Topology Optimization Method And Research Based On Smoothing The Dual Solution

The features of the existing structural topology optimization methods are introduced and analyzed in this theses. The non-differentiable problem of the design variable solutions expressed in a closed form at the Lagrange multiplier points for the dual solving approach of the conventional optimization algorithms, and the calculation error problem caused by the determination of the active and passive variable sets are mainly investigated in this theses. A structural topology optimization method for the minimum volume structure with displacement constraints is proposed, integrated with a smoothing dual solving technique proposed. Then, a corresponding algorithm and its examples are given in this theses.Firstly, in order to improve the computational efficiency and the reliability of the nonlinear optimization methods based on the gradient information and the convex, separable function approximations,a novel dual solving method of the inequality constrained nonlinear programming problem with simple bounds is proposed, based on the method of moving asymptotes(MMA).At first,according to the Karush-Kuhn-Tucker(KKT) conditions and the concept of approximated-approximations,a trust-region of design variables in each approximate sub-optimization model is introduced, and an approximate quadratic sub-optimization model is constructed. In order to solve the non-differentiable problem of the design variable solution expressed in a closed form at the Lagrange multiplier points for the dual problem, a mapping function is introduced, the non-smooth expressions of the design variable solutions are reformulated as smoothing functions of the Lagrange multipliers by using this novel smoothing function. A set of algorithm is proposed for the inequality constrained nonlinear programming problem with simple bounds based on the primal-dual theory.Secondly,for the structural topology optimization problem considering the minimum structural volume with displacement constraints, the smooth functions in the above-mentioned dual solving and the approach of the approximated approximations are introduced to the topology optimization process, a topology optimization method is proposed, based on the method of moving asymptotes(MMA). Several examples are given.The results of examples simulation show that the proposed method can resolve topological optimization problems with displacement constraints, and get better black/white distribution. It verifies the reliability and efficiency of the method and it indicates that the proposed method is of good theoretical and engineering application value.