Featured Cover Zhang, Weisheng; Meng, Yao; Yan, Xiaoye ...
International journal for numerical methods in engineering,
09/2023, Volume:
124, Issue:
17
Journal Article
Peer reviewed
Open access
The cover image is based on the Research Article Explicit topology optimization for graded lattice flexoelectric nanostructures via ersatz material model by Weisheng Zhang et al., ...https://doi.org/10.1002/nme.7255.
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Summary
As the aerospace and automotive industries continue to strive for efficient lightweight structures, topology optimization (TO) has become an important tool in this design process. However, ...one ever‐present criticism of TO, and especially of multimaterial (MM) optimization, is that neither method can produce structures that are practical to manufacture. Optimal joint design is one of the main requirements for manufacturability. This article proposes a new density‐based methodology for performing simultaneous MMTO and multijoint TO. This algorithm can simultaneously determine the optimum selection and placement of structural materials, as well as the optimum selection and placement of joints at material interfaces. In order to achieve this, a new solid isotropic material with penalization‐based interpolation scheme is proposed. A process for identifying dissimilar material interfaces based on spatial gradients is also discussed. The capabilities of the algorithm are demonstrated using four case studies. Through these case studies, the coupling between the optimal structural material design and the optimal joint design is investigated. Total joint cost is considered as both an objective and a constraint in the optimization problem statement. Using the biobjective problem statement, the tradeoff between total joint cost and structural compliance is explored. Finally, a method for enforcing tooling accessibility constraints in joint design is presented.
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3.
Featured Cover Jia, Zhiyuan; Luo, Yangjun; Takezawa, Akihiro ...
International journal for numerical methods in engineering,
09/2022, Volume:
123, Issue:
18
Journal Article
Peer reviewed
The cover image is based on the Research Article Topology optimization for realizing tailored self‐collimation in phononic crystals by Xiaopeng Zhang et al., https://doi.org/10.1002/nme.7004.
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In this paper, a level‐set‐based method is presented to deal with the multi‐material topology optimization of compliant mechanisms with stress constraints. A novel stress‐based multi‐material ...topology optimization model of compliant mechanisms is proposed. In this model, the multi‐material level set topology description model and the separable stress interpolation scheme are adopted. The weighted sum method is used to deal with the multi‐objective optimization of the output displacement and compliance of compliant mechanisms. The penalty of stresses is also considered in the objective function to control the local stress level in different materials. To solve the optimization problem, the parametric level set method is employed, and the sensitivity analysis is conducted. Application of the method is demonstrated by 2 numerical examples. Results show that the multi‐material structures without undesirable de facto hinges can be obtained. The output displacement and compliance of the compliant mechanisms are optimized, and stress constraints in different materials are simultaneously satisfied.
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This paper presents a systematic approach for topology optimization under uncertainty that integrates non-intrusive polynomial chaos expansion with design sensitivity analysis for reliability-based ...and robust topology optimization. Uncertainty is introduced in loading and in geometry to address the manufacturing variability. The manufacturing variability is modeled via a thresholding technique in which the threshold field is represented by a reduced dimensional random field. Response metrics such as compliance and volume are characterized as polynomial chaos expansions of the underlying uncertain parameters thus allowing accurate and efficient estimation of statistical moments, failure probabilities and their sensitivities. The number of simulations is reduced for linear structures under loading uncertainty by means of superposition. Efficiency of the non-intrusive polynomial chaos approach is highlighted by comparison with the Monte Carlo method in terms of the number of simulations. To demonstrate the effect of uncertainty, optimized designs that consider uncertainty are compared to those that do not. Comparisons of polynomial chaos expansion to existing analytical methods on a benchmark numerical example are also provided for reliability-based and worst case designs.
