Abstract

In this work, a meshless method, “natural neighbour radial point interpolation method” (NNRPIM), is applied to the one‐dimensional analysis of laminated beams, considering the theory of Timoshenko. The NNRPIM combines the mathematical concept of natural neighbours with the radial point interpolation. Voronoï diagrams allows to impose the nodal connectivity and the construction of a background mesh for integration purposes, via influence cells. The construction of the NNRPIM interpolation functions is shown, and, for this, it is used the multiquadratic radial basis function. The generated interpolation functions possess infinite continuity and the delta Kronecker property, which facilitates the enforcement of boundary conditions, since these can be directly imposed, as in the finite element method (FEM). In order to obtain the displacements and the deformation fields, it is considered the Timoshenko theory for beams under transverse efforts. Several numerical examples of isotropic beams and laminated beams are presented in order to demonstrate the convergence and accuracy of the proposed application. The results obtained are compared with analytical solutions available in the literature.