考虑宏观结构性能的多材料微结构拓扑优化设计

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (11) : 185-193.

论文

张磊1,2，倪绍豪1,2，蒋国璋1,2,3，张严1,2,3，宫逸文1,2

作者信息 +

Multi-material microstructure topology optimization design considering macroscopic structural performance

ZHANG Lei1,2, NI Shaohao1,2, JIANG Guozhang1,2,3, ZHANG Yan1,2,3, GONG Yiwen1,2

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文章历史 +

摘要

多孔微结构材料以其质量轻、比刚度/比强度高、抗冲击等优异力学性能，被广泛应用于航空航天等工程领域。相比单一材料设计，多材料设计可获得力学性能更优的微结构拓扑构型。拓扑优化是实现多材料布局设计的有效方法之一。本文通过构建基于差集的多材料水平集描述模型和交替活动相算法，提出了基于参数化水平集的的多材料微结构拓扑优化设计方法。首先，构建了基于差集的多材料水平集描述模型，利用N个水平集函数实现N+1相材料拓扑的精确描述。然后，引入交替活动相算法，将原始N+1相多材料优化问题分解为N(N+1)/2个双相材料优化子问题，以减少设计变量与约束条件，提高计算效率。最后，采用均匀化方法计算多材料微结构的等效弹性张量，以宏观结构柔度最小化为优化目标，各相材料用量为约束条件，构建多材料微结构拓扑优化模型，并利用优化准则法实现上述优化模型的高效求解。数值算例结果表明，所提方法可有效实现多材料微结构的拓扑优化设计，所设计微结构均具有光滑的结构边界和清晰的材料界面。

Abstract

Porous microstructure materials are widely used in aerospace and other engineering fields due to their excellent mechanical properties, such as lightweight, high specific stiffness/strength, and impact resistance. Compared with conventional design with one single material, topological design with multiple materials can provide a microstructure with better mechanical properties. And topology optimization is one of the effective design methods for multi-material layouts. This paper proposes a parametric level set-based multi-material microstructural topology optimization method by combining a difference-set-based multi-material level set description model and an alternating active phase algorithm. In this method, firstly, a difference-set-based multi-material level set description model is constructed to accurately describe the topologies of N+1 phase materials only by using N level set functions. Then, an alternating active phase algorithm is employed to split the original N+1 phase multi-material optimization problem into N(N+1)/2 binary-phase sub-problems, so as to reduce design variables and constraint conditions for improving computational efficiency. Finally, a numerical homogenization method is used to calculate the effective elastic tensor of a multi-material microstructure. With the minimum macrostructural compliance as objective function, and the allowable material amount of each phase as constraint condition, a topology optimization model for the multi-material microstructure is constructed. The optimization criteria algorithm is used to numerally solve the above optimization model. The numerical results show that the proposed method can effectively achieve the topological design of multi-material microstructures, and the resulting microstructures have also smooth structural boundaries and distinct material interfaces.

导出引用

张磊1,2，倪绍豪1,2，蒋国璋1,2,3，张严1,2,3，宫逸文1,2. 考虑宏观结构性能的多材料微结构拓扑优化设计[J]. 振动与冲击, 2024, 43(11): 185-193

ZHANG Lei1,2, NI Shaohao1,2, JIANG Guozhang1,2,3, ZHANG Yan1,2,3, GONG Yiwen1,2. Multi-material microstructure topology optimization design considering macroscopic structural performance[J]. Journal of Vibration and Shock, 2024, 43(11): 185-193

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