An Edge-smoothed Finite Element Method With A Bubble Function (bES-FEM) For Solid Mechanics Problems

Solid mechanics mainly studies principles of the displacement,motion,stress,strain and failure of the solid under the action of the load,temperature,humidity and other external factors.Solid mechanics is a very important problem in scientific computation and engineering calculation.The most commonly used methods for solving solid mechanics problems include finite element method and meshless method,but these methods have their own difficulties.The edge-smoothed finite element method is a new numerical method that improves the traditional finite element method.In order to improve the so-called over-stiffness of the lower order finite element method and improve the computational accuracy,the ES-FEM is proposed to reconstruct the compatible strain field.The reconstructed strain field named smoothed strain field is obtained over smoothing domains created on edges of the triangular cells.An edge-smoothed finite element method with a bubble function(bES-FEM)is presented and used to solve the static echanics problems and structural vibration problems in this paper.The bES-FEM uses the usual piecewise linear displacements but is supplemented with a bubble function in triangular elements.By this way,the bES-FEM forms a new displacement approximation function.Then it uses the same smoothing domain and smoothed strain field as the ES-FEM,and thus forms the system stiffness matrix by using Galerkin method.The results of numerical examples show that the bES-FEM has a high efficiency and a rapid convergence rate no matter in static or dynamic problems,and thus bES-FEM is a very potential numerical method.