This paper presents a highly efficient method to obtain high-resolution, near-optimal 3D topologies optimized for minimum compliance on a standard PC. Using an implicit geometry description we derive ...a single-scale interpretation of optimal multi-scale designs on a very fine mesh (de-homogenization). By performing homogenization-based topology optimization, optimal multi-scale designs are obtained on a relatively coarse mesh resulting in a low computational cost. As microstructure parameterization we use orthogonal rank-3 microstructures, which are known to be optimal for a single loading case. Furthermore, a method to get explicit control of the minimum feature size and complexity of the final shapes will be discussed. Numerical examples show excellent performance of these fine-scale designs resulting in objective values similar to the homogenization-based designs. Comparisons with well-established density-based topology optimization methods show a reduction in computational cost of 3 orders of magnitude, paving the way for giga-scale designs on a standard PC.
•Large-scale topology optimized designs are efficiently obtained on simple PC.•Near-optimal multi-scale designs can be obtained on a relatively coarse mesh.•De-homogenized designs perform excellent in terms of compliance on fine meshes.•Extensive verification studies are performed to compare with the state of the art.•A reduction in computational cost of at least three orders of magnitude is achieved.
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This study presents a hybrid reliability-based topology optimization (RBTO) method for handling epistemic and aleatory uncertainties. First, we establish a new triple-nested RBTO model based on fuzzy ...and probabilistic theory for describing the multi-source uncertainties. Subsequently, an efficient single-loop optimization method is proposed to degrade the triple-nested optimization problem into a deterministic optimization problem using the Karush–Kuhn–Tucker optimality condition. Furthermore, the sensitivities of the hybrid reliability constraint with respect to the random probabilistic variables, fuzzy variables, and deterministic design variables are derived using the adjoint variable method. Finally, a cantilever beam example, an L-shape beam design and a 3D example are tested to verify the validity of the proposed single-loop method.
•A novel RBTO model with nested triple loops is created under SIMP framework.•An efficient single-loop hybrid RBTO method is established.•The aleatory and epistemic uncertain sensitivity calculation technique is developed.•2D and 3D topology optimization examples illustrate the superiority of the proposed method.
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Significant advance in additive manufacturing (AM) is leading to a paradigm shift in design-for-manufacturing. The manufacturability concern over geometry complexity has largely been removed by AM, ...which will greatly promote design creativity. A representative paradigm shift is the increasing focus on lattice structures which can be efficiently manufactured by AM. Specifically, lattice structures have been used to replace conventional solid materials to reduce weight and enhance multi-functional properties. Hence, lattice structure topology optimization (LSTO) has drawn remarkable interest for being an optimal lattice infill design tool. Despite the extensive investigation on LSTO, this paper addresses a novel aspect in the concurrent optimization of lattice infill and design-dependent movable features, on which boundary conditions are prescribed. This type of problem has practical importance, such as cooling channel system (forced convective boundary) design used in different thermal management applications, which is challenging to solve numerically due to the increased complexity in sensitivity calculation. In the proposed method, parametric level set function is used to represent the movable feature geometry and accordingly, the thermal boundary conditions are implicitly applied. A detailed sensitivity analysis is performed to provide the effective sensitivity information for design update. Several numerical examples are provided to prove the effectiveness of the proposed method. In particular, the proposed methodology is applied to the concurrent optimization of cooling channels and the optimized design is printed out to demonstrate the manufacturability.
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Summary
The present study proposes a method of micro‐macro concurrent topology optimization for a two‐phase nonlinear solid to minimize the end compliance of its macrostructure undergoing large ...deformation. To reduce the computational costs to solve a 2‐scale boundary value problem under geometrically nonlinear setting, we use the so‐called method of decoupling multiscale structural analysis, in which the microscopic and macroscopic boundary value problems are decoupled in the homogenization process. An isotropic hyperelasticity model is used for the constitutive model for microstructures, while an orthotropic one is assumed to represent the macroscopic material behavior. Owing to this decoupling framework, the micro‐macro concurrent optimization problem can be split into 2 individual problems at the microscale and macroscale for the sake of algorithmic simplicity. Also, a 2‐scale adjoint sensitivity analysis can be performed within the framework of computational homogenization. It is verified from a series numerical examples that the proposed method is capable of computing the optimal structures at both microscale and macroscale, according to the level of applied load.
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We propose a novel topology optimization method to efficiently minimize the maximum compliance for a high‐resolution model bearing uncertain external loads. Central to this approach is a modified ...power method that can quickly compute the maximum eigenvalue to evaluate the worst‐case compliance, enabling our method to be suitable for large‐scale topology optimization. After obtaining the worst‐case compliance, we use the adjoint variable method to perform the sensitivity analysis for updating the density variables. By iteratively computing the worst‐case compliance, performing the sensitivity analysis, and updating the density variables, our algorithm achieves the optimized models with high efficiency. The capability and feasibility of our approach are demonstrated over various large‐scale models. Typically, for a model of size 512×170×170 and 69934 loading nodes, our method took about 50 minutes on a desktop computer with an NVIDIA GTX 1080Ti graphics card with 11 GB memory.
