随特征边界条件变化的二维设计域各向同性弹性材料拓扑优化

Q3 Engineering
Ngoc-Tien Tran
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引用次数: 0

摘要

拓扑优化(TO)作为设计人员和工程师在初始设计阶段的一种有用工具,已经越来越受欢迎。TO旨在优化设计的几何形状,以实现特定的目标,其范围可以从离散的网格状结构到连续体结构。本质上,几何是逐像素参数化的,每个元素或网格点的材料密度作为设计变量。然后,利用数学规划和基于解析梯度计算的优化方法来解决优化问题。在本文中,我们研究了在边界条件包括固定结构、支撑或外力变化的情况下,对各向同性材料进行拓扑优化时的材料分布。此外,我们研究了更多在设计域中存在材料孔的情况,这意味着材料的密度为零。在本研究中,采用改进的SIMP方法和滤波器灵敏度进行拓扑优化。研究的结果是优化的结构域和柔度随迭代次数的变化。结果表明,优化到第20次迭代时,大多数结构的柔度值趋于收敛。此外,如果施加在设计域上的力是对称的,则最优结构也表现出对称性。因此,材料的分布集中在支撑的位置。拓扑优化产生的设计既满足边界条件,同时节省材料和减少其质量。所得结果为各向同性弹性体材料结构优化设计提供了重要数据。在此基础上,它可以应用于具有不同要求和条件的真实物体
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Topology optimization of isotropic elastic materials in the two-dimensional design domain with changes in characteristic boundary conditions
Topology optimization (TO) has become increasingly popular as a useful tool for designers and engineers during the initial stages of design. TO aims to optimize the geometry of a design to achieve a specific objective, which can range from discrete grid-like structures to continuum structures. In essence, the geometry is parameterized pixel-by-pixel, with the material density of each element or mesh point serving as a design variable. After that, the optimization problem is addressed using mathematical programming and analytic gradient calculation-based optimization approaches. In this paper, we investigate the material distribution when performing topology optimization for an isotropic material with boundary conditions including fixed structures, supports, or external forces changing. In addition, we investigate more cases where there are material holes in the design domain, meaning that the density of the material is zero. In this study, the modified SIMP method and filter sensitivity are used for topology optimization. The results of the study are the optimized structural domains and the change in compliance according to the number of iterations. The results indicate that the compliance value of most structures reaches convergence after optimization up to the 20th iteration. Moreover, if the force applied to the design domain is symmetrical, the optimal structure also exhibits symmetry. Thus, the distribution of material is concentrated at the positions of the supports. Topology optimization produces designs that both meet boundary conditions while saving material and reducing their mass. The results obtained are important data for structural optimization design for isotropic elastomeric materials. From there, it can be applied to real objects with different requirements and conditions
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来源期刊
EUREKA: Physics and Engineering
EUREKA: Physics and Engineering Engineering-Engineering (all)
CiteScore
1.90
自引率
0.00%
发文量
78
审稿时长
12 weeks
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