Topology optimization method of continuum structure considering fail-safe design under stress constraints

In engineering structures, local damage can reduce significantly overall performance, attracting widespread attention. However, the existing topology optimization methods often overlook the impact of local damage on structural safety, limiting their effectiveness in addressing this challenge. To this end, a topology optimization method of continuum structures in terms of the fail-safe design principles is proposed, where the fixed-shape damage regions are designated as the local damage patterns. The optimal model is established with the objective of minimizing structural volume under stress constraints. An optimization algorithm is developed based on the independent continuous mapping (ICM) method, with sensitivity analysis conducted by using the adjoint method and optimization problem-solving carried out by using the dual programming theory. Using classic L-shaped beams as case, the effects of the distributions and shapes of local damage on the optimal configurations is investigated. Numerical results show that optimal configurations incorporating fail-safe design principles are more complex and contain greater redundancy, therefore reducing the sensitivity to local damage. Furthermore, the damage distributions and shapes yield varying topological configurations. The present method effectively identifies the most unfavorable damage distribution locations within structures, providing the valuable guidance for designing the safety performance of engineering structures.