Application of generalized finite difference method for elastoplastic torsion analysis of prismatic bars

Abstract

In this paper, the generalized finite difference method (GFDM) is employed for the elastic-plastic torsion analysis of prismatic bars, and the generalized finite difference numerical scheme of the elastic-plastic torsion governing equation is derived. This approach divides the computational domain into a series of overlapping sub-domains and constructs a system of linear equations based on Taylor series expansion and moving least squares. With the help of Picard's iterative method, the elastic solution is utilized as the initial guess to reach the elastic-plastic solution. The plastic nonhomogeneous term is then evaluated via radial basis function (RBF) interpolation. Since the generalized finite difference method does not require intra-domain integration and allows random distribution of nodes, it could simply deal with complex computational domain problems. In numerical experiments, the elastic-plastic torsion examples of square-section bars and linear guide rail reveal that the numerically developed generalized finite difference model is a reliable and effective analysis solution for elastic-plastic torsion problems of prismatic bars.