Keywords: parallel computing, fail-safe, topology optimization, multigrid methods.

This paper presents an efficient parallel implementation of topology optimization of continuum structures considering the local loss of stiffness due to material failure. Considering such a loss of stiffness, we can obtain operable designs after faults, providing fail-safe structural designs minimizing safety risks. We use a local model of failure removing the material stiffness in patches with a fixed shape, whereas we consider the damage scenarios using a Kreisselmeier-Steinhauser (KS) function to approximate the non-differentiable max-operator in the min-max formulation of the optimization problem minimizing the worst-case performance. The analysis of continuum structures using this fail-safe formulation is a computational challenge due to the need for solving as many finite element problems as damage scenarios. We solve such damage scenarios using a distributed memory conjugate gradient solver preconditioned by an algebraic multigrid (AMG) method. Inter-node communications drastically deteriorate the solver performance due to network latency. Thus, we propose a two-level parallel processing scheme using intra-node communications for solving the damage scenarios and inter-node communications for computing the approximation of the min-max formulation avoiding bandwidth problems. We evaluate the performance and scalability of the proposed methodology showing good performance and scalability.

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