Study on Sensitivity Analysis and Shape Optimization of FE-EFG Coupled Method

Abstract

The most advantage of meshless method is that it can alleviate the mesh constrained of node, and the distortion of mesh presented in the process of structural shape optimization can be completely avoided by integrating the meshless method into the shape optimization. In many meshless methods, the element-free Galerkin (EFG) method is one of the most promising and well-developed method for engineering application. However the EFG method is marked by some shortcoming, where the primary one is that there is much more computational cost and it is difficult in imposing the essential boundary condition. The advantage in both finite element (FE) method and EFG method can be developed by integrating coupled FE-EFG method into structural shape optimization. A collocation approach is introduced to couple firstly FE and EFG method with isoparametric quadrangle interface element between EF and meshless regions, and the interpolation function for the displacement at the interface element satisfies the linear consistency exactly. By taking derivative of discreteness equilibrium equation in FE method with respect to design variable, a numerical method for discreteness-based shape design sensitivity analysis using coupled FE-EFG method is obtained. The design sensitivity analysis of coupled FE-EFG method is completed by collocation approach at the interface element. The numerical method mentioned above is testified by examples. It can be observed excellent agreement between the numerical results and the analytical solution. Finally the shape optimization of fillet is achieved by using coupled FE-EFG method.