an:06004373
Zbl 1231.74432
Nguyen-Thoi, T.; Vu-Do, H. C.; Rabczuk, T.; Nguyen-Xuan, H.
A node-based smoothed finite element method (NS-Fem) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes
EN
Comput. Methods Appl. Mech. Eng. 199, No. 45-48, 3005-3027 (2010).
0045-7825
2010
j
74S05 74C10
numerical methods; meshfree methods; node-based smoothed finite element; method (NS-FEM); finite element method (FEM); upper bound; visco-elastoplastic analyses
Summary: A node-based smoothed finite element method (NS-FEM) was recently proposed for the solid mechanics problems. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh. In this paper, the NS-FEM is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes, respectively. The material behavior includes perfect visco-elastoplasticity and visco-elastoplasticity with isotropic hardening and linear kinematic hardening. A dual formulation for the NS-FEM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl-Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacement-dependent. The numerical results show that the NS-FEM has higher computational cost than the FEM. However the NS-FEM is much more accurate than the FEM, and hence the NS-FEM is more efficient than the FEM. It is also observed from the numerical results that the NS-FEM possesses the upper bound property which is very meaningful for the visco-elastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, NS-FEM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.