimization problem is solved by a gradient-based mathematical programming method. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed framework. [ABSTRACT FROM AUTHOR]

This paper presents a novel topology optimization method for designing structures with multiphase embedded components under minimum distance constraints in the level set framework. By using the level set representation for both the component layout and the host structure topology, the shapes of the components can be easily preserved, and optimal structural topologies with smooth boundary/material interface can be obtained. With the purpose of preventing the components moving too close to each other, a minimum distance constraint based on virtual boundary offset is proposed. Different from existing distance detection methods relying on explicit topology representation, the proposed constraint is imposed as a unified integral form, for which the design sensitivity can be readily obtained. Moreover, this constraint is effective for detecting the distance between any complex-shaped components. Several numerical examples are presented to demonstrate the validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

As a set theory-based convex model, the ellipsoidal model provides an attractive framework for treating uncertain-but-bounded variations in the structural reliability analysis and design optimization. However, improper modeling of the uncertainties may give rise to misleading non-probabilistic reliability analysis, thus result in either unsafe or over-conservative designs. This paper presents a systematic study on the mathematical formulation for constructing the minimum-volume ellipsoidal convex model using a given set of sample data, and shows its application in existing methods of non-probabilistic reliability analysis and design optimization of structures with bounded uncertainties. In this method, the uncertain parameters are first divided into groups according to their sources. For each individual group of uncertainties, the minimum-volume ellipsoid problem is reformulated into a semi-definite programming (SDP) problem and thus can be efficiently solved to its global optimum. Further, a linear transformation based on the eigenvalue analysis is employed to map the ellipsoidal model into a standard uncertainty space. This uncertainty modeling technique enables a compact and differentiable bound description of the parameter variations. Moreover, it has another useful property, the affine invariance, which is shown to be necessary for meaningful definition of a non-probabilistic reliability index. The effectiveness and efficiency of the present techniques for convex model construction and the corresponding reliability analysis are demonstrated with numerical examples of structural topology optimization problems with bounded variations arising from different sources. [ABSTRACT FROM AUTHOR]

It is often desirable to simultaneously optimize the damping and stiffness distribution in the design of shell structures incorporating damping material layers for achieving the best vibration mitigation performance. This paper investigates the integrated topology optimization of host structures and damping layers for reducing the vibration level in the presence of harmonic excitations. Therein, the global damping matrix is a nonproportional one due to distributed damping effects. For an efficient frequency response analysis of the system with nonproportional damping, reduced-order equations are obtained by using lower-order eigenvectors of the undamped system, and then the method of complex mode superposition is employed for solving the dynamic equations in the state space. In the optimization model, the vibration amplitudes at specified positions are taken as the objective function. The relative densities of the elements are considered as design variables, and an artificial damping material model relating the local damping properties to the elemental density variables is employed. The Rational Approximation of Material Properties model is adopted to avoid localized modes in low-density areas during the optimization process. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed framework. [ABSTRACT FROM AUTHOR]

It is impractical to implement arbitrary-shaped piezoelectric patches from the view point of manufacturability of fragile piezoelectric ceramics, thus using designable electrode layers to deliver desired actuation forces provides a more realistic option in engineering applications. This study develops a topological design method of surface electrode distribution over piezoelectric sensors/actuators attached to a thin-walled shell structure for reducing the sound radiation in an unbounded acoustic domain. In the optimization model, the sound pressure norm at specific reference points under excitations at a certain excitation frequency or in a given frequency range is taken as the objective function. The pseudo densities for indicating absence and presence of surface electrodes at each element are taken as the design variables, and a penalized relationship between the densities and the active damping effect is employed. The vibrating structure is discretized with finite element model for the frequency response analysis and the sound radiation analysis in the unbounded acoustic domain is treated by boundary element method. The applied voltage on each actuator is determined by the constant gain velocity feedback (CGVF) control law. The technique of the complex mode superposition in the state space, in conjunction with a model reduction transformation, is adopted in the response analysis of the system characterized by a non-proportional active damping property. In this context, the adjoint-variable sensitivity analysis scheme is derived. The effectiveness and efficiency of the proposed method are demonstrated by numerical examples, and several key factors on the optimal designs are also discussed. [ABSTRACT FROM AUTHOR]

