Research Of Topology Optimization Of Continuum Structure Based On Nodal Variables And Its Applications

The dissertation is focused on the research of topology optimization of continuumstructure based on nodal variables. The method of constructing continuous density filedbased on nodal variables and the method of suppressing the intermediate density nodes arediscussed. Then it is applied in topology of micro-structures.To suppress the checkerboard patterns and mesh-dependence in topology optimization,by using the bilinear interpolation function, the topology optimization density interpolationmodal based on nodal variables is established. As the density filed of the design domainswith C0continuity, which suppress the checkerboard patterns in the nature of mathematics.And then a modified updating technique for sensitivities information is proposed, byconstructing the relations of filter radius and grid density, which makes filter radius keepthe same as the grid density increasing. Then the modified sensitivity filter was employedin topology optimization based on nodal density, which solved mesh dependencyproblems.Considering the fact that the follow-up search of the optimal topology affected bydeleting a large number of high-relative-density elements, when the typical densityinterpolation approach, SIMP, is employed in the continuum structural topologyoptimization, a new density interpolation approach based on the Logistic function wasproposed. This method can punish the nodal densities which are lower than the given valueto0, while others are punished to1. Which avoid deleting a large number of intermediatedensity nodes. Several number examples show that the method can get the optimaltopology with less intermediate density nodes.Finally, macroscopic elasticity tensor of a periodic composite material is computed byusing homogenization method. And macroscopic elasticity tensor of a periodic compositematerial is written, which is proved correct by the number examples As there are alsonumerical instabilities in the topology optimization of micro-structure, especiallycheck-board pattern, the method proposed in the dissertation is applied in it, and get theoptimal structures with extreme elastic property without check-board pattern.