Rigobert S, Atalla N, Sgard F C
Laboratoire des Sciences de l'Habitat, DGCB URA CNRS 1652, Ecole Nationale des Travaux Publics de l'Etat, 69518 Vaulx-en-Velin Cedex, France.
J Acoust Soc Am. 2003 Nov;114(5):2607-17. doi: 10.1121/1.1616579.
Recently, a mixed pressure displacement [u, P] formulation based on Biot's poroelasticity equations has been presented for porous materials. This model leads to a reduction of the number of degrees of freedom required for the modeling of three-dimensional porous media in comparison to classical displacement-displacement [u, U] formulations. In this paper, an extension of the [u, P] formulation based on hierarchical elements is presented. First, a variant of the weak integral form of the [u, P] formulation is presented and its numerical implementation using hierarchical elements is detailed, together with the application of boundary and loading conditions. Numerical results are presented to show the accuracy and performance of the present approach. In particular, the importance of correctly capturing the coupling effects between the two phases is highlighted.
最近，基于比奥多孔弹性方程提出了一种用于多孔材料的混合压力位移[u, P]公式。与经典的位移-位移[u, U]公式相比，该模型减少了三维多孔介质建模所需的自由度数量。本文提出了基于分层单元的[u, P]公式的扩展。首先，给出了[u, P]公式弱积分形式的一个变体，并详细介绍了其使用分层单元的数值实现，以及边界条件和载荷条件的应用。给出了数值结果以展示本方法的准确性和性能。特别强调了正确捕捉两相之间耦合效应的重要性。
