Two-dimensional beams in rectangular coordinates using the radial point interpolation method

Abstract The three-dimensional Theory of Elasticity equations lead to a complex solution for most problems in engineering. Therefore, the solutions are typically developed for reduced systems, usually symmetrical or two-dimensional. In this context, computational resources allow the reduction of these simplifications. The most recognized methods of algebraic approximation of the differential equations are the Finite Differences Method and the Finite Element Method (FEM). However, they have limitations in mesh generation and/or adaptation. As follows, Meshless Methods appear as an alternative to these options. The present work uses the Radial Point Interpolation Method (RPIM) to evaluate the stress in two-dimensional beams in regions close to loading (Saint Venant's Principle). Formulations based on the Fourier Series Theory and the RPIM are presented. Multiquadrics Radial Basis Functions were used to obtain the stiffness matrix. Two numerical examples demonstrate the validity of the RPIM for the proposed theme. The results were obtained from the formulations cited and the Finite Element Method for comparison.