Evolutionary topology optimization of continuum structures with stress constraints

• Published in: Structural and multidisciplinary optimization Vol. 59; no. 2; pp. 647 - 658
• Main Authors: Fan, Zhao, Xia, Liang, Lai, Wuxing, Xia, Qi, Shi, Tielin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2019; Springer Nature B.V
• Subjects: Compliance; Composite materials; Computational Mathematics and Numerical Analysis; Constraints; Engineering; Engineering Design; Lagrange multiplier; Methods; Optimization; Research Paper; Stress concentration; Theoretical and Applied Mechanics; Topology optimization; BESO; Topology optimization; Stress constraint; Multiple constraints
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-018-2090-4

In this work, we propose to extend the bi-directional evolutionary structural optimization (BESO) method for compliance minimization design subject to both constraints on volume fraction and maximum von Mises stress. To this end, the aggregated p -norm global stress measure is first adopted to approximate the maximum stress. The conventional compliance design objective is augmented with p -norm stress measures by introducing one or multiple Lagrange multipliers. The Lagrange multipliers are employed to yield compromised designs of the compliance and the p -norm stress. An empirical scheme is developed for the determination of the Lagrange multipliers such that the maximum von Mises stress could be effectively constrained through the controlling of the aggregated p -norm stress. To further enforce the satisfaction of stress constraints, the stress norm parameter p is assigned to a higher value after attaining the objective volume. The update of the binary design variables lies in the computationally efficient sensitivity numbers derived using the adjoint method. A series of comparison studies has been conducted to validate the effectiveness of the method on several benchmark design problems.