Analytical sensitivity in topology optimization for elastoplastic composites

• Published in: Structural and multidisciplinary optimization 2015-09, Vol.52 (3), p.507-526
• Main Authors: Kato, Junji, Hoshiba, Hiroya, Takase, Shinsuke, Terada, Kenjiro, Kyoya, Takashi
• Format: Article
• Language: English
• Subjects: Composite materials; Computational Mathematics and Numerical Analysis; Damage assessment; Deformation; Dependence; Elastoplasticity; Energy absorption; Engineering; Engineering Design; Equilibrium equations; Finite difference method; Material properties; Order parameters; Parameter sensitivity; Regularization; Research Paper; Sensitivity analysis; Theoretical and Applied Mechanics; Topology optimization
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-015-1246-8

The present study proposes a topology optimization of composites considering elastoplastic deformation to maximize the energy absorption capacity of a structure under a prescribed material volume. The concept of a so-called multiphase material optimization , which is originally defined for a continuous damage model, is extended to elastoplastic composites with appropriate regularization for material properties in order to regularize material parameters between two constituents. In this study, we formulate the analytical sensitivity for topology optimization considering elastoplastic deformationand its path-dependency. For optimization applying a gradient-based method, the accuracy of sensitivities iscritical to obtain a reliable optimization result. The proposed analytical sensitivity method takes the derivative of the total stress which satisfies equilibrium equation instead of that of the incremental stress and does not need implicit sensitivity terms. It is verified that the proposed method can provide highly accurate sensitivity enough to obtain reliable optimization results by comparing with that evaluated from the finite difference approach.