This paper investigates topology optimization of the piezoelectric actuator/sensor coverage attached to a thin-shell structure to improve the active control performance for reducing the dynamic response under transient excitations. The constant gain velocity feedback (CGVF) control algorithm is considered and the structural dynamic response under the corresponding active damping effect is evaluated with a direct time integration method. In the mathematical formulation of the considered topology optimization model, the time integral of the displacement response over a specified time interval of interest is taken as the objective function. The pseudo-densities describing the piezoelectric material distribution are taken as the design variables, and a penalization model on the structural stiffness and piezoelectric effect is employed. The adjoint-variable sensitivity analysis scheme for a general integral function within a given time interval is derived, which facilitates a gradient-based mathematical programming solution of the optimization problem. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of piezoelectric layers. Also, the influences of the control gain and the integration time intervals in the objective function on the optimal solutions are discussed. The proposed method can be used for providing useful guidance to the layout design of the actuator/sensor layers attached to a thin-shell structure subject to dynamic excitations, in particular impact forces. It is also confirmed that the achieved vibration reduction is mainly due to improvement of the active control performance rather than changes of the structural dynamic stiffness/mass property. [ABSTRACT FROM AUTHOR]

Based on the element-free Galerkin (EFG) method, an analysis-independent density variable approach is proposed for topology optimization of geometrically nonlinear structures. This method eliminates the mesh distortion problem often encountered in the finite element analysis of large deformations. The topology optimization problem is formulated on the basis of point-wise description of the material density field. This density field is constructed by a physical meaning-preserving interpolation with the density values of the design variable points, which can be freely positioned independently of the field points used in the displacement analysis. An energy criterion of convergence is used to resolve the well-known convergence difficulty, which would be usually encountered in low density regions, where displacements oscillate severely during the optimization process. Numerical examples are given to demonstrate the effectiveness of the developed approach. It is shown that relatively clear optimal solutions can be achieved, without exhibiting numerical instabilities like the so-called 'layering' or 'islanding' phenomena even in large deformation cases. This study not only confirms the potential of the EFG method in topology optimization involving large deformations, but also provides a novel topology optimization framework based on element-free discretization of displacement and density fields, which can also easily incorporate other meshless analysis methods for specific purposes. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new adaptive refinement strategy for topology optimization is proposed. [•] Independent error controls applied to separated displacement and density fields. [•] Analysis mesh is refined to improve computational accuracy within local regions. [•] Density field is refined to improve boundary description quality. [•] High-accuracy and high-quality solutions at less cost than fixed mesh approach. [ABSTRACT FROM AUTHOR]

Carbon nanotube (CNT) junctions have a wide range of potential applications in nanoelectronic devices, whose performance strongly relies on the stability of the junctions. The tensile strength and failure mode of zigzag junctions are investigated under different strain rates, temperatures, and geometrical dimensions. Firstly, both the modified transition state theory model and molecular dynamics (MD) simulations reveal that the yield strain of a junction depends linearly on the temperature and logarithmically on the strain rate. Moreover, MD simulations show that the yield strain is also affected by the curvature of the junction and the limit yield strain can be predicted by considering an unwrapped junction with the minimal curvature. Secondly, a junction may undergo a brittle or a ductile failure mode and the brittle–ductile transition (BDT) is dependent on the strain rate, temperature and geometrical dimension. The dominant geometrical factor affecting the failure modes is shown to be the aspect ratio rather than merely the diameter or length. Also, the BDT temperature, strain rate and aspect ratio is obtained. These findings may help to gain a deeper understanding of the tensile behaviour of CNT junctions and to provide a useful guidance for the design of CNT junction-based nanoelectronic devices. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the sensitivity analysis of structural acoustic performance in presence of non-proportional damping and optimal layout design of the damping layer of vibrating shell structures under harmonic excitations. The structural system with a partially-covered damping layer has a non-proportional global damping matrix. Therefore, the method of complex mode superposition in the state space is employed in the dynamic response analysis. The sound pressure is calculated with the structural response solution by using the boundary element method. In this context, an adjoint variable scheme for the design sensitivity analysis of sound pressure is developed. In the optimal design problem, the design objective is to minimize the structural vibration-induced sound pressure at a specified point in the acoustic medium by distributing a given amount of damping material. An artificial damping material model that has a similar form as in the SIMP approach is employed, and the relative densities of the damping material are considered as design variables. Numerical examples are given to illustrate the validity and efficiency of this approach. The influences of the excitation frequency, the damping coefficients and the locations of the reference point on the optimal topologies are also discussed. [Copyright &y& Elsevier]

