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Reducing the vulnerability of a platform, i.e., the risk of being affected by hostile objects, is of paramount importance in the design process of vehicles, especially aircraft. A simple and effective way to decrease vulnerability is to introduce protective structures to intercept and possibly stop threats. However, this type of solution can lead to a significant increase in weight, affecting the performance of the aircraft. For this reason, it is crucial to study possible solutions that allow reducing the vulnerability of the aircraft while containing the increase in structural weight. One possible strategy is to optimize the topology of protective solutions to find the optimal balance between vulnerability and the weight of the added structures. Among the many optimization techniques available in the literature for this purpose, multiobjective genetic algorithms stand out as promising tools. In this context, this work proposes the use of a in-house software for vulnerability calculation to guide the process of topology optimization through multi-objective genetic algorithms, aiming to simultaneously minimize the weight of protective structures and vulnerability. In addition to the use of the in-house software, which itself represents a novelty in the field of topology optimization of structures, the method incorporates a custom mutation function within the genetic algorithm, specifically developed using a graph-based approach to ensure the continuity of the generated structures. The tool developed for this work is capable of generating protections with optimized layouts considering two different types of impacting objects, namely bullets and fragments from detonating objects. The software outputs a set of non-dominated solutions describing different topologies that the user can choose from. [ABSTRACT FROM AUTHOR]

This research aims to evaluate the impact of the initial cell configuration and the limit volume fraction on the generation of mechanical metamaterial cells. The procedure was developed using a methodology based on preprocessing, processing, and post processing to facilitate fast exploration of metamaterial cell space design. The initial cell consisted of a square or cube of material with a central circular or spherical void diameters of 10 mm, 20 mm, and 30 mm. Additionally, the generation process employed three volume fractions limits (30%, 40%, and 50%) and eleven objective functions. These functions intended to generate cells that maximize stiffness in one or multiple directions and cells with maximum compressibility or shear modulus. Some of the obtained cells with tailored mechanical properties exhibit novel geometrical configurations. The results highlight volume fraction as the most significant factor in the generation process, with well-defined metamaterial cells produced using an initial volume fraction of 50% and low to medium void diameters. [ABSTRACT FROM AUTHOR]

The efficient development of electric vehicles is essential to drive society towards sustainable development. Designing a lightweight frame is a key strategy to improve the economy and environment, increase energy efficiency, and reduce carbon emissions. Taking an automatic loading and unloading mixer truck as the research object, a force analysis of its frame was conducted under six typical working conditions. A size optimization method based on a hybrid model of the Kriging model and the analytic hierarchy process (AHP) is proposed. An approximate model of the mass and maximum stress of the frame was established using the Kriging model, and the Kriging model was optimized by using the multi-objective genetic optimization algorithm and the AHP method. Meanwhile, topology optimization was introduced to improve the structural performance of the frame and reduce its weight. The optimization results show that the overall weight of the frame is reduced by 11.96% compared to the pre-optimization period, though it still meets the material performance specifications. By comparing the iterative curves of the single Kriging model with those of the AHP model, it can be seen that the initial optimization efficiency of the hybrid model is about twice as much as that of the AHP model, and the final optimization result is improved by about 3.6% compared with the Kriging model. This validates the hybrid model as an effective tool for the multi-objective optimization of electric vehicle frames, providing more efficient and accurate optimization results for frame design. [ABSTRACT FROM AUTHOR]

Additive manufacturing allows the creation of geometries otherwise impossible to achieve through traditional technologies in mechanical components. These geometries can be obtained using algorithms to optimize the mass distribution. Topology Optimization algorithms are one of the tools most applied in design for additive manufacturing and lightweight engineering. These optimization techniques require Finite Element Method tools to evaluate and compare the mechanical behavior of different geometrical solutions. The optimization results are closely related to boundary conditions, objectives, and constraints. Therefore, one of the issues is the necessity to evaluate different parameter settings to improve the result in terms of light weight, strength, and easy printability. This article shows a working method for using topological optimization to lighten a connecting rod. The resultant model is optimized considering Additive Manufacturing. [ABSTRACT FROM AUTHOR]

