A novel twice-interpolation finite element method for solid mechanics problems  

作　　者：C. Zheng S. C. Wu X. H. Tang J. H. Zhang 

机构地区：[1]State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, 610065 Chengdu, China [2]State Key Laboratory of Digital Manufacturing and Equipment Technology, Huazhong University of Science and Technology, 430074 Wuhan, China [3]Department of Mechanical Engineering,Centre for Advanced, Computations in Engineering Science (ACES),National University of Singapore, Singapore 117576, Singapore

出　　处：《Acta Mechanica Sinica》2010年第2期265-278,共14页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(50474053,50475134 and 50675081);the 863 project (2007AA042142)

摘　　要：Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.

关 键 词：Twice-interpolation finite element method·Stress smoothing Volumetric locking Mesh distortion 

分 类 号：O34[理学—固体力学] O241.82[理学—力学]