This paper investigates robust design optimization of truss structures with uncertain-but-bounded parameters and loads. The variations of the cross-sectional areas, Young's moduli and applied loads are treated with non-probabilistic ellipsoid convex models. A robustness index for quantitatively measuring the maximal allowable magnitude of system variations is presented, and the design problem is then formulated as to maximize the minimum of the robustness indices for all the concerned design requirements under a given material volume constraint. For circumventing the difficulty associated with the max-min type problem, an aggregate function technique is employed to construct a smooth objective function. The computational scheme for the sensitivity of the robustness index is derived on the basis of optimum sensitivity analysis. The optimization problem is then solved by using the GCMMA optimizer. Numerical examples illustrate the validity and effectiveness of the present formulation and solution techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel topology description model for topology optimization problems with embedded movable holes, combining the ability of the level set model for accurate geometrical description of the prescribed hole shapes, and the high efficiency of the material density-based method. By this means, any arbitrary hole shapes can be represented accurately and smoothly, while the topological changes can be easily handled by the material distribution model. An explicit mathematical expression is defined to obtain the actual structural layout by combing both models. Moreover, an effective model for the non-overlap constraint is proposed in a unified and systematic manner to avoid the overlaps between the holes and between each hole and the design domain boundary. Therein, the non-overlap constraint for all the embedded holes is imposed as a single explicit integral constraint over the design domain, thus avoiding the difficulties in the overlap detection of multiple arbitrary-shaped geometries. Such a non-overlap constraint is accurate and differentiable, facilitating an analytical design sensitivity analysis. Numerical examples are given to demonstrate the effectiveness and efficiency of the present method. [Copyright &y& Elsevier]

Abstract: This paper presents an adaptive density point refinement approach for continuum topology optimization on the basis of an analysis-mesh separated material density field description based on nodal design variables. The Shepard interpolants are used to construct a strictly range-restricted density field over the design domain with the density design variables defined on a density point grid. Since the density points are defined independent of the finite element mesh, it is easy to refine the density point grid without remeshing the finite element model. A refinement criterion is given to identify the gray transitional regions to be adaptively refined in the subsequent optimization iterations. With such a refinement scheme, the topology optimization can start from a relatively coarse density point grid but still yields a desired higher resolution of the structural boundaries in the final design. Because refinements are only performed when and where necessary, this method is able to improve the boundary description quality of the optimal result with much less design variables as compared with the case of global refinement, and therefore can greatly reduce the computational burden involved in the sensitivity analysis and optimization process. Moreover, the percentage of transitional regions in the final solutions can also be reduced. Compared with using a uniformly globally-dense density point arrangement, this approach can achieve similar optimal designs but with much less computational cost. Numerical examples are given to demonstrate the effectiveness and efficiency of the present approach. [Copyright &y& Elsevier]

Abstract: Carbon nanotube-based intramolecular junctions can function as rectifying diodes and switches in circuits and thus possesses the promising potential to be applied in nano-scale electronic devices. Due to their slender and unsymmetrical geometry, intramolecular junctions are prone to buckling under compression and the resulting structural instability will eventually leads to structural or electrical failure. Thus, it is important to explore the mechanical behaviors of intramolecular junctions subject to compressive loads. In this study, molecular dynamical simulations are carried out to investigate the compressive behaviors of intramolecular junctions at finite temperature, while carbon nanotubes are also studied as reference. The simulation results indicate that the strain rate effect is negligible within relatively low loading-rate range but the critical strain increases significantly under higher loading rate. At an extremely high strain rate, the intramolecular junctions will crush immediately. It is also predicted that local deformation will be introduced at high environmental temperature. Moreover, with increasing tube length, the instability mode of the intramolecular junctions transfers from shell buckling to column buckling and the critical aspect ratio is lower than that of carbon nanotubes due to presence of the Stone–Wales defects. [Copyright &y& Elsevier]

This paper aims to develop a method that can automatically generate the optimal layout of reinforced concrete structures by incorporating concrete strength constraints into the two-material topology optimization formulation. The Drucker-Prager yield criterion is applied to predict the failure behavior of concrete. By using the power-law interpolation, the proposed optimization model is stated as a minimum compliance problem under the yield stress constraints on concrete elements and the material volume constraint of steel. The ε-relaxation technique is employed to prevent the stress singularity. A hybrid constraint-reduction strategy, in conjunction with the adjoint-variable sensitivity information, is integrated into a gradient-based optimization algorithm to overcome the numerical difficulties that arise from large-scale constraints. It can be concluded from numerical investigations that the proposed model is suitable for obtaining a reasonable layout which makes the best uses of the compressive strength of concrete and the tensile strength of steel. Numerical results also reveal that the hybrid constraint-reduction strategy is effective in solving the topology optimization problems involving a large number of constraints. [ABSTRACT FROM AUTHOR]

