Research On The Topology Optimization Using The Adaptive EFG Method

Currently, following the topology optimization and mesh-free method has beendeveloped more mature, the structural topology optimization based on mesh-free methodhas been widely researched. There still have many issues for the process of discrete andsolving on the mesh-free Galerkin method topology optimization should be resolved: suchas computational instability and low efficiency, when the method of research is completed.In the paper the two-dimensional structure topology optimization based on the adaptivemesh-free Galerkin been researched, the main contents summarized as follows:1. An adaptive procedure based on the gradient of the strain energy density isdeveloped for the element-free Galerkin method. It comprises nodal strain energy densityand a local domain refinement technique. Taking the nodal strain energy density as theobject of error estimates, finding the nodal adding criteria based on the gradient of thestrain energy density, and completed the nodal local refinement according the nodal addingmethod. Finally obtain the new result using the new nodes distribution. The numericalexperiments in this paper show that this adaptive element-free Galerkin method is efficient.2. The structural topology optimization based on element free Galerkin (EFG) methodis investigated, as the design variables are huge in the discrete models, the separatepoint-clouds of results and the solution is difficult to obtain, the purpose of using nodaldensity as design variable based on adaptive EFG method. The topology optimizationmethod is built by selecting nodal density as design variable and making minimumcompliance as objective function. According the first results of topology optimization inthe initial design domain with spare nodes, taking the nodal density as nodal addingcriterion to selected the nodes which need to be refinement, and completed those nodesrefinement. Following that accord the new nodes distribution to obtain a new topologyoptimization, and take the next adaptive refinement until finding the clear topologystructures. The results obtained show that the proposed adaptive EFG method of topologyoptimization can reduce the effective number of design variables and improve thecomputational efficiency.3. On the basis of the formerly achievement of the adaptive meshless method, thecompliant mechanisms topology optimization based on element free Galerkin (EFG)method is proposed. Superiority of the topology optimization for the compliant mechanismbased on the adaptive EFG method, as the compliant mechanisms have larger-displacement character, which take good used of the advantage of the meshless method not need grid,mesh reconstructed and improve the optimal efficiency, that develop the meshless methodapplied field.In paper the element-free method has flexible nodes, the adaptive method for themechanical analysis and structure topology optimization based on the mesh-free Galerkinmethod are proposed. It comprises nodal strain energy density, a local domain refinementtechnique and variable update method. The numerical experiments in this paper shown thatthe correctness and superiority of this adaptive element-free Galerkin method and improvethe optimization efficiency, finally applied to the compliant mechanism topologyoptimization.