This paper applies topology optimization in combination with a genetic algorithm to design a coating structure for sound absorption in underwater applications. The coating is designed with a high broadband acoustic absorption of 0.94 ranging from 1 to 10 kHz by optimizing the cavity topology and the dimensions of the embedded steel scatterers. This study demonstrates the application process of the topology optimization with a genetic algorithm method and the optimization results of the optimization process stages. The absorption mechanism of the topology design is analyzed. The effects of different cavity compositions, steel scatterers, design ideas, material parameters, and acoustic incident angles on the sound absorption coefficients are investigated. These acoustic structures and the method provide more ideas for the design of coating structures for underwater sound absorption. [ABSTRACT FROM AUTHOR]

Arthroplasty is commonly performed to treat advanced osteoarthritis or other degenerative joint conditions; however, it can also be considered for young patients with severe joint damage that significantly limits their functionality and quality of life. Young patients are still at risk of aseptic mobilization and bone resorption due to the phenomenon of stress shielding that causes an uneven distribution of tensions along the femoral contact surface prosthesis. This phenomenon can be limited by choosing the material of the prosthesis appropriately or by varying its stiffness, making sure that its mechanical behavior simulates that of the femur as much as possible. The aim of this study is to evaluate the mechanical strength of a prosthesis optimized both in shape and material and compare the results with a standard titanium prosthesis. Methods: Through three-dimensional modeling and the use of finite element method (FEM) software such as ANSYS, the mechanical behavior of traditional prosthesis and prosthesis optimized topologically respecting the ASTM F2996-13 standard. Results: With topological optimization, there is a stress reduction from 987 MPa to 810 MPa with a mass reduction of 30%. When carbon fiber is used, it is possible to further reduce stress to 509 MPa. Conclusions: The reduction in stress on the femoral stem allows an optimal distribution of the load on the cortical bone, thus decreasing the problem of stress shielding. [ABSTRACT FROM AUTHOR]

Intellectual biochemical detection is an essential part of a smart society, which is important for future personal health management. The judgment process of health level should be carried out by comprehensive consideration of multiple indicators. To achieve that, multi-substance sensors are necessary. Due to the high-throughput and rapid detection characteristics, the multi-material testing microfluidic devices are promising bio-monitoring devices. To ensure the detection accuracy of the multi-substance-detection microfluidic devices, the topological structure of the channels must be designed carefully. Not only the flow rate but also the substance residue is decided by the topological structure of the channels. Thus, in this paper, we report a genetic algorithm-based topological optimization method for microfluidic devices. The material residue is modeled as the energy dissipation caused by friction. The topology and the position of the inlet and outlets are jointly optimized to minimize the energy dissipation with different desired flow rates at the outlets. The proposed genetic algorithm-based two-tier method enhanced global search ability. The simulation and experiment results show that our algorithm can decrease the energy dissipation on the premise of ensuring the outlet flow rate with comparable computational complexity. [ABSTRACT FROM AUTHOR]

A coupling of moving morphable void and component approach for the topology optimization of hydrogel structures involving recoverable large deformation is proposed in this paper. In this approach, the geometric parameters of moving morphable voids and components are set as design variables to respectively describe the outline and material distribution of hydrogel structures for the first time. To facilitate the numerical simulation of large deformation behavior of hydrogel structures during the optimization process, the design variables are mapped to the density field of the design domain and the density field is then used to interpolate the strain energy density function of the element. Furthermore, the adjoint sensitivity of the optimization formulation is derived and combined with the gradient-based algorithm to solve the topology optimization problem effectively. Finally, two representative numerical examples of the optimization of isotropic hydrogel structures are used to prove the effectiveness of the proposed method, and the optimization design of an anisotropic bionic hydrogel structure is presented to illustrate the applicability of the method. Experimental results are also presented to demonstrate that the explicit topologies obtained from the method can be directly used in the manufacture of hydrogel-based soft devices. [ABSTRACT FROM AUTHOR]