The sensitivity analysis of rigid viscoplastic deformation processes with application to metal preform design optimization is investigated. For viscoplastic constitutive models, the deformation process is path-dependent in nature and thus the sensitivity analysis of the deformation history is formulated in an incremental procedure. To this end, an algorithm is derived on the basis of the time integration scheme used in the primary finite element analysis, where the contact conditions are treated with the penalty method. The discretized equilibrium equations, as well as the time integration equations, are directly differentiated with respect to the design variables. The discrete form of the sensitivity equations is then solved with procedures similar to those used in the direct analysis, where the secant matrix decomposed in the direct analysis can also be utilized at each time instant. Thus the sensitivity of the deformation history is evaluated in a step-wise procedure. The present algorithm can be employed for the optimization of metal forming processes. The accuracy of the proposed sensitivity analysis as well as its applicability are demonstrated by numerical examples with reference to preform design optimization problems, where the aggregate function method is employed for converting the non-smooth Min–max type objective function into a numerically tractable one. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal distribution of damping material in vibrating structures subject to harmonic excitations by using topology optimization method. Therein, the design objective is to minimize the structural vibration level at specified positions by distributing a given amount of damping material. An artificial damping material model that has a similar form as in the SIMP approach is suggested and the relative densities of the damping material are taken as design variables. The vibration equation of the structure has a non-proportional damping matrix. A system reduction procedure is first performed by using the eigenmodes of the undamped system. The complex mode superposition method in the state space, which can deal with the non-proportional damping, is then employed to calculate the steady-state response of the vibrating structure. In this context, an adjoint variable scheme for the response sensitivity analysis is developed. Numerical examples are presented for illustrating validity and efficiency of this approach. Impacts of the excitation frequency as well as the damping coefficients on topology optimization results are also discussed. [ABSTRACT FROM AUTHOR]

The mechanism and the characteristics of the cable-deck coupled nonlinear vibration in a cable-stayed bridge are studied using numerical methods. A simple three-degrees-of-freedom (d.f.) model, with one independent d.f. for modeling the bridge deck movement, is proposed for describing the nonlinear interactions between the in-plane/out-of-plane vibration of the cable and the oscillation of the bridge deck. The governing equations are discretized with the Galerkin method and then solved with a numerical time integration algorithm. It is pointed out that the periodic variation of cable tension caused by vibration of a bridge deck will lead to the parametric resonance of the stay cable under certain tuning conditions. Numerical results also confirm that energy transfer between different vibration modes and beating phenomenon of the cable-deck vibration may be exhibited in the case of parametric resonance. [ABSTRACT FROM PUBLISHER]

Abstract: This paper presents an efficient topology optimization strategy for seeking the optimal layout of continuum structures exhibiting asymmetrical strength behaviors in compression and tension. Based on the Drucker–Prager yield criterion and the power-law interpolation scheme for the material property, the optimization problem is formulated as to minimize the material volume under local stress constraints. The ε-relaxation of stress constraints is adopted to circumvent the stress singularity problem. For improving the computational efficiency, a grouped aggregation approach based on the Kreisselmeier–Steinhauser function is employed to reduce the number of constraints without much sacrificing the approximation accuracy of the stress constraints. In conjunction with the adjoint-variable sensitivity analysis, the minimization problem is solved by a gradient-based optimization algorithm. Numerical examples demonstrate the validity of the present optimization model as well as the efficiency of the proposed numerical techniques. Moreover, it is also revealed that the optimal design of a structure with pressure-dependent material may exhibit a considerable different topology from the one obtained with pressure-independent material model. [Copyright &y& Elsevier]

