COMPLAS 2023

Reaction-Diffusion Equation-Based Topology Optimization of Lightweight Elastoplastic Structures by Exact Volume Constraint

  • Cui, Yi (Nagoya University)
  • Takahashi, Toru (Nagoya University)
  • Matsumoto, Toshiro (Nagoya University)

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As an alternative to the original Solid Isotropic Material with Penalization (SIMP) approach, topology optimization of lightweight elastic structures via reaction-diffusion equation has re- cently attracted considerable attention. More recently, an exact volume constraint method for the latter has been proposed [1], which paves the way towards structural topology optimization under exact boundary representations. However, for elastoplastic structures, such an approach has never been achieved. It is hence of great engineering importance to perform lightweight design of elastoplastic structures by topology optimization. For elastoplasticity, the stress update algorithm involving Newton-Raphson iteration is a well- established approach in FEM solvers such as ABAQUS. Through the predictor-corrector scheme, the effective stress at each material point is able to satisfy the yield criterion. As a result, com- pared with linear elasticity without stress constraint, local stress by considering elastoplasticity cannot exceed the local yield stress. For this purpose, the assumption of small strain plasticity should be enough in this study. Regarding the sensitivity analysis of elastoplastic structures, topological derivative, instead of density derivative is employed. The advantage of the former in the case of elastoplasticity is that it avoids evaluating the density derivative of the elastoplastic stiffness tensor, which is far more complicated than the elastic one. Since plastic deformation is confined to the region with stress concentration, the topological derivative is simplified for ease of implementation. The numerical implementation is built on the ABAQUS-PYTHON platform by utilizing its powerful nonlinear solver. A user material subroutine of ABAQUS is coded to redefine material constants based on the current level set function. Our results demonstrate that the proposed exact volume constraint is still effective considering elastoplasticity, which paves towards topology optimization of lightweight elastoplastic struc- tures under exact boundary representations. REFERENCES [1] CuiY.,TakahashiT.,MatsumotoT.,Anexactvolumeconstraintmethodfortopologyoptimization via reaction-diffusion equation. (in press). Computers and Structures, 2023.