Stress constrained multi-material topology optimization with the ordered SIMP method

Xu, Shuzhi; Liu, Ji‐Kai; Zou, Bin; Li, Quhao; Ma, Yongsheng

doi:10.1016/j.cma.2020.113453

Cited by 76 publications

(14 citation statements)

References 47 publications

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“…They resolve the geometric connectivity and manufacturability issues and possess unique combinations of physical properties (e.g., high strength-to-weight ratio, high energy absorption, and high thermal conductivity) [43,44,45]. In addition, variable-density cellular structures make the density map manufacturable with a single material to avoid using costly multi-material techniques [46,47,48,49]. First-generation variable-density cellular structures were designed using simple repeating elements such as cubic trusses with variable strut thickness [50] or hexagonal cells with variable hole diameter [51,52].…”

Section: Variable-density Cellular Structures and Inverse Homogenizat...mentioning

confidence: 99%

IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

Wang,

Chen,

et al. 2021

Preprint

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Variable-density cellular structures can overcome connectivity and manufacturability issues of topologicallyoptimized, functionally graded structures, particularly when those structures are represented as discrete density maps. One naïve approach to creating variable-density cellular structures is simply replacing the discrete density map with an unselective type of unit cells having corresponding densities. However, doing so breaks the desired mechanical behavior, as equivalent density alone does not guarantee equivalent mechanical properties. Another approach uses homogenization methods to estimate each pre-defined unit cell's effective properties and remaps the unit cells following a scaling law. However, a scaling law merely mitigates the problem by performing an indirect and inaccurate mapping from the material property space to singletype unit cells. In contrast, we propose a deep generative model that resolves this problem by automatically learning an accurate mapping and generating diverse cellular unit cells conditioned on desired properties (i.e., Young's modulus and Poisson's ratio). We demonstrate our method via the use of implicit function-based unit cells and conditional generative adversarial networks. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (relative error < 5%), 2) create functionally graded cellular structures with high-quality interface connectivity (98.7% average overlap area at interfaces), and 3) improve the structural performance over the conventional topology-optimized variabledensity structure (84.4% reduction in concentrated stress and extra 7% reduction in displacement).

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Section: Variable-density Cellular Structures and Inverse Homogenizat...mentioning

confidence: 99%

IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

Wang,

Chen,

et al. 2021

Preprint

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show abstract

“…On the other hand, there are still some open issues evolving around TO. These issues are mainly concerned with the aesthetic problem [42]; additive manufacturing problems related to large overhanging members [43][44][45][46], the remodeling of the optimized structure due to poor shape geometry [47]; stress-related problems [48][49][50]; the application of manufacturing constraints [14]; the optimization of multi-scale and multi-material structures [16][17][18][19][20], etc.…”

Section: Introductionmentioning

confidence: 99%

Guidelines for Topology Optimization as Concept Design Tool and Their Application for the Mechanical Design of the Inner Frame to Support an Ancient Bronze Statue

2021

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For the past few decades, topology optimization (TO) has been used as a structural design optimization tool. With the passage of time, this kind of usage of TO has been extended to many application fields and branches, thanks to a better understanding of how manufacturing constraints can achieve a practical design solution. In addition, the advent of additive manufacturing and its subsequent advancements have further increased the applications of TO, raising the chance of competitive manufacturing. Design for additive manufacturing has also promoted the adoption of TO as a concept design tool of structural components. Nevertheless, the most frequent applications are related to lightweight design with or without design for assembly. A general approach to integrate TO in concept designs is still missing. This paper aims to close this gap by proposing guidelines to translate design requirements into TO inputs and to include topology and structural concerns at the early stage of design activity. Guidelines have been applied for the concept design of an inner supporting frame of an ancient bronze statue, with several constraints related to different general design requirements, i.e., lightweight design, minimum displacement, and protection of the statue’s structural weak zones to preserve its structural integrity. Starting from the critical analysis of the list of requirements, a set of concepts is defined through the application of TO with different set-ups (loads, boundary conditions, design and non-design space) and ranked by the main requirements. Finally, a validation of the proposed approach is discussed comparing the achieved results with the ones carried out through a standard iterative concept design.

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“…24 Then, many multi-material topology optimization methods with the SIMP method are developed, such as the discrete material optimization method, 25 the recursive material interpolation 26 and the ordered SIMP interpolation. 27 The methods based on the implicit function-based methods include color level set 28 and phase field methods using the Allen-Cahn system, 29 or Cahn-Hilliard model. 30 Yin et al 31 developed a method for the topology optimization of multiple materials compliant mechanisms using a peak function material interpolation scheme.…”

Section: Introductionmentioning

confidence: 99%

Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

Zhan

Sun

Liu

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Multi-material compliant mechanisms design enables potential design possibilities by exploiting the advantages of different materials. To satisfy mechanical/thermal impedance matching requirements, a method for multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition is presented in this study. In the optimization model, the element stacking method is employed to describe the material distribution and handle material-dependent boundary condition. The maximization of the output displacement of the compliant mechanism is developed as the objective function and the structural volume of each material is the constraint. Fictitious domain approach is applied to circumvent the numerical instabilities in topology optimization problem with geometrical nonlinearities. The method of moving asymptotes is applied to solve the optimization problem. Several numerical examples are presented to demonstrate the validity of the proposed method. The optimal topologies of the compliant mechanisms obtained by the proposed method can satisfy the specified material-dependent boundary condition.

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Stress constrained multi-material topology optimization with the ordered SIMP method

Cited by 76 publications

References 47 publications

IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

Guidelines for Topology Optimization as Concept Design Tool and Their Application for the Mechanical Design of the Inner Frame to Support an Ancient Bronze Statue

Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

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