The Constraint Qualification Of Truss Topology Optimization And The Convergence Analysis Of The Perturbation Approach

This dissertation is concerning problems of truss topology optimization under local buckling constraints. A new approach for the solution of singular problems caused by stress and local buckling constraints is proposed. At first, a second order smooth-extended technique is used to make the disjoint feasible domains connected after that the so-called ε-relaxed method, is applied to eliminating the singular optima from problem formulation. By employing this approach, the singular optimum of the original problem caused by stress and local buckling constraints can be searched approximately by employing the algorithms developed for sizing optimization problems with high accuracy.The dissertation first present two equivalent mathematical models of the truss topology optimization with stress and local buckling constraints. Secondly, it explores constraint qualifications needed in the first-order optimality conditions for internal-bar-force-constrained problem and its perturbation problem, showing that the constraint qualification in the perturbation problem are much easier to satisfy than those for the original one. Furthermore, it is proved that the optimal value function is continuous and the optimal solution mapping is outer semi-continuous and the function of the optimal value as well as the feasible domain mapping are continuous with respect to a perturbation parameter e at the original, which results in the convergence of the discrete version of the perturbation approach. Some numerical results are reported in last part of the dissertation.