Galerkin Meshless Formulations for 3D Beam Problems

The main idea of meshless methods is to approximate the unknown field by a linear combination of shape functions built without having recourse to a mesh of the domain. The computational domain is discretized using a set of scattered nodes. The shape functions associated with a given node is then built considering the weight functions whose support overlaps the one of the weight function of this node; thus, there is actually no need to establish connectivities between the different nodes as in the finite element method. Monte-Carlo integration techniques are promising schemes in the context of meshless techniques. The purpose of the present paper is to implement in EFG a new body integration technique for the evaluation of the stiffness matrix that does not rely on a partition of the domain into cells, but rather points. Numerical examples based on three-dimensional elasticity problems are presented to examine the accuracy and convergence of the proposed method. In this context, Quasi-Monte Carlo integration techniques are used. The results are compared to traditional EFG. Conclusions are drawn concerning the proposed techniques and its capabilities.