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This article presents an approach for the topology optimization of frame structures composed of nonlinear Timoshenko beam finite elements (FEs) under time‐varying excitation. Material nonlinearity is considered with a nonlinear Timoshenko beam FE model that accounts for distributed plasticity and axial–shear–moment interactions through appropriate hysteretic interpolation functions and a yield/capacity function, respectively. Hysteretic variables for curvature, shear, and axial deformations represent the nonlinearities and evolve according to first‐order nonlinear ordinary differential equations (ODEs). Owing to the first‐order representation, the governing dynamic equilibrium equations, and hysteretic evolution equations can thus be concisely presented as a combined system of first‐order nonlinear ODEs that can be solved using a general ODE solver. This avoids divergence due to an ill‐conditioned stiffness …