Topology Optimization Of Continuum Structure Mode Based On EFGM

Topology optimization is a new research field which appears in the field of optimization following shape optimization and size optimization. The topology optimization design of mode is more complicated than static topological optimization. At present, most of the study in structure analysis of topology optimization is based on using Finite Element Method. A new numerical method—Element-free Galerkin (EFG) method is used for solving two-dimensional continuum structure mode topology optimization problems in this paper. The main contents are summarized as follows:1. The basic principle of approximate technique in EFG method—moving least-squares (MLS) is introduced. Boundary condition is imposed by using the penalty function method, and then different equations of continuum structure motion and corresponding eigen-equation of the vibration are obtained. The modal analysis algorithm is implemented with program written, the numerical results are compared with FEM, and it shows that the EFG method is feasible in the field of modal analysis.2. A mathematical model for continuum structure topology optimization is established based on EFG method by using SIMP method and OC method, taking the relative density of Gauss integral points as design variables and selecting maximizing the first eigen-frequency as objective function. The update scheme for the density is deduced by its sensitivity analysis. Filtering technology is introduced to eliminate the checkerboard patterns in the optimization, and then two examples of mode topology optimization are finished. The results obtained are compared with FEM, and it shows that the algorithm is exactly correct.3. The numerical instabilities exist in topology optimization are introduced and a new topology optimization model of continuum structure based on EFG method is built. It takes nodal density as design variables and selects maximizing the first eigen-frequency as objective function, and then the derivation of its sensitivity analysis is studied. The problem about localized modes and repeated eigen-values in topology optimization are also studied, and some ways are suggested to solve these problems. The mode topology optimizations of the regular beam and the beam with holes are studied. The results show that taking nodal density as design variables can eliminate the checkerboard patterns in the optimization.4. The variation state of the first eigen-frequency after optimization is studied, and according to the optimization results, the dependence of the background grid is discussed, then the size of background grid partition is suggested.In a word, EFG method is successfully used in structure mode topology optimization in this paper, and the improved model can effectively eliminate the checkerboard and porous problems and improve the efficiency. The study makes a good use of EFG method and pioneers a new way for continuum structure mode topology optimization.