Additive Manufacturing (AM) has become popular for rapid prototyping and it is presently widely used in different branches of industry because of its advantages such as freedom of design, mass customization, waste minimization and the ability to manufacture complex shape. AM is the process of making 3D object from computer model data by depositing of material layer by layer. Topology optimization is iterative modifying the shape and optimizing material within a given designs space for load, boundary condition thus leading to weight reduction of components. Thus, to form lightweight components which have great advantage where energy consumption is minimal, topology optimization is used. Reducing weight and decreasing the material usage while keeping the product functions are the main challenges. Studies on the integration of the topology optimization and additive manufacturing, specifically mass reduction attract considerable attention. The topology optimization process is employed in this case study, to redesign a lightweight automotive brake pedal to show the potential of topology optimized design for additive manufacturing. As a result of this study 54.07% weight reduction was achieved in the total mass. The thermo-mechanical analysis for additive manufacturing showed that the part without topological optimization 108 MPa of stress and 1,099 mm of displacement were obtained and after optimization they were 196,1 MPa and 1,295 mm, respectively. [ABSTRACT FROM AUTHOR]

This paper describes a methodology for modifying a tooth for the ability to transmit torque in one direction only. It presents two methods (analytical and numerical) of tooth mass reduction while maintaining functional features of the whole transmission. The results of the above mentioned methodology are presented on the example of a mass-produced transmission. [ABSTRACT FROM AUTHOR]

• The mechanics of the vein domains are revealed to be correlated with morphology. • The layout of wing veins is explained by multi-objective optimization. • Structural biology is evolved based on the gradient optimization. The intricate network of veins on dragonfly wings has captured the attention of many researchers due to its fascinating configuration and excellent mechanical properties. In this paper, based on the observation of the layout of the vein domains on the hind wing of dragonfly, the types of domains were characterized from the aspects of area and shape. The numerical analysis revealed that different shaped domains enhance either stiffness or vibration stability of the wing. According to this feature, a multi-objective gradient optimization algorithm based on stiffness, mass transport efficiency and first order frequency was proposed. Associated by the size constraints, the optimal layout of the venation was obtained and subsequently used to generate the Voronoi patterns, whose positions and shapes could be further optimized by an evolutionary algorithm to match the mechanical analysis results. The effectiveness of this multi-cellular configuration was verified by testing the bending and vibration stability of the additive manufactured model. The aerodynamic simulation analysis of this flapping wing structure was also investigated. This study has important implications for understanding the evolutionary mechanisms of venation on biological wings and designing reinforcement for sheets. [ABSTRACT FROM AUTHOR]

• Optimal design of various periodic unit cells aiming at high thermal conductivity. • Schemes to modulate porous microstructure based on topology optimization. • Computational and experimental validation of effective thermal conductivity with error less than 10 %. Porous structures are lightweight and thus possess tailorable thermophysical properties through topological design. A multi-constraint topology optimization scheme is developed for designing 2D periodic lattice material with controllable porosity and optimal thermal conductivity. The porosity, pore size and specific surface area are modulated by imposing local density constraints, and thus the structure-determined thermal conductivity can be systematically investigated. The isotropic porous structures after optimization show effective thermal conductivity close to the Hashin-Shtrikman theoretical bound. The specific surface area of base cell is enlarged with imposing local density constraint. In addition, microstructure with anisotropic thermal conductivity can be also obtained. The samples of lattice structure are additively manufactured via selective laser melting, and the thermal conductivities are experimentally validated with deviation within 10 %. The proposed porous structures with targeted porosity have potential application in skeleton embedded with phase change materials. [ABSTRACT FROM AUTHOR]

In recent years, new methods have been developed to synthesize complex porous and micro-structured geometry in a variety of ways. In this work, we take these approaches one step further and present these methods as an efficacious design paradigm. Specifically, complex micro-structure geometry can be synthesized while optimizing certain properties such as maximal heat exchange in heat exchangers, or minimal weight under stress specifications. By being able to adjust the geometry, the topology and/or the material properties of individual tiles in the micro-structure, possibly in a gradual way, a porous object can be synthesized that is optimal with respect to the design specifications. As part of this work, we exemplify this paradigm on a variety of diverse applications. • Support for microstructures design with graded heterogeneous materials. • A framework for editing microstructures, affecting individual tiles' geometry, topology, and material. • Direct support for (isogeometric) analysis of microstructures. [ABSTRACT FROM AUTHOR]

