Topology Optimization Based On Smoothed Finite Element Methods

The present paper studies the formulation and algorithm for topology optimization of continuum structures by combining the smoothed finite element method with nodal density based topology optimization method. The smoothed finite element method (SFEM) for2D elastic problemshad been proposed by GuiRong Liu et al. in recent years. Compared with conventional finite element method, SFEM is capable obtaining more accurate result and more flexible in domain discretization for particular problems. Nodal density method has the CO continuity which leads the density field within each element varies spacially, by which checkerboard pattern problem can be circumvented. By combining the SFEM and the nodal density method, the present paper proposes a topology optimization framework for continuum structures on Matlab. In this paper, the density filed discretization is independent fromthe displacement field discretization. Nodal-based Smoothed Finite Element Method (NS-FEM) is adopted in calculation of displacement field, and the material layout is described by the density field which is constructed by interpolating the nodal density variables. The density field distribution within design domain is constructed using Shepard interpolation function. The solid isotropic material penalization (SIMP) methodis employed in the formulation of topology optimization. The method of moving asymptotes (MMA) algorithm is adopted to solve the optimization problem.Numerical examples investigate topology optimization problems without adopting any sensitivity filtering technique (which can avoid numerical instability), by analyzing and comparing obtained results the following conclusions are drawn:(1) It is applicable of combining SFEM and nodal density method in solving topology optimization problems, and numerical instability such like checkerboard pattern and islanding phenomenon can be avoided;(2) Based on the assumption of "representing density of the whole smooth local region with central nodal density" discussing the distribution regularity of the displacement field nodes and the density field nodes and analyzing and comparing obtained results, this text proposes the ideal nodes distribution principle of these two field.