기하비선형을 고려한 위상최적설계의 안정성을 위한 변위 보정법

Abstract

This paper proposes the displacement adaptation technique for preventing the numerical instability in nonlinear topology optimization. Since the tangent stiffness matrix often becomes negative definite or indefinite with the topological variable in nonlinear finite element analysis, the analysis results can be inaccurate and even cannot be obtained. To avoid this problem, the proposed method detects the distorted elements in low density area and replaces the nodal displacements of them into adaptive displacements. The adaptive displacements are obtained by solving the sub-optimization problem, which minimizes the distorted mesh in the detected domain. To verify the effectiveness of the proposed method, several benchmarking structural design problems with consideration of the large deformation are provided.