Researches On Continuum Structure Topology Optimization Method Based On Active Constraint Technique

With developments of the computational technique and the additive manufacturing technique,the structural topology optimization technique is of important theoretical and engineering application.In order to improving the computational efficiency and the reliability of existing the nonlinear optimization methods based on the gradient information and the convex separable function approximations,and improving and reconstructing the structural topology optimization method based on the dual theory,a novel smoothing dual solving method of the inequality constrained nonlinear programming problem is proposed,based on the method of moving asymptotes(MMA).Then,an active constraint structural topology optimization(ACSTO)for the minimum compliance problem with a volume constraint is proposed,and ACSTO framework is basically constructed for two kinds of topology optimization problems.Firstly,the characteristics of existed structural topology optimization methods were been carefully investigated,a convex and separable quadratic approximate functions for structural compliances and displacements are formed,based on MMA approximations with respect to topology variables and the concept of approximated approximations with respect to reciprocal intervening variables.In order to solving 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 based on the smoothing primal-dual theory.Secondly,combining the variable displacement constraint limit measures,an active constraint structural topology optimization(ACSTO)is improved,based on MMA and the smoothing primal-dual method,and a corresponding algorithm is constructed.And the method is extended to the compliance optimization problem.Then,a topology optimization method of a structural compliance minimizing problem with multiple constraints and structural volume constraint is proposed,based on the proposed active constraint technique.Finally,comparisons and analyses of several examples are given to demonstrate that the proposed optimization methods may provide a series of near clear profiles of topologies,it is easy to extract the optimum and an inferior optimal structure from the solutions obtained during the optimization process,and the proposed methods are reliable and effective.