A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes

作者：Nguyen Thoi T^*; Vu Do H C; Rabczuk T; Nguyen Xuan H

来源：Computer Methods in Applied Mechanics and Engineering, 2010, 199(45-48): 3005-3027.

DOI：10.1016/j.cma.2010.06.017

• Numerical methods
• Meshfree methods
• Node-based smoothed finite element
• method (NS-FEM)
• Finite element method (FEM)
• Upper bound
• Visco-elastoplastic analyses

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.

• 出版日期2010