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Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material). Using a finite elements discretization (FEM) of the PDE and functional we obtain an integer programming problem. Due to approximation error of the FEM discretization, optimization problem becomes mesh-depended and possess false, physically inadequate optimums, while functional value heavily depends on the fineness of discretization scheme used to compute it. To alleviate this problem, we propose regularization of given functional by error estimate of the FEM discretization. This regularization provides robustness of solutions and improves obtained functional values as well. While the idea is broadly applicable, in this paper we apply our method to the heat conduction optimization. Problems of this type are of practical importance in design of heat conduction channels, heat sinks and other types of heat guides. [ABSTRACT FROM AUTHOR]

High-quality hex meshes are crucial for finite element analysis. However, geometric smoothing techniques applied for improving the quality of a hex mesh cannot ensure that the requirements of finite element analysis are satisfied. Therefore, to address this challenge, in this paper, we present a novel approach for topological optimization of a hex mesh based on frame field and sheet adjustment. Our approach improves the quality of the worst elements of the hex mesh by optimizing its topological structure. The approach first builds an initial frame field from the input hex mesh and then optimizes it to obtain a resultant high-quality frame field. Next, according to the initial and optimized frame fields, the process determines the most problematic sheet that degrades the quality of the hex mesh. Finally, based on the high-quality frame field and the current topological structure of the hex mesh, our approach uses sheet operations to adjust the structure of this most problematic sheet. Experimental results demonstrate that our topological optimization approach can effectively improve the minimum Scaled Jacobian value of the hex mesh. [ABSTRACT FROM AUTHOR]

Topology optimization is a mathematical approach that optimizes the layout for the given design constraints such as loading and boundary conditions so that the optimum design obtained performs its function. In different types of loading conditions such as single load or multiple load topological optimization result in the best use of a material for a body in given volume constraints. In topological optimization the structural compliance is minimized while satisfying a constraint on the volume of the structure. This paper represents the topological optimization of the fork-end (double eye) of a knuckle joint with the objective to reduce the mass of an existing fork-end of a knuckle joint of an automobile or locomotive by applying the optimization technique. Reducing the weight of an automobile part will result in the overall weight reduction of a vehicle, thus, its energy consumption demands decrease thereby improving its fuel efficiency. The topological optimization was done using a finite element solver, ANSYS. The ANSYS Parametric Design Language was employed for utilizing the topological optimization capabilities of the commonly used finite element solver ANSYS. Solid92 elements were used to model and mesh the fork end of the knuckle joint in ANSYS. The optimality criteria method was used for topological optimizing the fork end of a knuckle joint. [ABSTRACT FROM AUTHOR]

The use of custom implants has recently gained increasing importance in craniofacial surgery in order to optimize preoperative planning and reduce operative time. The design of patient-specific implants plays an important role to restore craniofacial bone. Nevertheless, the design method has become the bottleneck. In this study, a new design method of a maxillofacial prosthesis based on the topology optimization was proposed to realize lightweight custom implants. At first, parametric predesign of the optimized model was carried out to ensure that the optimized model conformed to the main physiological anatomical structure and recover basic function structure. Then, the design region is defined under given load and boundary conditions. The material interpolation technique of SIMP with the penalization factor is adopted to get the final optimized 3D model. Finally, the experimental results verify that the method of topology optimization for the maxillofacial prosthesis proposed is efficient. [ABSTRACT FROM AUTHOR]

Recent works introduced topology optimization in the design of robots, but the proposed methodologies led to a local optimization of the performance. Moreover, most of performance indices used are not in strong relation with easy-to-understand technological requirements. We propose a methodology that is able to perform a topology optimization for robots, valid globally in the workspace or for a set of given trajectories, and which is based on the use of technology-oriented performance criteria. In order to enforce the chosen performance indices to be valid globally, optimal robot configurations or trajectories for which extreme performance will be attained are computed, and iteratively updated. In order to decrease the computational time associated with these performance indices, we exploit the structure of the elastic models in order to reduce their computational complexity. Finally, we use an optimization algorithm called the Linearization Method which gives results in a computational time equivalent to standard topology optimization algorithms, but its implementation is less complex and makes it quite easy to perform modification or improvement. The methodology is applied for the design of a five-bar mechanism. We show that our approach leaded to a robust optimization of the robot performance over the whole workspace. [ABSTRACT FROM AUTHOR]

