Topology optimization of 2D‐frame structures with path‐dependent response

This paper deals with topology stiffness optimization of a ground structure consisting of rectangular 2D‐beam elements with path‐dependent response. The objective of the optimization is to minimize the compliance of the structure when the mass is prescribed. The path‐dependent response of the structure is due to the plastic hinges at the ends of the beam elements. The plastic hinges are modelled through yield surfaces giving the interaction between the stress resultants when the cross‐section is fully plastified. In combination with the yield surface a simple hardening rule is applied. The geometrical non‐linearities are also included, so the beam elements can perform large rigid body rotations. The finite element solution is obtained with an implicit backward Euler algorithm. From the finite element solution the analytical sensitivities are computed using the direct method.