Augmenting low-order finite element method with partial nodal strain smoothing for flow-deformation analysis of geomechanical problems

In this study, the application of a numerical technique referred to as partial node-based smoothed finite element method (PNS-FEM) in flow-deformation analysis of problems in geomechanics is presented. The PNS-FEM is developed by augmenting the computation of the stiffness and permeability matrices of the domain in the linear finite element method (FEM) with partial nodal strain smoothing. The PNS-FEM takes advantage of contradicting errors of the solutions of the linear FEM and the node-based smooth point interpolation method (NSPIM) to yield close-to-exact solutions. The formulation of the PNS-FEM and the steps required to develop a PNS-FEM code from an FEM code are thoroughly presented. The performance of the PNS-FEM is then examined through five numerical examples concerning linear and nonlinear porous materials undergoing various types of loading. The results show that partial nodal smoothing is a very simple, yet effective, technique to considerably improve the performance of the linear FEM in coupled problems of geomechanics.