Phononic crystals (PnCs) are artificially made materials composed of periodically arranged structures capable of manipulating acoustic/elastic wave propagation characteristics. In this paper, an improved fast plane wave expansion method (IFPWEM) is developed to obtain the band structures of PnCs. In the method presented, the continuity of the algorithm has been improved by eliminating the jump discontinuity points as well as decreasing the number of wave vectors used. Implementing these changes results in increased computational efficiency when compared to the traditional fast plane wave expansion method (FPWEM). In order to increase the band gap width produced by the PnCs, an adaptive genetic algorithm is adopted to optimize the PnCs structural topology for in-plane wave mode ( xy mode). The numerical results yielded from optimization of two-dimension (2D) PnCs with a symmetric square lattice microstructure verifies that the efficiency of the IFPWEM is significantly greater than the conventional FPWEM and finite element methods. [ABSTRACT FROM AUTHOR]

High-quality hex meshes are crucial for finite element analysis. However, the quality of a hex mesh improved by geometric smoothing cannot guarantee to satisfy the requirement of finite element analysis. To this end, this paper puts forward an approach to topological optimization of hex mesh based on frame field and sheet operations, which improves the quality of the worst elements of the hex mesh by optimizing its topological structure. The approach first builds an initial frame field on the input hex mesh and optimizes it to obtain a high-quality frame field. Then, the problematic sheet that leads to the poor quality of the hex mesh is determined according to the initial and optimized frame fields. Finally, the structure of the problematic sheet is adjusted based on the high-quality frame field and sheet operations. Experimental results demonstrate that our topological optimization approach can effectively improve the minimal Scaled Jacobian value of the hex mesh. [ABSTRACT FROM AUTHOR]

For the purpose of improving structural dynamic reliability, a topological optimization methodology for maximizing the dynamic response reliability index is proposed based on the bi-directional evolutionary structural optimization (BESO) method. The objective of the present study is to maximize the dynamic response reliability index at specified points on the structure under random excitation, subject to volume constraints on multi-phase materials over the admissible design domain. The sensitivity of the dynamic response reliability index with respect to the design variables is derived. The optimization procedure of the extended BESO method is presented. A series of numerical examples in both 2D and 3D are presented to demonstrate the effectiveness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this work we introduce a novel method for creating behaviors in cellular automata: optimizing the topology of the cellular substrate while maintaining a single simple update rule. We study the effect of altering the shape of a 3D cellular automaton and local signaling ability of each of its cells on the ability of that automaton as a whole to give rise to emergent locomotion behavior. This system optimizes for the physically embodied interactions between a cellular automaton with an external physically simulated world, rather than optimizing directly for a computational ability internal to the automaton itself. We give each cell in the automaton the ability to have an internal “excited” state, and also the ability to perform a physical action (volumetric contraction and expansion) as a result of that state. We then employ an evolutionary algorithm to optimize for the locomotion ability of the “robot” resulting from the behavior of this embodied automaton. We demonstrate a number of diverse topologies which lead to effective locomotion behaviors in this paradigm. We believe that creating complex behavior from simple rules in a complex substrate not only opens up questions about cellular automata, but also provides insights towards the study of morphological computation and embodied cognition. [ABSTRACT FROM AUTHOR]

This paper studies the optimization problem of topological active net (TAN), which is often seen in image segmentation and shape modeling. A TAN is a topological structure containing many nodes, whose positions must be optimized while a predefined topology needs to be maintained. TAN optimization is often time-consuming and even constructing a single solution is hard to do. Such a problem is usually approached by a “best improvement local search” (BILS) algorithm based on deterministic search (DS), which is inefficient because it spends too much efforts in nonpromising probing. In this paper, we propose the use of micro-differential evolution (DE) to replace DS in BILS for improved directional guidance. The resultant algorithm is termed deBILS. Its micro-population efficiently utilizes historical information for potentially promising search directions and hence improves efficiency in probing. Results show that deBILS can probe promising neighborhoods for each node of a TAN. Experimental tests verify that deBILS offers substantially higher search speed and solution quality not only than ordinary BILS, but also the genetic algorithm and scatter search algorithm. [ABSTRACT FROM PUBLISHER]