Abstract: This paper presents a non-local density interpolation strategy for topology optimization based on nodal design variables. In this method, design variable points can be positioned at any locations in the design domain and may not necessarily coincide with elemental nodes. By using the Shepard family of interpolants, the density value of any given computational point is interpolated by design variable values within a certain circular influence domain of the point. The employed interpolation scheme has an explicit form and satisfies non-negative and range-restricted properties required by a physically significant density interpolation. Since the discretizations of the density field and the displacement field are implemented on two independent sets of points, the method is well suited for a topology optimization problem with a design domain containing higher-order elements or non-quadrilateral elements. Moreover, it has the ability to yield mesh-independent solutions if the radius of the influence domain is reasonably specified. Numerical examples demonstrate the validity of the proposed formulation and numerical techniques. It is also confirmed that the method can successfully avoid checkerboard patterns as well as “islanding” phenomenon. [Copyright &y& Elsevier]

Abstract: This paper investigates the formulation and numerical solution of reliability-based optimization of structures exhibiting grouped uncertain-but-bounded variations. Based on the multi-ellipsoid convex model description for grouped uncertain-but-bounded parameters, the mathematical definition of a non-probabilistic reliability index is presented for quantified measure of the safety margin. The optimal design is then formulated as a nested optimization problem. A method based on concerned performance is proposed for regularization of the reliability index constraints. The expensive computation of the non-probabilistic reliability index and its derivative is thus avoided. Numerical examples are given to illustrate the validity and efficiency of the present method. [Copyright &y& Elsevier]

Abstract: This paper investigates the combined optimization of bi-material structural layout and actuation voltage distribution of structures with embedded in-plane piezoelectric actuators. The maximization of the nodal displacement at a selected output port is considered as the design objective. A two-phase material model with power-law penalization is employed in the topology optimization of the actuator elements and the coupled surrounding structure. In order to incorporate the actuation voltage directly into the design for achieving the best overall actuation performance, element-wise voltage design variables are also included in the optimization. For the purpose of easy implementation of the electric system, the allowable voltage levels at an individual element are confined to three discrete values, namely zero and two prescribed values with opposite signs. To this end, a special interpolation scheme between the tri-level voltage values and the design variables is used in the optimization model. Based on the design sensitivity analysis of the objective function, the combined optimization problem is solved with the MMA algorithm. Numerical examples are presented to demonstrate the applicability of the proposed optimization model and numerical techniques. The optimal solutions also confirmed that larger output displacement can be achieved by introducing voltage design variables into the design problem. [Copyright &y& Elsevier]

Abstract: Intramolecular junctions (IMJs) formed by connecting two arbitrary carbon nanotubes (CNTs) can act as functional building blocks in circuits and components of CNT-based electronics devices. While extensive studies have been conducted on the atomic structural as well as electrical properties of IMJs and great advances have been achieved, mechanical response of IMJs under large deformation, which may exert significant effects on their electrical properties, are still not fully explored. In this paper, both molecular dynamics (MD) simulation and finite element (FE) analysis are employed to investigate the buckling behavior of IMJs under axial compression. The strain rate effects are firstly studied in the MD simulations. It is found that the critical compressive strain is not sensitive to the strain rate of relatively low range, but it exhibits a strong dependency upon the strain rate under high speed compression. In particular, a different failure mode may occur under ultra-high loading velocities. Based on the discussion on the strain rate effects, a reasonable loading velocity is suggested to be adopted in the subsequent MD simulations. In this study, the results of both the MD simulations and the FE analyses indicate that the critical compressive strain is dependent upon the length, radial dimensions of the IMJ but insensitive to the chirality of the IMJ. The comparison between the results of the MD simulations and the FE analyses also confirms that the FE analysis is able to provide useful insights into the compressive behavior of CNT-based IMJs with a much less computational cost. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the reliability assessment of structures exhibiting both stochastic and bounded uncertainties by using a probability and convex set mixed model. The safety measure of a structure is quantified by a reliability index defined by a nested minimization problem. An iterative procedure is developed for seeking the worst-case point and the most probable failure point in the standard uncertainty space. Numerical examples are given to demonstrate the applicability of the probability and convex set mixed model representation in the structural reliability assessment, as well as to illustrate the validity and effectiveness of the proposed numerical method. [Copyright &y& Elsevier]

