Micro‐macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis

Kato, Junji; Yachi, Daishun; Kyoya, Takashi; Terada, Kenjiro

doi:10.1002/nme.5571

Cited by 41 publications

(14 citation statements)

References 40 publications

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“…where V(x) is the structural volume considering the material densities in each ele-ment as optimization variables that belong to the interval [0, 1]. С 0 and C(x) are the initial -and current structural compliance values [19][20][21][22][23]. Formulations 1 and 2 are fundamental forms and can be implemented with some topology optimization approaches such as SIMP (Solid Isotropic Microstructure with Penalty), homogenization approach and many recent methods have been recently developed to extend the topology optimization to some advanced area such as additive manufacturing [24][25][26].…”

Section: Deterministic Topology Optimizationmentioning

confidence: 99%

Reliability-Based Topology Optimization Using Two Alternative Inverse Optimum Safety Factor Approaches: Application to Bridge Structures

Kharmanda

Antypas

Dyachenkо

2020

Engineering Technologies and Systems

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Introduction. The Deterministic Topology Optimization model provides a single solution for a given design space, while the Reliability-Based Topology Optimization model provides several reliability-based topology layouts with high-performance levels. The objective of this work is to develop two strategies that can provide the designer with two categories of resulting topologies. Materials and Methods. Two alternative approaches based on the Inverse Optimum Safety Factor are developed: the first one is called the Objective-Based IOSF Approach and the second one is called Performance-Based IOSF Approach. When dealing with bridge structures, the uncertainty on the input parameters (boundary conditions, material properties, geometry, etc.) and also output parameters (compliance, etc.) should not be ignored. The sensitivity analysis is the fundamental idea of both developed approaches, identifies the role of each parameter on the structural performance. In addition, the optimization domain choice is important when eliminating material that should not affect the structure functioning. Results. Two numerical examples on a 2D bridge structure are presented to demonstrate the efficiency of the developed approaches. When considering a certain reliability level, the Reliability-Based Topology Optimization leads to two different configurations relative to the Deterministic Topology Optimization one. When increasing the reliability levels, the quantity of materials decreases that leads to an increase in the number of holes in the structures. Discussion and Conclusion. In addition to their simplified implementation, the developed alternative approaches can be considered as two generative tools to produce two different categories (families) of solutions where an alternative choice between two functions (objective/performance) is presented.

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Section: Deterministic Topology Optimizationmentioning

confidence: 99%

Reliability-Based Topology Optimization Using Two Alternative Inverse Optimum Safety Factor Approaches: Application to Bridge Structures

Kharmanda

Antypas

Dyachenkо

2020

Engineering Technologies and Systems

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“…where the term = / is the usual tangent structural stiffness matrix calculated by 22) in which the tangent moduli / is obtained from material subroutine.…”

Section: Finite Element Formulationmentioning

confidence: 99%

Computational design of finite strain auxetic metamaterials via topology optimization and nonlinear homogenization

Zhang

Khandelwal

2019

Computer Methods in Applied Mechanics and Engineering

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A novel computational framework for designing metamaterials with negative Poisson's ratio over a large strain range is presented in this work by combining the density-based topology optimization together with a mixed stress/deformation driven nonlinear homogenization method. A measure of Poisson's ratio based on the macro deformations is proposed, which is further validated through direct numerical simulations. With the consistent optimization formulations based on nonlinear homogenization, auxetic metamaterial designs with respect to different loading orientations and with different unit cell domains are systematically explored. In addition, the extension to multimaterial auxetic metamaterial designs is also considered, and stable optimization formulations are presented to obtain discrete metamaterial topologies under finite strains. Various new auxetic designs are obtained based on the proposed framework. To validate the performance of optimized designs, a multiscale stability analysis is carried out using the Bloch wave method and rank-one convexity check. As demonstrated, short and/or long wavelength instabilities can occur during the loading process, leading to a change of periodicity of the microstructure, which can affect the performance of an optimized design.

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“…Several authors have also incorporated damage materials models into the topology design of continuum structures 37,41‐43,45 . More recently, advances in high‐performance computing have set the stage for the computationally intensive design of nonlinear structures based on multiscale topology optimization 50‐55 …”

Section: Introductionmentioning

confidence: 99%

Multiscale design of nonlinear materials using a Eulerian shape optimization scheme

Najafi

Safdari

Tortorelli

et al. 2021

Numerical Meth Engineering

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Motivated by recent advances in manufacturing, the design of materials is the focal point of interest in the material research community. One of the critical challenges in this field is finding optimal material microstructure for a desired macroscopic response. This work presents a computational method for the mesoscale‐level design of particulate composites for an optimal macroscale‐level response. The method relies on a custom shape optimization scheme to find the extrema of a nonlinear cost function subject to a set of constraints. Three key “modules” constitute the method: multiscale modeling, sensitivity analysis, and optimization. Multiscale modeling relies on a classical homogenization method and a nonlinear NURBS‐based generalized finite element scheme to efficiently and accurately compute the structural response of particulate composites using a nonconformal discretization. A three‐parameter isotropic damage law is used to model microstructure‐level failure. An analytical sensitivity method is developed to compute the derivatives of the cost/constraint functions with respect to the design variables that control the microstructure's geometry. The derivation uncovers subtle but essential new terms contributing to the sensitivity of finite element shape functions and their spatial derivatives. Several structural problems are solved to demonstrate the applicability, performance, and accuracy of the method for the design of particulate composites with a desired macroscopic nonlinear stress‐strain response.

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Micro‐macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis

Cited by 41 publications

References 40 publications

Reliability-Based Topology Optimization Using Two Alternative Inverse Optimum Safety Factor Approaches: Application to Bridge Structures

Reliability-Based Topology Optimization Using Two Alternative Inverse Optimum Safety Factor Approaches: Application to Bridge Structures

Computational design of finite strain auxetic metamaterials via topology optimization and nonlinear homogenization

Multiscale design of nonlinear materials using a Eulerian shape optimization scheme

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