Topology optimization under displacement and softening constraints

This paper proposes a two-step optimization algorithm to carry out simultaneously an optimal size and topology synthesis of truss-like 2D structures made of strain softening materials, which invariably would cause severe physical instability. Satisfaction of serviceability conditions is also ensured by the inclusion of appropriate constraints. The proposed technique is based on the ubiquitous ground structure concept. Member cross-sectional areas are used as design variables. The governing formulation takes the form of a challenging nonconvex and nonsmooth optimization problem, known as a mathematical program with equilibrium constraints or MPEC.The equilibrium constraints are the complementarity conditions used to describe the softening material behavior. Each design step involves updating the ground structure and processing the MPEC using a nonlinear programming based penalty algorithm