Does the upper bound solution property of the Node-based Smoothed Point Interpolation Methods (NSPIMs) hold true in coupled flow-deformation problems of porous media?

摘要

It has been shown that a recently developed class of numerical solutions referred to as node-based smoothed point interpolation methods (NSPIMs) can provide an upper bound solution in energy norm for force-driven elasticity problems. In this study, bound solution property of the NSPIMs is examined in plane-strain coupled problems of porous media, to explore how the presence of pore water pressure affects this feature of the NSPIMs. Brief descriptions of the governing differential equations and the formulation of the NSPIMs are first presented, followed by the discretised form of the governing equations. The bound solution properties of three popular NSPIMs in poro-elasticity problems are then thoroughly investigated, both theoretically and numerically, and compared to those of the linear FEM. The results show that the upper bound solution property of the NSPIMs is lost in coupled problems of poro-elasticity due to the coupling effects of the fluid phase.