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Gaussian processes (GP) form a well-established predictive tool which provides a natural platform for tackling high-dimensional random input data in challenging simulations. This paper introduces a ...generic framework for integrating Gaussian Processes with risk-based structural optimization. We solve robust and reliability-based design problems in the context of stress-based topology optimization under imperfections in geometry and material properties, and loading variability. We construct independent GPs for primal and adjoint quantities, namely the global maximum von Mises stress and its sensitivity where we enhance the computational efficiency by leveraging the information from multiresolution finite element simulations. The GP framework naturally lends itself to modeling noise in data. We investigate the effect of numerical modeling error in high-fidelity simulations via a noisy GP emulator and provide a pareto curve that shows the robustness of optimal design with respect to the noise level. We provide a posteriori error estimates that quantify the discrepancy between the noisy emulator and true simulations, and verify them with a numerical study. We demonstrate our approach on a benchmark L-shape structure which exhibits stress concentration, a compliant mechanism design and a heat sink design. We also provide practical guidelines for estimation of failure probability and its sensitivity to facilitate reliability-based topology optimization.
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This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with ...imprecise probability is integrated into the multi-scale concurrent topology optimization (CTO) framework. To describe the imprecise probabilistic uncertainty efficiently, the type I hybrid interval random model is adopted. An improved hybrid perturbation analysis (IHPA) method is formulated to estimate the expectation and stand variance of the objective function in the worst case. Combined with the bi-directional evolutionary structural optimization (BESO) framework, the robust designs of the structure and its composite material are carried out. Several 2D and 3D numerical examples are presented to illustrate the effectiveness of the proposed method. The results show that the proposed method has high efficiency and low precision loss. In addition, the proposed RCTO approach remains efficient in both of linear static and dynamic structures, which shows its extensive adaptability.
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This article describes a method for the continuum-based topology optimization of structures made of discrete elements. In particular, we examine the optimization of linearly elastic planar structures ...made of bars of fixed width and semicircular ends. The design space for the optimization consists of the endpoint locations of the bar’s medial axes and their out-of-plane thicknesses. To circumvent re-meshing upon design changes, we project the design onto a fixed analysis grid using a differentiable geometry projection that results in a density field indicating the fraction of solid material anywhere in the design space, as in density-based topology optimization methods. The out-of-plane thickness is penalized so that the optimizer is capable of removing bars during the optimization. The differentiability of the projection allows for the computation via the chain rule of design sensitivities of responses of interest, and therefore it allows for the use of robust and efficient gradient-based optimization methods. Notably, this approach makes it easier to fabricate optimal designs by using off-the-shelf stock material. Furthermore, the method considers the case where bars overlap at their joints (i.e. their thicknesses are added at the joint) and when they do not. Finally, our proposed method naturally accommodates the imposition of several fixed length scales. We demonstrate the proposed approach on classical problems of compliance-based topology optimization and identify its benefits as well as research directions to be addressed in the future.
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This paper proposes a novel technique for large-scale
partial
topology optimization of dynamic engineering structures by utilizing substructuring techniques and repetitive geometry.
Partial
topology ...optimization refers to a design domain that only covers a part of the overall analysis domain, involving multiple subdomains. While large-scale topology optimization techniques for static systems have made significant progress over the past few decades, techniques for dynamic systems, especially those in the frequency domain, face challenges due to matrix conditioning and preconditioning problems for iterative solvers. To overcome these challenges, this paper dramatically reduces the system's size through a substructuring approach to utilize a direct linear solver. Using a bottom-up style substructuring technique, all the finite element (FE) models are defined separately and in parallel, and the FE models in the non-design domains are approximated using the idea of repetitive geometry with the same discretization, while the models in the design remain intact. This approach eliminates conventional model reduction-based topology optimization problems, such as eigen-analysis and recovery processes for every iteration. The proposed technique enables a more realistic and feasible design of large-scale engineering structures in the frequency domain. Several numerical examples verify the performance of the presented method for partial topology optimization of large-scale models. Overall, this paper provides a novel and efficient approach to partial topology optimization for dynamic engineering structures, opening up new possibilities for realistic and feasible design in the frequency domain.
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