Topology optimization of damage‐resistant structures with a predefined load‐bearing capacity

Abstract

This article presents a novel strategy for structural topology optimization considering damage. In engineering practice, structures are typically designed to have a certain load-bearing capacity, with a minimal material volume or cost. We aim to optimize the topology of a structure to have a minimal weight while guaranteeing a predefined load capacity, considering the softening behavior of quasi-brittle materials. Two different optimization strategies are presented: a fully nonlinear strategy and a simplified strategy. The fully nonlinear strategy relies on existing nonlinear damage models, which require iterative solution methods, for structural analysis and the computation of the corresponding sensitivities. The simplified strategy uses a simplified damage model, which computes a structure's damage distribution in only one step, greatly reducing computation time. The accuracy of the simplified damage model is controlled by occasional nonlinear simulations-without sensitivity analysis-to calibrate the results. Benchmark tests compare the simplified optimization strategy with the fully nonlinear optimization strategy. While the simplified damage model does not have the same accuracy as nonlinear damage models, results show similar optimized topologies and structural efficiency, with a significant improvement regarding computation time for the simplified optimization strategy.

Topology Optimization to Fracture Resistance: A Review and Recent Developments

“…For these materials, failure cannot easily be expressed in terms of a maximal stress or strain. By constraining the stress to be lower than the yield stress, the optimized designs will be structurally safe but overly conservative since the behavior beyond yielding or damage initiation is not considered [136]. To overcome these limitations, authors have introduced TO approaches including fully nonlinear and path-dependent simulations.…”

“…A nonlocal damage model was developed by Noël et al in [149] in the framework of a level-set TO. More recently, Barbier et al [136] considered minimization of volume in a structure by solving an elastic problem with nonlinear damage model [150] under a maximum loading capacity, including a fully nonlinear strategy and a simplified strategy, where damage was computed into the structure in only one step.…”