Research On Topology Optimization Methods Of Continuum Structure Based On Variable Density Method

Topology optimization techniques can find the optimal material density distribution which forms the optimal structure design object under the determined loads and constraints, so that the layout of the whole structure could be more scientific, reasonable, and thus bring enormous economic benefits. Against the shortcomings of the current research works in topology optimization, this paper analyzed the research status in the field of topology optimization, and studied the model building, optimization solving algorithms and the application of continuum structure topology optimization.First of all, for lack of convergence rate in the numerical solution methods of topology optimization problems, the writer modeled this problem with SIMP (Solid Isotropic Microstructures with Penalization) model based on variable density method, and proposed the Newton optimization criteria method based on double-point iteration(Double-point Iteration for Newton Optimization Criteria, DINTOC). Some numerical examples of two-dimensional and three-dimensional structures are carried out, which show that the proposed method has superiority of better optimization results and fast convergence.Secondly, considering the influences on the speed of convergence caused by the moving limits within the iteration scheme of the design variables, the writer proposed a self-adaptive mechanism to adjust the moving limits. Several test examples are carried out and comparative analysis of the results proved that the proposed method has superiority of efficiency.Thirdly, the multiple loading cases of two-dimensional and three-dimensional continuum structure topology optimization had been studied. The DINTOC based method had been constructed to solve these multiple loading cases. Through the test of a few two-dimensional and three-dimensional cases, the efficiency of the used method has proved.Finally, the writer used software MATLAB to build prototype system which supported by the theory and technology develop in this paper on topology optimization of continuum structures. And then the system had been tested by one test case.