Topology optimization of heat transfer and elastic problems based on element differential method

Zhang, Siqi; Xu, Bing‐Bing; Gao, Zhonghao; Jiang, Geng-Hui; Zheng, Yong-Tong; Liu, Huayu; Jiang, Wen-Wei; Yang, Kai; Gao, Xiao‐Wei

doi:10.1016/j.enganabound.2023.01.026

Cited by 4 publications

(2 citation statements)

References 29 publications

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“…Figure 6 shows the evolution process of material distribution in the cantilever beam optimization process of case 1. The final optimization results can be obtained after 36 iterations, significantly fewer than the SIMP method (Zhang et al, 2023; Zhu et al, 2021), and has high computational efficiency. The BESO method has only two design variables, x min and one prevents generating gray elements during iteration.…”

Section: Numerical Examplesmentioning

confidence: 99%

Topology optimization structure design of shape memory alloy with multiple constraints

Dong,

Jiang,

et al. 2024

Journal of Intelligent Material Systems and Structures

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As an emerging functional material, shape memory alloy (SMA) exhibits remarkable mechanical properties and finds diverse applications across industries. This paper presents a topology optimization framework based on the bi-directional evolutionary structural optimization (BESO) method for designing SMA structures, which maximizes structural stiffness under multiple constraints of specified volume fraction, displacement, and fundamental frequency. A phenomenological constitutive model is utilized to simulate the mechanical behavior of SMA accurately. The unit virtual load method is employed to determine sensitivities. Several optimized SMA beam structures and simply-supported cube structures are designed under different thermal-mechanical loads, and their displacement, mean compliance, and fundamental frequency are evaluated throughout the optimization process. The results demonstrate that the proposed framework successfully customizes the SMA topology structure with adjustable displacement and fundamental frequency, and the optimized schemes exhibit more considerable deformation and more uniform mechanical properties than their initial counterparts. The proposed framework has higher computational efficiency than the traditional SIMP-based SMA topology optimization design method.

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Section: Numerical Examplesmentioning

confidence: 99%

Topology optimization structure design of shape memory alloy with multiple constraints

Dong,

Jiang,

et al. 2024

Journal of Intelligent Material Systems and Structures

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“…Afterwards, the FBM was successfully applied to heat conduction problems [41], contact problems [42], non-linear elasticity [43], and fracture mechanics [44]. Also, many novel numerical methods have been proposed based on the idea of the FBM, such as the finite-and infinite-block Petrov-Galerkin method [45] and the element differential method [46][47][48]. The associated studies all demonstrated the superiority of the FBM.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form

Fu,

Yang,

Zhou

et al. 2023

Materials

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In this paper, the application of the strong-form finite block method (FBM) to three-dimensional fracture analysis with functionally graded materials is presented. The main idea of the strong-form FBM is that it transforms the arbitrary physical domain into a normalized domain and utilizes the direct collocation method to form a linear system. Using the mapping technique, partial differential matrices of any order can be constructed directly. Frameworks of the strong-form FBM for three-dimensional problems based on Lagrange polynomial interpolation and Chebyshev polynomial interpolation were developed. As the dominant parameters in linear elastic fracture mechanics, the stress intensity factors with functionally graded materials (FGMs) were determined according to the crack opening displacement criteria. Several numerical examples are presented using a few blocks to demonstrate the accuracy and efficiency of the strong-form FBM.

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Analysis of dynamic coupled thermoelasticity problems based on element differential method

Tan,

Xu,

Zheng

et al. 2024

International Journal of Heat and Mass Transfer

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Topology optimization of heat transfer and elastic problems based on element differential method

Cited by 4 publications

References 29 publications

Topology optimization structure design of shape memory alloy with multiple constraints

Topology optimization structure design of shape memory alloy with multiple constraints

Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form

Analysis of dynamic coupled thermoelasticity problems based on element differential method

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