Meshless analysis of Timoshenko beams based on a locking-free formulation and variational approaches

Abstract

A meshless method is developed, based on subdomain variational formulations and a local Petrov–Galerkin approximation, along with the locking-free formulation, for the analysis of bending of a thick beam. The local point interpolation method is employed to construct both trial and test functions. The present method is a truly meshless method based only on a number of randomly located nodes. No global background integration mesh is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. Effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated. Problems of thick and thin beams under various loading, and boundary conditions are analysed by the proposed method and the numerical results are compared with analytical solutions. The contact problem for beam by means of subdomain variational inequalities and the meshless method has also been investigated.