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A method for the topology optimization of structures composed of nonlinear beam elements based on a hysteretic finite element modeling approach is presented. In the context of the optimal design of structures composed of truss or beam elements, studies reported in the literature have mostly considered linear elastic material behavior. However, certain applications require consideration of the nonlinear response of the structural system to the given external forces. Particular to the methodology suggested in this paper is a hysteretic beam finite element model in which the inelastic deformations are governed by principles of mechanics in conjunction with first-order nonlinear ordinary differential equations. The nonlinear ordinary differential equations determine the onset of inelastic deformations and the approximation of the signum function in the differential equation with the hyperbolic tangent function permits the …