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Mechanical cloaks can hide objects and make them unfeelable by reproducing the surrounding displacement field without the objects and cloaks. In the existing works, mechanical cloaks have been ...considered for hiding a void, while this work develops a generic method to design cloaks for solids with a given stiffness. As materials with properties beyond natural materials are required to achieve this task, metamaterials with spatially varying microstructures are employed in this work. Similar to the functionally graded material, the present metamaterial has graded stiffness from the cloak to the surrounding region, via graded material volume fractions in the microstructures. Therefore, we present a multiscale topology optimization model that considers the cloak macrostructure and material microstructures, by which concurrent optimization of the structural topology and material properties of mechanical cloaking devices is investigated. The optimization model is implemented via (1) novel mathematical formulations for material microstructures based on the finite element method (FEM) and (2) an extended moving iso-surface threshold (MIST) method with a multi-volume fraction topology update scheme. Numerical examples are provided for multiscale design cases for cloaking a void or stiffer solid (e.g., wood, copper, and diamond), and also include finite element analysis (FEA) of the resulting multiscale metamaterials.
•New formulations for designing material microstructure in mechanical cloaking.•Method for concurrent multiscale optimization of cloaking materials and structure.•Generic cloaking design method for hiding voids or solids with given stiffness.
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47.
Topology Optimization for Beginners YAJI, Kentaro
Journal of the Japan Society for Precision Engineering,
2019, Volume:
85, Issue:
11
Journal Article
•A novel convexity-oriented time-dependent reliability-based topology optimization (CTRBTO) scheme is proposed.•The full-dimensional convex set collocation approach is presented to reveal the convex ...process of displacement responses.•The convex time-dependent reliability (CTR) index is defined and its design sensitivity about design variables is deduced.
In this work, a novel convexity-oriented time-dependent reliability-based topology optimization (CTRBTO) framework is investigated with overall consideration of universal uncertainties and time-varying natures in configuration design. For uncertain factors, the initial static ones are quantified by the convex set model and nodal dynamic responses are then expressed by the convex process model, where both the boundary rules and time-dependency properties are revealed by the full-dimensional convex-set collocation theorem. Unlike the original deterministic constraints in topology optimization schemes, a new convex time-dependent reliability (CTR) index is defined to give a reasonable failure judgment of local dynamic stiffness and impel the overall CTRBTO strategy. In addition, the gradient-based iterative algorithm is utilized to guarantee the computational robustness and the CTR-driven design sensitivities are explicitly analyzed by the Lagrange multiplier method. Several numerical examples are used to illustrate the effectiveness of the proposed method, and numerical results reflect the significance of this study to a certain extent.
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Supercapacitors exhibit fast charging/discharging ability and have attracted considerable attention within the automotive, aerospace, and telecommunication industries. Porous carbons, prized for ...their high electrical conductivity and high surface area, have been attractive candidates for supercapacitor electrodes. Moving to thick electrodes is one strategy to further increase energy density due to a higher volume fraction of active material. However, thick electrodes suffer from sluggish charged species transport, which is why thin electrodes are currently favored. In this work, we investigate the use of computational optimization and additive manufacturing to design and fabricate thick porous electrodes with improved performance. Electrode performance was maximized by designing their morphologies via topology optimization and printing by projection micro stereolithography (PμSL) using commercial resin (PR48). The PR48 resin was then pyrolyzed (PR48-P) to create the final conductive electrode. The optimized PR48-P electrodes exhibited 99% improvement in capacitance compared to control electrodes printed with cubic lattice morphologies. To further improve performance, we formulated a resin combining graphene oxide (GO) and trimethylolpropane triacrylate (TMPTA). Electrodes printed with 3 wt% GO in TMPTA exhibited improved capacitance retention after pyrolysis compared to the PR48-P electrodes. This work demonstrates the benefits of using topology optimization to design electrodes and material development to improve functional properties of 3D printable electrodes.
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•3D printing of complex shaped electrodes by projection micro stereolithography.•Topology optimization is used to design porous electrodes with optimal energy density.•Adding graphene oxide into photocurable resin improves the capacitance retention of supercapacitors.
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Thermal‐mechanical coupling environments extensively exist for engineering structures. How to effectively reduce thermoelastic deformation is distinctly important. Cellular structures have superior ...performances in stiffness and multi‐functionality with lightweight, and an excellent design can be expected by reasonably designing the microstructural topology and their distributions. However, existing studies are limited to designing homogenous cellular structures for thermoelastic response problems, although heterogeneous cellular structures have larger design spaces. This article intends to investigate the topology optimization problem for designing a special type of heterogeneous cellular structure, that is, quasi‐periodic cellular structure, for thermoelastic responses. The quasi‐periodic cellular structure is a composition of microstructures with similar but not the same topology across the macro domain, which ensures a good compromise between manufacturability and performance. By introducing the erode‐dilate operators to describe quasi‐periodic cellular structural topology, a simple single‐loop topology optimization model for minimizing the deformation variance of specific lines with multi‐material and multi‐constraint is established. Three types of design variables are included, and their sensitivity analyses are derived for using the gradient‐based optimization solver to obtain updates simultaneously. Designs with shape‐preserving and required stiffness under thermoelastic loadings can be obtained. The examples presented show the capabilities of the proposed procedure and validate the effectiveness of the quasi‐periodic cellular structures in improving structural performance for thermoelastic problems.
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