Topology optimization for energy dissipation design of lattice structures through snap-through behavior

Deng, Hao; Cheng, Lin; Liang, Xuan; Hayduke, Devlin; To, Albert C.

doi:10.1016/j.cma.2019.112641

Cited by 54 publications

(18 citation statements)

References 56 publications

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“…An adjoint method and the chain rule are employed here to obtain the sensitivities with respect to the design variables. More details regarding sensitivity analysis of buckling‐induced design can be found in Reference .…”

Section: Buckling‐induced Topology Optimization Design Based On P‐gsmmentioning

confidence: 99%

“…Guo and Zhang et al proposed a homogenization framework with the use of asymptotic analysis to achieve the fast design of devices filled with quasiperiodic microstructure, where a mapping function is implemented to transform an infill graded microstructure to a spatially periodic configuration. Some other advanced multiscale design methods for simultaneous achieving macro‐ and microscale topology optimization or nonlinear metamaterial design can be found in References .…”

Section: Introductionmentioning

confidence: 99%

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Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

Deng

2020

Numerical Meth Engineering

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A new topology optimization scheme called the projection-based ground structure method (P-GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P-GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing-oriented design, the manufacturing abilities are the key factors to constrain the feasible design space, for example, minimum length and geometry complexity. Conventional density-based method, where each element works as a variable, always results in complex geometry with large number of small intricate features, while these small features are often not manufacturable even by 3D printing and lose its geometric accuracy after postprocessing. The proposed P-GSM is an effective method for controlling geometric complexity and minimum length for optimal design, while it is capable of designing self-supporting structures naturally. In optimization progress, some bars may be disconnected from each other (floating in the air). For buckling-induced design, this issue becomes critical due to severe mesh distortion in the void space caused by disconnection between members, while P-GSM has ability to overcome this issue. To demonstrate the effectiveness of proposed method, three different design problems ranging from compliance optimization to buckling-induced mechanism design are presented and discussed in details. K E Y W O R D Sbuckling-induced design, functionally graded lattice, projection-based ground structure method, self-support design, topology optimization

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Section: Buckling‐induced Topology Optimization Design Based On P‐gsmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

Deng

2020

Numerical Meth Engineering

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“…[16][17][18][19][20][21][22][23] Meanwhile, several other advanced TO methods are proposed in recent years. [24][25][26][27][28][29][30][31][32] In recent years, designing the flexible electronics, soft robots and wearable electronic devices draw great attention from academia and industry due to their extraordinary mechanical response. [33][34][35] Such devices and structures usually experience large deformations under external loading conditions, which is different from the traditional stiff structure design.…”

Section: Introductionmentioning

confidence: 99%

“…Kato et al 47 proposes a method of micro-macro concurrent TO for a two-phase nonlinear solid to minimize the end compliance of its microstructure undergoing large deformation. Some other related works can be found in References 28,30,48,49. For structures experiencing large deformation, local buckling phenomenon always happens, which makes the force-displacement response highly nonlinear. Compared with TO design under finite deformation, designing buckling-induced device is more challenging.…”

Section: Introductionmentioning

confidence: 99%

A density‐based boundary evolving method for buckling‐induced design under large deformation

Deng

2020

Numerical Meth Engineering

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This paper proposes a density-based boundary evolving algorithm for continuum-based topology optimization. The boundary of voids in the design domain is described by RBF (radial basis function) function controlled by RBF knots in polar coordinate, where the voids are projected onto a fixed grid using Heaviside function. For merging overlapped multiple voids, the p-norm function is introduced to describe composite density field. The differentiability of the projection-based boundary description algorithm allows for the sensitivity analysis via the chain rule, and therefore, it enables an efficient gradient-based optimization method. The goal of this paper is to optimize the initial design to generate buckling-induced mechanism under large deformation, and without loss of generality, the hyperelastic material model is chosen to describe the material behavior. Notably, this method possesses the merit of level set method, where the intermediate density only exists at the boundary of topology shape. At the same time, the proposed method is still in the density-based optimization framework and standard sensitivity analysis of density-based methods can be directly derived based on the chain rule. Several numerical examples are presented and discussed in detail to demonstrate the effectiveness of the proposed density-based boundary evolving method.

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“…This method has been developed to allow for complete design freedom by varying the local density of the structure, and therefore does not require a description and parametrization of the geometry beforehand. [23] While topology optimization was initially used to solve mechanical design problems such as maximizing structural stiffness using a limited amount of material, [24][25][26] it gradually expanded towards other research areas such as optics, [27][28][29][30] phononics, [31] material science, [32][33][34] and fluid mechanics. [35] Importantly, most of the algorithms use gradient information of the objective function and constraints to reach a local or global minimum.…”

mentioning

confidence: 99%

Inverse Design of Mechanical Metamaterials That Undergo Buckling

Oliveri

Overvelde

2020

Adv Funct Materials

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Metamaterials are man‐made materials which get their properties from their structure rather than their chemical composition. Their mesostructure is specifically designed to create functionalities not found in nature. However, despite the broad variety of metamaterials developed in recent years, a straightforward procedure to design these complex materials with tailored properties has not yet been established. Here, the inverse design problem is tackled by introducing a general optimization tool to explore the range of material properties that can be achieved. Specifically, a stochastic optimization algorithm is applied and its applicability to disjoint problems is demonstrated, with a focus on tuning the buckling properties of mechanical metamaterials, including experimental verification of the predictions. Besides this problem, this algorithm can be applied to a large variety of systems that, because of their complexity, would be challenging otherwise. Potential applications range from the design of optomechanical resonators, acoustic band gap materials, to dielectric metasurfaces.

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Topology optimization for energy dissipation design of lattice structures through snap-through behavior

Cited by 54 publications

References 56 publications

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

A density‐based boundary evolving method for buckling‐induced design under large deformation

Inverse Design of Mechanical Metamaterials That Undergo Buckling

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