Bi-directional evolutionary topology optimization of geometrically nonlinear continuum structures with stress constraints

• Published in: Applied Mathematical Modelling Vol. 80; pp. 771 - 791
• Main Authors: Xu, Bin, Han, Yongsheng, Zhao, Lei
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.04.2020; Elsevier BV
• Subjects: Adjoint method; Approximation; BESO method; Density; Geometrically nonlinearity; Heuristic methods; Lagrange multiplier; Optimization; Sensitivity; Sensitivity analysis; Stiffness; Stress constraints; Topology optimization; Topology optimization; BESO method; Adjoint method; Stress constraints; Sensitivity analysis; Geometrically nonlinearity
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.12.009

•The stress-constrained topology optimization model of geometrically nonlinear structure is first proposed.•The adopted p-norm global stress measure can well restrain the stress level and solve the stress concentration problem.•The compliance increases and the stress distribution becomes smoother with the strict stress constraint.•The maximal stress and compliance of geometry nonlinear stiffness design are smaller than those for linear design. This paper proposes a design method to maximize the stiffness of geometrically nonlinear continuum structures subject to volume fraction and maximum von Mises stress constraints. An extended bi-directional evolutionary structural optimization (BESO) method is adopted in this paper. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low density elements. The maximum von Mises stress is approximated by the p-norm global stress. By introducing one Lagrange multiplier, the objective of the traditional stiffness design is augmented with p-norm stress. The stiffness and p-norm stress are considered simultaneously by the Lagrange multiplier method. A heuristic method for determining the Lagrange multiplier is proposed in order to effectively constrain the structural maximum von Mises stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topology variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several benchmark design problems.