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

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.