Abstract  Using a quantified measure for non-probab ilistic reliability based on the multi-ellipsoid convex model, the topology optimization of continuum structures in presence of uncertain-but-bounded parameters is investigated. The problem is formulated as a double-loop optimization one. The inner loop handles evaluation of the non-probabilistic reliability index, and the outer loop treats the optimum material distribution using the results from the inner loop for checking feasibility of the reliability constraints. For circumventing the numerical difficulties arising from its nested nature, the topology optimization problem with reliability constraints is reformulated into an equivalent one with constraints on the concerned performance. In this context, the adjoint variable schemes for sensitivity analysis with respect to uncertain variables as well as design variables are discussed. The structural optimization problem is then solved by a gradient-based algorithm using the obtained sensitivity. In the present formulation, the uncertain-but bounded uncertain variations of material properties, geometrical dimensions and loading conditions can be realistically accounted for. Numerical investigations illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques. The computational results also reveal that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than conventional deterministic approaches. The proposed method can be regarded as an attractive supplement to the stochastic reliability-based topology optimization. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a non-probabilistic reliability-based topology optimization method for the design of continuum structures undergoing large deformations. The variation of the structural system is treated with the multi-ellipsoid convex model, which is a realistic description of the parameters being inherently uncertain-but-bounded or lacking sufficient probabilistic data. The formulation of the optimal design is established as a volume minimization problem with non-probabilistic reliability constraints on the geometrically nonlinear structural behaviour. In order to circumvent numerical difficulties in solving the nested double-loop optimization problem, a performance measure-based approach is employed to transform the constraint on the reliability index into one on the concerned performance. In conjunction with an efficient adjoint variable scheme for the sensitivity analysis of reliability constraints, the optimization problem is solved by gradient-based mathematical programming methods. Three numerical examples for the optimization design of planar structures are presented to illustrate the validity and applicability of the proposed method. The obtained optimal solutions show the importance of incorporating various uncertainties in the design problem. Moreover, it is also revealed that the geometrical nonlinearity needs to be accounted for to ensure satisfaction of the reliability constraints in the optimal design of structures with large deformation. [Copyright &y& Elsevier]

Abstract: The topology optimization of load-bearing structural components for reducing attitude control efforts of miniature space vehicles is investigated. Based on the derivation of the cold gas consumption rate of three-axis stabilization actuators, it is pointed out that the attitude control efforts associated with cold gas micro thrusters are closely related to the mass moment inertia of the system. Therefore, the need to restrict the mass moments of inertia of the structural components is highlighted in the design of the load-bearing structural components when the attitude control performance is concerned. The optimal layout design of the space vehicle structure considering attitude control effort is, thus, reformulated as a topology optimization problem for minimum compliance under constraints on mass moments of inertia. Numerical techniques for the optimization problem are discussed. For the case of a single constraint on the mass moment of inertia about a given axis, a design variable updating scheme based on the Karush–Kuhn–Tucker optimality criteria is used to solve the minimization problem. For the problem with multiple constraints, mathematical programming approach is employed to seek the optimum. Numerical examples will be given to demonstrate the validity and applicability of the present problem statement. [Copyright &y& Elsevier]

Abstract: This paper investigates the optimal spatial distribution of single-channel actuation voltage in static structural shape control problem. It is pointed out that single-channel actuation voltage input for shape control applications is of practical importance due to its ease of implementation. The Mindlin plate theory is used in the finite element modeling of laminates with piezoelectric layers. The optimal distribution of the single-channel actuation voltage is formulated as a discrete optimization problem with tri-level design variables, where a least-square function measuring the structural shape error is to be minimized under a constraint on the control effort. Such a problem is then transformed into a continuous one by introducing element-wise artificial design variables defining the topological feature of the control voltage distribution. A power-law function relating the design variables and the applied voltages is proposed to penalize intermediate values of the design variables. Based on the sensitivity analysis, the problem is solved effectively using the MMA algorithm tailored for constrained least-square problems. Numerical examples presented demonstrate the validity of the proposed problem formulation and numerical approaches. [Copyright &y& Elsevier]

• Robust topological design under bounded loads and material uncertainty is studied. • A new ellipsoid convex model for bounded random loads is proposed. • Loads are assumed uniformly distributed according to the maximum entropy theorem. • Spatially correlated material uncertainty is modeled as a random field by EOLE. • Polynomial chaos expansion with sparse grid rule is used in uncertainty analysis. Design optimization considering uncertainties arising from different sources has been one of the hotspots in the area of structural optimization. This paper presents a robust topology optimization method for structures with bounded loads and spatially correlated material uncertainties. We first develop a new model for random structural loads with bounded nature, in which the uncertain load components are assumed to be uniformly distributed within a convex set represented by an ellipsoid model. This model is then combined with the random field discretized by means of the expansion optimized linear estimation to provide uncertainty modelling of structures exhibiting both load and material uncertainties. The robust topological design problem is formulated as a bi-criteria optimization problem for minimizing the mean value and standard deviation of the structural compliance under these uncertainties. The polynomial chaos expansion, in conjunction with the sparse grid quadrature rule, is employed for calculating the statistical moments of the structural responses. The adjoint sensitivity analysis scheme is derived, and a gradient based optimizer is employed for updating the design variables. Numerical examples show that the structural designs obtained by the proposed robust topology optimization method exhibit higher robustness against uncertainties as compared with their deterministic counterpart. [ABSTRACT FROM AUTHOR]

