Topology optimization of a load-bearing structure via the method of convex linearization

A method of topology optimization based on the convex linearization approach is proposed. The problem formulation implies minimization of the strain energy of a structure subject to volume constraint. The solution is based on explicit, convex and separable Lagrangian approximation with the involvement of the duality theory. A non-linear model is used to relate design variables (density) and elastic properties of the material (modulus of elasticity). The sensitivity of the gain function and the constraint function is analyzed. The basic design formulae for the iteration algorithm of topology optimization are obtained. A number of test problems that correspond to the basic load states: tension, shear and torsion are considered. For all cases the load-carrying factor is calculated: both analytically and with the use of finite-element models. The resulting topologies are shown to be in full compliance with engineering concepts of theoretically optimal structures.