Research Of EFGM Structure Topology Optimization Based On Adaptive Scheme

Currently, the topology optimization based on finite element structural analysis has been developed more mature, but the problems of the topology optimization based on element free method still have many issues to be resolved; such as computational instability and low efficiency. Based on element free Galerkin method and SIMP interpolation scheme, the adaptive technology is used for studying two-dimensional continuum structure topology optimization in this paper. the main courses are summarized as follows:1. Taking the displacement of the discrete node as the object of the error estimates, and adopting H1 norm to posteriori error solution, a posteriori error estimates identification is using to get the high-error regions based on element free Galerkin method structural analysis. Then the appropriate adaptive technology is used to add nodes in the high-error regions. By comparing the results of the different adaptive schemes, the results demonstrated that the selected adaptive node refinement scheme in the adaptive element free Galerkin method is feasible.2. In response to the problems of low efficiency and instability results from using nodal density for design variables in the topology optimization, an adaptive technology method is proposed, which takes the nodal density as the design variables and with its values as a judge criterion. In the condition of dispersing the initial design domain with sparse nodes, it is according to the nodal density that obtained in the process of topology optimization, and then adding nodes gradually by the adaptive node refinement scheme which has been demonstrated, and stopping the node refinement until the distance between the adjacent nodes is less than the fixed value. In this way, the efficiency of optimization is improved by reducing the design variables. The algorithm is implemented with MATLAB, and numerical results show that the method is feasible and effective.3. The numerical instabilities exist in adaptive topology optimization is analyzed, and the factors of impact on the calculation accuracy of EFGM is introduced, and a new method for background mesh is built to solve these problems. It calculates the energy norm error estimates of background by using stress error indicator, and then combined with the radius of influence domain of the weight function, to calculate the accuracy of background in the different situation of nodes distribution for getting a reasonable proportion of the background mesh. The algorithm is implemented through the MATLAB program and the numerical results show that the method can effectively improve the accuracy of adaptive topology optimization, and ensure its efficiency. In this paper, took the advantage of meshless method to verify the adaptive node refinement scheme, and applied it to the topology optimization, to improve the optimization efficiency, and overcome common problems in topology optimization. Meshless Adaptive topology optimization technology provides a new idea, which has broad prospects.