Geometrically Nonlinear Analysis for Elastic Beam Using Point Interpolation Meshless Method

Abstract

The intrinsic beam theory, as one of the exact beam formulas, is quite suitable to describe large deformation of the flexible curved beam and has been widely used in many engineering applications. Owing to the advantages of the intrinsic beam theory, the resulted equations are expressed in first-order partial differential form with second-order nonlinear terms. In order to solve the intrinsic beam equations in a relative simple way, in this paper, the point interpolation meshless method was employed to obtain the discretization equations of motion. Different from those equations by using the finite element method, only the differential of the shape functions are needed to form the final discrete equations. Thus, the present method does not need integration process for all elements during each time step. The proposed method has been demonstrated by a numerical example, and results show that this method is highly efficient in treating this type of problem with good accuracy.