Structural stability and artificial buckling modes in topology optimization

• Published in: Structural and multidisciplinary optimization Vol. 64; no. 4; pp. 1751 - 1763
• Main Authors: Dalklint, Anna, Wallin, Mathias, Tortorelli, Daniel A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021; Springer Nature B.V; Springer Science + Business Media
• Subjects: Applied Mechanics; Artificial buckling modes; Asymptotes; Buckling; Computational Mathematics and Numerical Analysis; Constraints; Eigenvalue problem; Eigenvalues; Energy transition; Engineering; Engineering and Technology; Engineering Design; Maskinteknik; Mechanical Engineering; Nonlinear elasticity; Nonlinear response; Optimization; Research Paper; Stability; Stability analysis; Structural response; Structural stability; Teknik; Teknisk mekanik; Theoretical and Applied Mechanics; Topology optimization; Topology optimization; Eigenvalue problem; Stability; Nonlinear elasticity; Artificial buckling modes; Energy transition
• DOI: 10.1007/s00158-021-03012-z
• ISSN: 1615-147X

This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.