基于修正偶应力理论的应力最小化双向渐进结构拓扑优化方法

张漫哲; 顾水涛; 冯志强

doi:10.21656/1000-0887.450038

基于修正偶应力理论的应力最小化双向渐进结构拓扑优化方法

doi: 10.21656/1000-0887.450038

1. 重庆大学土木工程学院，重庆 400040;
2. 西南交通大学力学与航空航天学院，成都 610031

详细信息

作者简介:
张漫哲（1999—），男，硕士生（E-mail: 2238428037@qq.com）;顾水涛（1979—），男，教授（E-mail: gust@cqu.edu.cn）;冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.

通讯作者:
冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.

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- 文章访问数: 13
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出版历程
- 收稿日期: 2024-02-22
- 修回日期: 2024-03-17

Bidirectional Evolutionary Topology Optimization for Stress Minimization Based on the Modified Couple Stress Elasticity

1. School of Civil Engineering， Chongqing University， Chongqing 400040， P.R.China;
2. School of Mechanics and Engineering， Southwest Jiaotong University，Chengdu 610031， P.R.China

摘要

摘要: 研究并探讨了基于应力的双向渐进结构拓扑优化（BESO）法在修正偶应力弹性理论中的应用.该方法允许对尺寸问题相关的微观结构均质连续体进行拓扑优化.其通过引入一种与尺寸相关的，基于修正偶应力理论的，非经典等效应力的新颖公式，对经典的BESO技术进行了扩展，并在体积约束的条件下进行应力最小化设计.设计变量的迭代更新依赖于灵敏度分析，其涉及对目标函数p范数全局应力的直接求导.理论中涉及高阶弹性，因此为了满足有限元实现时需要的C¹节点连续性，在插值中将传统的Lagrange插值与一个含待定系数的插值函数相结合.通过三个不同的数值算例，分析了尺寸效应对应力优化设计过程及结果的影响.同时探讨了其他参数包括范数p值和材料体积分数的作用.获得的研究结果证明了所提出的基于应力的BESO方法在涉及尺寸效应相关的拓扑优化设计方向的潜力.
- 拓扑优化 /
- BESO /
- 基于应力 /
- 修正偶应力 /
- 尺寸效应
Abstract: The application of stress-based bidirectional evolutionary structural optimization (BESO) in the context of the modified couple stress elasticity theory was investigated. This methodology allows for structure optimization of homogenized continuum with a microstructural composition of size effects. The classical BESO technique was extended through the introduction of a novel formulation of couple stress based non-classical equivalent stress, and the minimization design was conducted under the constraint of volume criterion. The iterative update of design variables relies on the sensitivity analysis involving direct derivation of the enriched p-norm global stress with couple stress contributions. Since the high-order elasticity is involved, the FEM implementation requires at least the C¹ nodal continuity. Thus, a Lagrangian finite element complemented by additional integration functions was implemented. The method was validated with 3 distinct cases through investigation of the size effects on the stress optimization and the subsequent structure design. The impacts of other parameters including the norm p value and the material volume fraction, were explored. The results demonstrate the potential of the proposed stress-based BESO method in addressing structural optimization of problems involving size effects.
- topology optimization /
- BESO /
- stress-based /
- modified couple stress /
- size effect

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基于修正偶应力理论的应力最小化双向渐进结构拓扑优化方法

doi: 10.21656/1000-0887.450038

作者简介:
张漫哲（1999—），男，硕士生（E-mail: 2238428037@qq.com）;顾水涛（1979—），男，教授（E-mail: gust@cqu.edu.cn）;冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.

通讯作者:
冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.

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Bidirectional Evolutionary Topology Optimization for Stress Minimization Based on the Modified Couple Stress Elasticity

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基于修正偶应力理论的应力最小化双向渐进结构拓扑优化方法

doi: 10.21656/1000-0887.450038

作者简介: 张漫哲（1999—），男，硕士生（E-mail: 2238428037@qq.com）;顾水涛（1979—），男，教授（E-mail: gust@cqu.edu.cn）;冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.

通讯作者: 冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.

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Bidirectional Evolutionary Topology Optimization for Stress Minimization Based on the Modified Couple Stress Elasticity

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出版历程

目录

作者简介:
张漫哲（1999—），男，硕士生（E-mail: 2238428037@qq.com）;顾水涛（1979—），男，教授（E-mail: gust@cqu.edu.cn）;冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.

通讯作者:
冯志强（1963—），男，教授，博士生导师（通讯作者. E-mail: zhiqiang.feng@univ-evry.fr）.