Evolutionary topology optimization of elastoplastic structures

Abstract

We have recently proposed in (Fritzen et al., Int J Numer Methods Eng 106 (6): 2016) an evolutionary topology optimization model for the design of multiscale elastoplastic structures, which is in general independent of the applied material law. Facing the variability of the final design for minor parameter changes when dealing with plastic structural designs, we further improve the robustness and the effectiveness of the BESO optimization procedure in this work by introducing a damping scheme on sensitivity numbers and by progressively reducing the sensitivity filtering radius. The damping scheme constraining the variance of the sensitivity numbers stabilizes the topological evolution process in particular for dissipative structural designs. By setting initially a large filter radius value and reducing it gradually, the emergence of the redundant structural branches, which are to be eliminated afterwards and Liang Xia are the main reasons deteriorating the design process, could be avoided. The robustness and the effectiveness of the improved model has been validated by means of benchmark numerical examples of conventional homogeneous structures.

Topology Optimization Applications on Engineering Structures

“…Fritzen et al [119] taken nonlinear elastoviscoplastic microscopic RVE into account at all points of the macroscopic design domain by using BESO. Later, Xia et al [120] introduced a damping scheme on sensitivity numbers to the same approach. Zhu et al [121] used bidirectional evolutionary level-set method allowing automatic hole generation.…”

Current and future trends in topology optimization for additive manufacturing

“…Wallin et al [191] proposed topology optimization considering finite elastoplastic deformation and also Zhang et al [192] introduced an approach assuming anisotropic elastoplasticity based on the adjoint method [184]. Xia et al [193] adopted BESO method for elastoplastic structure design. Li et al [194] employed kinematic hardening model based on von Mises plasticity to capture the well-known Bauschinger effect under cyclic loads.…”

Material nonlinear topology optimization considering the von Mises criterion through an asymptotic approach: Max strain energy and max load factor formulations

“…In (11), the term U( , u( ))/ e can be evaluated explicitly. In order to evaluate the remaining term, we substitute one of the state equations T ( , u ( )) = ( , u ( )) f 0 into (11) to obtain the expression…”

“…Despite its level of maturity, most previous studies focused on linear materials and omitted the nonlinearity of real-life materials. Plastic material models addressed in topology optimization problems include the works of Yuge and Kikuchi, 1 Swan and Kosaka, 2 Maute et al, 3 Schwarz et al, 4 Yoon and Kim, 5 Bogomolny and Amir, 6 James and Waisman, 7 Kato et al, 8 Nakshatrala and Tortorelli, 9 Wallin et al, 10 Xia et al, 11 and Alberdi and Khandelwal, 12 which is just a small sample of references in the field. Due to material path dependence, the sensitivity will also be path dependent.…”