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.

已经表明，最近开发的一类数字解决方案称为基于节点的平滑点插值方法（NSPIM），可以为力驱动的弹性问题提供能量范数的上限解决方案。在这项研究中，在多孔介质的平面应变耦合问题中研究了NSPIM的束缚固溶特性，以探讨孔隙水压力的存在如何影响NSPIM的这一特征。首先介绍了控制微分方程的简要说明和NSPIM的公式，然后是控制方程的离散形式。然后在理论和数值上彻底研究了三种常见的NSPIM在孔隙弹性问题中的束缚解性质，并与线性有限元法进行了比较。