A nearest-nodes finite element method with local multivariate Lagrange interpolation

In the proposed nearest-nodes finite element method (NN-FEM), finite elements are used only for numerical integration; while shape functions are constructed in a similar way as in meshless methods, i.e. by using a set of nodes that are the nearest to a concerned quadrature point. Some of the nodes may be from adjacent elements. A recently developed local multivariate Lagrange interpolation method is used to construct shape functions. In the above way, the proposed NN-FEM inherits most of the merits from both the finite element method and meshless methods. The major attractive features of NN-FEM include: analysis results are insensitive to element distortion; a crack can propagate along an arbitrary path; with element adjacency information, time spent on searching nearest nodes is much shorter than that used by a meshless method for identifying nodes covered under an influence domain.