Meshless analysis of the obstacle problem for beams by the MLPG method and subdomain variational formulations

In this paper, subdomain variational formulations are presented to describe the bending problem of thin beams, which is then analysed by using the MLPG meshless method. Particular attention is paid to the solution of the obstacle problem for beams by means of subdomain variational inequalities and the MLPG method. 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. Problems of thin beams under various loading, and boundary conditions, as well as the obstacle problem for beams are analysed by the proposed method and the numerical results are compared with analytical solutions. Some parameters which affect the performance of the present method are also investigated.