Robust topology optimization for uncertainty in load positions of transient dynamic loading

This paper presents a novel framework for robust topology optimization (RTO) of structures under transient loading with uncertainty in load positions. To achieve this, the generalized-α method is used to compute the system’s dynamic response due to transient loading. A density-based topology optimization (TO) approach is adopted to minimize the dynamic response while adhering to a specified volume constraint. The RTO problem is formulated as a bi-criteria optimization task, minimizing both the mean and variance of the dynamic response across all deterministic cases within the load position bounds. The material stiffness is interpolated using the modified solid isotropic material with penalization (SIMP) method. The Helmholtz filter is applied directly to the state problem mesh, eliminating the need for neighboring element information and providing a memory-efficient alternative for handling 3D problems. The design variables are iteratively updated using the optimality criteria (OC) method. The proposed framework’s effectiveness is demonstrated through a series of numerical examples. Results reveal that RTO designs achieve a significant reduction of approximately 60%–92% in the dynamic response’s standard deviation compared to deterministic designs. This highlights the framework’s ability to mitigate the effect of load position uncertainties, offering a effective tool for designing robust structures under transient loading conditions.