We consider a problem of control of a distributed system in a polygonal domain and prove that its singular coefficient is expressible solely by means of its data. We subsequently study a numerical aspect of this problem using the topological optimization method. The paper provides for a representation of the topological gradient of the Dirichlet problem in this polygonal domain. [ABSTRACT FROM AUTHOR]

This paper describes the application of topological optimization method to heel counter in the practical designing process of running shoes. The heel counter has an important role to control the excessive calcaneous eversion in a series of running motion. This control is called as shoe stability, which is one of the most important requirement functions in shoe designing. At the same time shoe weight should be reduced because the runners’ fatigue can be intimately interrelated with shoe weight. Both these functions, stability and lightness are conflicting parameters. The optimization method has been developed to satisfy some requirement functions and widely applied to industrial fields. By using the topological optimization method, the optimized heel counter with enough stability and weight reduction was practically designed. In order to check the validity of the counter manufactured, the stability of running shoes with the heel counter was quantitatively evaluated in the practical running motion analyses and compared with that of the conventional heel counter. Therefore it was confirmed that the topological optimization method was so powerful tool in the practical designing process of running shoes. [ABSTRACT FROM AUTHOR]

This work presents the topology optimization of bi-dimensional structures in plane stress state, considering a bidirectional scheme of optimization, incorporating a penalization parameter that maximizes the stiffness, considering the kinematic constraints. An open source code was implemented in MATLAB, with capabilities to find the optimal structures for a certain volume fraction, modified to obtain the optimal structure considering a limited or admissible displacement. Two classical problems in the literature are analyzed by introducing the developed concepts. The results obtained indicate that, for a particular state of charge, it is possible to define different configurations for maximum rigidity, depending on the displacement considered. Each one of these configurations is structured on the basis of compression and tension elements that resemble a lattice, with almost uniform tensional distribution in each element. The relevance of this work is that it allows you to display the existence of maximum configurations, depending on the limit or admissible displacement and how this converges to a structure with uniform stress levels. [ABSTRACT FROM AUTHOR]

This paper introduces a new design approach to synthesize multiple degrees-of-freedom (DOF) flexure-based parallel mechanism (FPM). Termed as an integrated design approach, it is a systematic design methodology, which integrates both classical mechanism synthesis and modern topology optimization technique, to deliver an optimized multi-DOF FPM. This design approach is separated into two levels. At sub-chain level, a novel topology optimization technique, which uses the classical linkage mechanisms as DNA seeds, is used to synthesize the compliant joints or limbs. At configuration level, the optimal compliant joints are used to form the parallel limbs of the multi-DOF FPM and another stage of optimization was conducted to determine the optimal space distribution between these compliant joints so as to generate a multi-DOF FPM with optimized stiffness characteristic. In this paper, the design of a 3-DOF planar motion FPM was used to demonstrate the effectiveness and accuracy of this proposed design approach. [ABSTRACT FROM AUTHOR]

The main objective of this work is the application of the topological optimization procedure to heat transfer problems considering multiple materials. The topological derivative ( D T ) is employed for evaluating the domain sensitivity when perturbed by inserting a small inclusion. Electronic components such as printed circuit boards (PCBs) are an important area for the application of topological optimization. Generally, geometrical optimization involving heat transfer in PCBs considers only isotropic behavior and/or a single material. Multiple domains with anisotropic characteristics take an important role on many industrial products, for instance when considering PCBs which are often connected to other components of different materials. In this sense, a methodology for solving topological optimization problems considering anisotropy and multiple regions with embedded heat sources is developed in this paper. A direct boundary element method (BEM) is employed for solving the proposed numerical problem. [ABSTRACT FROM AUTHOR]

In the high-speed milling process of large end milling cutter, the stress of cutter caused by centrifugal force accounts for a large proportion of the total stress of the cutter and has a great influence on the milling process. In this paper, an end milling cutter with a diameter of 2,800 mm used on large and high-speed aluminum blank milling machine tools is taken as a research object, and the equations of internal stress caused by centrifugal force have been derived by using analytic method. On this basis, the factors affecting the internal stress were analyzed. Furthermore, the analytic results and the finite element analysis results were compared in order to confirm their correctness. Finally, according to the results of stress analysis, structure topology optimization design for large end milling cutter was carried out in order to reduce the weight and centrifugal force of the cutter. [ABSTRACT FROM AUTHOR]