Abstract: The study addresses the perturbation-based stochastic finite element analysis and the robust design optimization of deformation processes of inelastic solids. The perturbation equations for the stochastic moment analysis of both steady-state and non-stationary processes are presented. An iteration scheme based on the secant system operator is given for the solution of the perturbation equations in case that a tangent matrix is not available. The robust design of deformation processes is stated as a two-criteria optimal design problem that attempts best mean properties of the outcome at minimum variability. The task is solved using optimization techniques based on sequential quadratic programming in conjunction with the stochastic finite element analysis. The proposed method is applied to the design of an extrusion die for robustness with respect to friction variability, and to a workpiece preform design problem. The numerical results show the potential of the method for applications regarding the design of robust deformation processes. [Copyright &y& Elsevier]

Abstract: The robust design of non-linear structures with path-dependent response is stated as a two-criteria optimization problem and is solved by the method of mathematical programming. To this end, the perturbation technique is applied in conjunction with the incremental loading procedure for the response moment analysis of path-dependent non-linear structural systems with random parameters. Furthermore, the sensitivities of mean and variance of the structural performance function are evaluated using direct differentiation in the framework of perturbation based stochastic finite element analysis. By introducing a weighting factor in the compound objective––resp. desirability function, and feasibility indices in the constraints, the mathematical model of structural robust design problem is formulated and is solved with a gradient-based algorithm. Numerical examples demonstrate the applicability of the presented method. [Copyright &y& Elsevier]

The robust design of structures with stochastic parameters is studied using optimization techniques. The first two statistical moments of the stochastic parameters including design variables are considered in conjunction with the second-order perturbation method for the approximation of mean value and variance of the structural response. In this framework, the sensitivities of the mean values and variances of the structural performance function with respect to the design variables are calculated for use in the optimization task. The robust design of structures is formulated as a multi-criteria optimization problem, in which both the expected value and the standard deviation of the objective function are to be minimized. The robustness of the feasibility is also taken into account by involving the variability of the structural response in the constraints. The two-criteria optimization problem is converted into a scalar one and is then solved by a gradient based optimization algorithm. To demonstrate the applicability of the presented method, numerical examples are given, involving static and dynamic response. [Copyright &y& Elsevier]

• A novel method is developed for constructing the minimum-volume ellipsoid convex model with outlier detection using samples of uncertain parameters. • The local outlier factor, combined with the k-nearest Natural Neighbor concept, serves as indicators for outliers in a given set of samples. • The minimum-volume ellipsoid convex model enclosing all the identified normal samples is constructed with the SDP formulation, which is highly efficient and able to ensure global optimality of the problem. • The obtained ellipsoid convex models avoid over-conservativeness induced by outliers in uncertainty modeling and robust topology optimization. The ellipsoid convex model can be suitably used for structural analysis and design optimization under uncertain-but-bounded parameters and loads. Such a model can be constructed using measured samples of the uncertainties. However, the presence of outliers is often unavoidable due to system fluctuations in the measurements. Thus, it is necessary to detect any outliers among the samples before constructing the uncertainty model to prevent over-conservativeness. To this end, the present paper proposes a rational approach for constructing ellipsoid convex models with outlier detection. The concept of the local outlier factor (LOF) is utilized, in conjunction with the k-nearest natural neighbor to adaptively determine the neighborhood range. Then the outliers are detected using the scaled median absolute deviation method, based on the LOF values obtained. Finally, the minimum-volume ellipsoid convex model is constructed with a mathematically strict and efficient semi-definite programming formulation using the normal samples. The validity of the proposed approach is demonstrated with numerical examples. The application of the constructed uncertainty model in non-probabilistic robust topology optimization is demonstrated, and the results show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• A 'directional damping' concept is proposed for viscoelastic composite design. • A topology optimization model is developed for directional damping composites. • Optimized directional damping designs notably outperform the isotropic designs. • Optimized microstructures show similarities with bio-inspired wavy design. • Potential application of directional damping is shown by an airless tire design. Design of architected functional materials that possess desired damping performance is a topic of great interest in both academic research and industrial applications. This study investigates the concept of 'directional damping' for viscoelastic composites and develops a topology optimization framework to achieve directional damping design. Microstructures with both load-bearing capacity and dominant damping in the prescribed direction are obtained by maximizing the loss factor while imposing stiffness constraints. An optimized directional damping microstructure design exhibits a loss factor 1.8 times higher than the isotropic design in the prescribed direction. It is found that the optimized configurations with curved viscoelastic strips are similar to wavy 'suture' lines in the beaks of woodpeckers, which possess outstanding energy absorption performance. We have also verified the superiority of the directional damping design through numerical simulations and experiments of the microstructured composites. The experiment results show significant reduction of peak response for the directional damping design compared to the isotropic counterpart. To demonstrate the application potential of the optimized unit cell microstructures, a novel conceptual airless tire that exhibits improved stiffness and shock absorption performance is designed and validated through both numerical simulations and experiments. [Display omitted] [ABSTRACT FROM AUTHOR]

