SUMMARYIn finite element formulations for poroelastic continua a representation of Biot's theory using the unknowns solid displacement and pore pressure is preferred. Such a formulation is possible either for quasi-static problems or for dynamic problems if the inertia effects of the fluid are neglected. Contrary to these formulations a boundary element method (BEM) for the general case of Biot's theory in time domain has been published (Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach. Lecture Notes in Applied Mechanics. Springer: Berlin, Heidelberg, New York, 2001.). If the advantages of both methods are required it is common practice to couple both methods. However, for such a coupled FE/BE procedure a BEM for the simplified dynamic Biot theory as used in FEM must be developed.Therefore, here, the fundamental solutions as well as a BE time stepping procedure is presented for the simplified dynamic theory where the inertia effects of the fluid are neglected. Further, a semi-analytical one-dimensional solution is presented to check the proposed BE formulation. Finally, wave propagation problems are studied using either the complete Biot theory as well as the simplified theory. These examples show that no significant differences occur for the selected material.
Convolution Quadrature Method (CQM)-based Boundary Element formulations are up to now used only in dynamic formulations. The main difference to usual time-stepping BE formulations is the way to solve the convolution integral appearing in most timedependent integral equations. In the CQM formulation, this convolution integral is approximated by a quadrature rule whose weights are determined by the Laplace transformed fundamental solutions and a linear multistep method.In principle, for quasi-static poroelasticity there is no need to apply the CQM because time-dependent fundamental solutions are available. However, these fundamental solutions are highly complicated yielding very sensitive algorithms. On the contrary, the CQM based BE formulation proposed here is very robust and yields comparable results to other methodologies. This formulation is tested in 2-d in comparison with a Finite Element Method and analytical results.
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