A meshless local Kriging method for large deformation analyses

Abstract

In this paper, a well-developed meshless numerical technique, local Kriging (LoKriging) method, is used to develop the LoKriging formulation for the large deformation problems, which are geometrically nonlinear. This is the first work for the geometrically nonlinear analyses by this meshless local weak-form method. In the LoKriging method, the Kriging interpolation is employed to construct the meshless shape functions. The spline function with high continuity is used as the weight function. The discrete equations of the large deformation analysis for two-dimensional solids are obtained using the local weak-forms, and based on the total Lagrangian (TL) approach. The presently developed LoKriging method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak-form. Several numerical examples of the two-dimensional geometrically nonlinear analysis are presented to illustrate the performance of the present LoKriging method. The present nonlinear LoKriging formulation is also used for the large deformation analysis of the microelectromechanical systems (MEMS) device. The numerical results are compared with the experimental results. Very good results are obtained. All these applications have demonstrated that the present LoKriging method is very effective for the large deformation analyses, because it avoids all mesh distortion issues.