Stress-based topology optimization using maximum entropy basis functions-based meshless method

IF 8.7 2区 工程技术 Q1 Mathematics
Imran Khan, Zahur Ullah, Baseer Ullah, Siraj-ul-Islam, Wajid Khan
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引用次数: 0

Abstract

This paper presents volume-constrained stress minimization-based, topology optimization. The maximum entropy (maxent) basis functions-based meshless method for two-dimensional linear elastic structures is explored. This work focuses to test the effectiveness of the meshless method in handling the stress singularities during the topology optimization process. The commonly used moving least square basis functions are replaced with maximum entropy basis functions, as the latter possess weak Kronecker delta property which leads to the finite element method (FEM) like displacement boundary conditions imposition. The maxent basis functions are calculated once at the beginning of the simulation and then used in optimization at every iteration. Young’s modulus for each background cell is interpolated using the modified solid isotropic material with penalization approach. An open source pre-processor CUBIT is used. A comparison of the proposed approach with the FEM is carried out using a diverse set of problems with simple and complex geometries of structured and unstructured discretization, to establish that maxent-based meshless methods perform better in tackling the stress singularities due to its smooth stress field.

Abstract Image

使用基于最大熵基函数的无网格法进行基于应力的拓扑优化
本文提出了基于体积约束应力最小化的拓扑优化方法。探讨了基于最大熵(maxent)基函数的二维线性弹性结构无网格方法。这项工作的重点是测试无网格法在拓扑优化过程中处理应力奇异性的有效性。常用的移动最小平方基函数被最大熵基函数取代,因为后者具有弱 Kronecker delta 特性,可导致类似有限元法(FEM)的位移边界条件施加。最大熵基函数在模拟开始时计算一次,然后在每次迭代时用于优化。每个背景单元的杨氏模量使用修正的各向同性固体材料和惩罚方法进行插值。使用的是开源预处理器 CUBIT。通过对结构化和非结构化离散的简单和复杂几何形状的各种问题进行比较,确定了基于 maxent 的无网格方法因其应力场平滑而在处理应力奇异性方面表现更佳。
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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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