Topology Optimization Method And Its Application Research Based On Varying Constraint Limits

This thesis mainly makes research on the topological optimization design of quasi-periodic continuum structures and the minimum weight topological optimization of continuum structure based on varying frequency limits and design space adjustment.It is difficult to solve the topology optimization problem for a long-narrow structure with variable cross-section using conventional algorithm. In order to solve this problem, a new method for topology optimization of quasi- periodic continuum structures is proposed, which is based on the ideas of the variable displacement constraint limits. To satisfy the quasi-periodic constraint, the design domain is divided into a certain number of similar sub-regions which have the same number of elements, and the relevance of the relevant elements in different sub-regions are established. A set of mathematical programming formula and its procedure are proposed, which is based on the idea of the independent, continuous and mapping method. And a set of displacement approximate formulation is derived and a new topology optimization method is developed and implemented. Several simulation examples have been completed, and their results show that the proposed method is of validity and effectiveness.For the minimum weight topological optimization problem with frequency constraints, and a new structural topological optimization method is proposed by introducing the rational approximation material model, which is based on the ideas of varying frequency constraint limits and design space adjustments. Several simulation examples show that the topologies obtained by the proposed method are of good 0-1 distribution property, there is stronger ability to obtain the optimum topology than the method of evolutionary structural optimization and the Solid Isotropic Microstructures with Penalty method, and verify that this algorithm is robust and feasible.