A finite element model for poroelastic beams with axial diffusion

The finite element method is used for those fluid-saturated poroelastic rod s in which diffusion is possible only in the axial direction as a result of the microgeometry of the solid skeleton material. Variational principles a re developed first for this purpose. Two types of variables, the displaceme nts and pore pressure, are involved in the time dependent functionals. The method of Lagrange multipliers is employed in order to include the flow equ ations (generalized Darcy's law) into the Euler-Lagrange equations of the f unctionals. A mixed finite element scheme is then presented based on one of the variational functionals obtained. Numerical solutions for both types o f variables are found to coincide well with the existing analytical solutio ns. Some interesting results are demonstrated which are not available by an alytical methods. (C) 1999 Elsevier Science Ltd. All rights reserved.