A Co-Rotational Meshfree Method for the Geometrically Nonlinear Analysis of Structures

Abstract

This paper presents a co-rotational beam formulation, which is used for geometric nonlinear analysis with the differential reproducing kernel (DRK) approximation collocation method. The present formulation, based on the Timoshenko beam hypothesis, is capable of effectively solving geometrically nonlinear problems such as large deformation, postbuckling, lateral buckling, and snap-through problems. The kinematics have been constructed with the concept of co-rotational formulation adopted in the finite element method (FEM). A meshfree method based on the differential reproducing kernel (DRK) approximation collocation method, combined with the Newton–Raphson method, is employed to solve the strong forms of the geometrically nonlinear problems. The DRK method takes full advantage of the meshfree method. Moreover, only a scattered set of nodal points is necessary for the discretization. No elements or mesh connectivity data are required. Therefore, DRK will be able to completely circumvent the problems of mesh dependence and mesh distortion. The effectiveness of this study and its performance are shown through several numerical applications.

Keywords

• differential reproducing kernel
• meshless method
• co-rotational
• nonlinear analysis
• stability
• postbuckling