A fully smoothed finite element method for analysis of axisymmetric problems

A fully smoothed finite element method is developed to model axisymmetric problems by incorporating a special integral into the Cell-based, Node-based and Edge-based Smoothed Finite Element Method (CS-FEM, NS-FEM, ES-FEM), respectively. The special integral is done by combining Gauss divergence theorem with the evaluation of an indefinite integral, which can be used for treatment of the axisymmetric term in strain matrix and shape function in mass matrix. Applying the special integral and smoothing technique, all the domain integrals in stiffness matrix and mass matrix can be smoothed and rewritten as boundary integrals of smoothing cells. Then the stiffness matrix and mass matrix of element are computed by a simple summation over the smoothing cells. In this work, the proposed method is extended to static and structure dynamic analysis of axisymmetric problems. Numerical examples show that the proposed method can yield good performance even for extremely irregular elements.