Note on spatial gradient operators and gradient-based minimum length constraints in SIMP topology optimization

Yang, Kaike; Fernández, Eva; Niu, Cao; Duysinx, Pierre; Zhu, Jihong; Zhang, Weihong

doi:10.1007/s00158-019-02269-9

Cited by 23 publications

(6 citation statements)

References 14 publications

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Section: Topology Optimization Model For Prescribed Two-way Shape-mor...mentioning

confidence: 99%

“…The allowed material volume fraction V fra of the design domain was set below V 0 . The geometric minimum length scale constraints g s and g v [34,42] for both the solid and void material were introduced into the topology optimization model to obtain "black and white" designs. δ s and δ v represent the upperbound values.…”

Section: Topology Optimization Model For Prescribed Two-way Shape-mor...mentioning

confidence: 99%

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Topology Optimization of Shape Memory Alloy Actuators for Prescribed Two-Way Transforming Shapes

Yang,

Luo,

Yuan

et al. 2024

Actuators

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This paper proposes a new topology optimization formulation for obtaining shape memory alloy actuators which are designed with prescribed two-way transforming shapes. The actuation behaviors of shape memory alloy structures are governed by austenite-martensite phase transformations effected by thermal-mechanical loading processes; therefore, to realize the precise geometric shape variations of shape memory alloy actuators, traditional methods involve iteration processes including heuristic structural design, numerical predictions and experimental validation. Although advanced structural optimization methods such as topology optimization have been used to design three-dimensional (3D) shape memory alloy actuators, the maximization/minimization of quantities such as structural compliance or inaccurate stroke distances has usually been selected as the optimization objective to obtain feasible solutions. To bridge the gap between precise shape-morphing requirements and efficient shape memory alloy actuator designs, this paper formulates optimization criteria with quantitatively desired geometric shapes, and investigates the automatic designs of two-way prescribed shape morphing shape memory alloy structures based on the proposed topology optimization method. The super element method and adjoint method are used to derive the analytical sensitivities of the objective functions with respect to the design variables. Numerical examples demonstrate that the proposed method can obtain 3D actuator designs that have the desired two-way transforming shapes.

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Section: Topology Optimization Model For Prescribed Two-way Shape-mor...mentioning

confidence: 99%

Section: Topology Optimization Model For Prescribed Two-way Shape-mor...mentioning

confidence: 99%

Topology Optimization of Shape Memory Alloy Actuators for Prescribed Two-Way Transforming Shapes

Yang,

Luo,

Yuan

et al. 2024

Actuators

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“…We use the structural gradient approach to provide limitation on the overhang angle, wherein edge of the structure is detected to limit its slope [16]. In this work, the Prewitt operator, a discrete differentiation operator, is used to compute the approximate gradient of the image intensity function [31]. It uses a 3×3 elements mask to approximate the gradient of element , as shown in Fig.…”

Section: Gradient-based Overhang Constraintmentioning

confidence: 99%

Topology optimization for additive manufacturing with length scale, overhang, and building orientation constraints

Kumar¹,

Fernández²

2022

Preprint

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This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging parts without the use of sacrificial supporting structures, and the printing directions. These constraints are geometrically addressed and implemented. The minimum size on solid and void zones is imposed through a well-known filtering technique. The sacrificial support material is reduced using a constraint that limits the maximum overhang angle of parts by comparing the structural gradient with a critical reference slope. Due to the local nature of the gradient, the chosen restriction is prone to introduce parts that meet the structural slope but that may not be self-supporting. The restriction limits the maximum overhang angle for a user-defined printing direction, which could reduce structural performance if the orientation is not properly selected. To ease these challenges, a new approach to reduce the introduction of such non-self-supporting parts and a novel method that includes different printing directions in the maximum overhang angle constraint are presented. The proposed strategy for considering the minimum size of solid and void phases, maximum overhang angle, and printing direction, is illustrated by solving a set of 2D benchmark design problems including stiff structures and compliant mechanisms. We also provide MATLAB codes in the appendix for educational purposes and for replication of the results.

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“…Additionally, three-field SIMP methods utilizing nonlinear projection techniques tend to yield 0-1 designs, and the minimum size may not be strictly satisfied [42,43]. Based on the threefield SIMP method, a robust formulation considering corrosion and expansion operations as well as a geometric constraint method without additional finite element analysis were proposed [44,45]. Meanwhile, the minimum length scale control of the topology design can be imposed using a structural skeleton [46] and an image morphology operator [47].…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Liu¹,

Wang²,

Liu³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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Continuum topology optimization considering the vibration response is of great value in the engineering structure design. The aim of this study is to address the topological design optimization of harmonic excitation structures with minimum length scale control to facilitate structural manufacturing. A structural topology design based on discrete variables is proposed to avoid localized vibration modes, gray regions and fuzzy boundaries in harmonic excitation topology optimization. The topological design model and sensitivity formulation are derived. The requirement of minimum size control is transformed into a geometric constraint using the discrete variables. Consequently, thin bars, small holes, and sharp corners, which are not conducive to the manufacturing process, can be eliminated from the design results. The present optimization design can efficiently achieve a 0-1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies. Additionally, the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric, which is a distinct difference from the static optimization design. Hence, one-half of the design domain cannot be selected according to the load and support symmetry. Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization, and to improve the design manufacturability.

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Note on spatial gradient operators and gradient-based minimum length constraints in SIMP topology optimization

Cited by 23 publications

References 14 publications

Topology Optimization of Shape Memory Alloy Actuators for Prescribed Two-Way Transforming Shapes

Topology Optimization of Shape Memory Alloy Actuators for Prescribed Two-Way Transforming Shapes

Topology optimization for additive manufacturing with length scale, overhang, and building orientation constraints

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

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