Structural Dynamic Topology Optimization and Sensitivity Analysis Based on RKPM

Abstract

A numerical method for structural dynamic topology optimization and sensitivity analysis is presented by using RKPM. In this paper, the relative density of node and maximum fundamental eigenfrequency is respectively chosen as design variable and the objective function, and then the mathematical model for dynamic topology optimization based on RKPM is built. During the process of modeling, some effective measures are taken to dispose the multi-eigenvalues and localized modes. Subsequently, the sensitivity analysis equation is proposed by using Direct Differentiation Method. Finally, by integrating the above sensitivity analysis with Optimality Criteria method, the dynamic topology optimization of an example is performed successfully. Numerical example shows that both checkboards and localized eigenmodes do not occur during topology optimization, and it indicates the proposed method is valid.

Topology Optimization for Nonlinear Kirchhoff Plate Using RKPM

“…Gong et al [4] and Zheng et al [5] developed the topology optimization formulation based on the Element-free Galerkin method (EFG) and the stress constraint. Zhang et al [6] studied the structural dynamic topology optimization based on RKPM and nodal relative density. Cho et al [7] and Zhou et al [8] performed the topology optimization for large deformation nonlinearly structure and linear elastostatics plane problem by using RKPM, respectively.…”

“…are very similar to plane stress problem in terms of form, but in fact the global stiffness matrix of plane stress problem is a (2 ) (2 )IP IP * × *square matrix[6], while K and α K in Eq. (7) have been degenerated into ( ) IP IP × square matrices, and great change takes place in the corresponding computational matrices,…”