Repeatedly solving the generalized eigenvalue problems by far dominates the computational cost in large-scale topology optimization involving natural frequency constraints. This study proposes a method for dynamic topology optimization problems considering natural frequencies using successively executed iterations for the structural analysis and design. By using the Rayleigh quotients as approximations of the natural frequencies and achieving sequential approximation of the eigenpairs through inverse iteration-like procedures to improve the eigenvectors along with the topological evolution of the structure, the method avoids solving the time-consuming eigenvalue problem in each design iteration. This makes the method particularly suitable for large-scale frequency-constrained topology optimization problems. The convergence property of the method is analyzed under the assumption of sufficiently small design changes between two successive design iterations. Numerical examples regarding frequency and frequency gap constraints show that this method is able to realize concurrent convergence of the eigenvalue analysis and design optimization, and is more efficient than the conventional double-loop approach. • We propose an iterative method of topology optimization considering eigen frequencies. • Successive iterations of analysis and design are based on eigenpair approximation. • Inverse iteration-like procedures are performed to improve eigensolutions. • The method avoids solving time-consuming eigenvalue problem in each design iteration. • The convergence property is analyzed, and repeated eigenvalues are also treated. [ABSTRACT FROM AUTHOR]

Buckling failure is a major concern in lightweight lattice core sandwich structures (LCSSs). This study proposes an efficient method for designing LCSSs with superior buckling strength under uniaxial compression. In this approach, the buckling-resistant non-uniform shapes of single struts with different slenderness and inclination are first identified, and then they are directly used to replace uniform struts in LCSSs. This method can save considerable design time compared to conventional methods, which require conducting optimizations on entire LCSSs. Numerical results demonstrate that four designed representative non-uniform LCSSs can gain over 15% improvement in buckling strength compared to their counterpart uniform LCSSs. This improvement is even comparable to the solutions from optimizations on entire LCSSs. Two LCSSs with non-uniform struts are 3D printed, and the test results validate at least 10% improvement in compressive strength. Based on the proposed method, various LCSSs with superior buckling strength could be designed for different loadings. [ABSTRACT FROM AUTHOR]

Large-scale natural frequency-related topology optimization problems pose a great challenge due to the high computational cost required by the iterative computation of the system eigenvalues and their sensitivities in each design iteration. This paper presents a new framework based on a multi-step relay strategy in conjunction with the idea of successive iteration of analysis and design (SIAD), to find high-quality solutions at affordable computational costs. The method starts from a relatively coarse finite element discretization, and then use gradually refined meshes to improve the design resolution. For a given level of mesh resolution, the method interleaves the eigenvalue solution routine with the optimization iterations to achieves sequential approximations of the eigenpairs along with the structural design evolution, thus avoiding the time-consuming eigenpair analysis in each optimization iteration. By sequentially solving the optimization problem and projecting intermediate designs and the corresponding approximate eigenmodes from a coarser mesh onto finer meshes, the proposed multi-step relay method can further substantially alleviate the computational burden and generate high-resolution boundaries in the final design. Numerical examples show that this method can be used to solve natural frequency maximization topology optimization problems with millions of degrees of freedom on a desktop workstation, and is much more efficient than the conventional double-loop method. [ABSTRACT FROM AUTHOR]