# Bibliography - Z. H. Wang

- Scherer, George, Jean Hervé Prévost, and Z. H. Wang, 2009:
**Bending of a Poroelastic Beam with Lateral Diffusion**. *International Journal of Solids and Structures*, **46(18-19)**, doi:10.1016/j.ijsolstr.2009.05.016 3451-3462

[ Abstract ]Bending an elastic beam leads to a complicated 3D stress distribution, but the shear and transverse stresses are so small in a slender beam that a good approximation is obtained by assuming purely uniaxial stress. In this paper, we demonstrate that the same is true for a saturated poroelastic beam. Previous studies of poroelastic beams have shown that, to satisfy the Beltrami–Michell compatibility conditions, it is necessary to introduce either a normal transverse stress or shear stresses in addition to the bending stress. The problem is further complicated if lateral diffusion is permitted. In this study, a fully coupled finite element analysis (FEA) incorporating the lateral diffusion effect is presented. Results predicted by the “exact” numerical solution, including load relaxation, pore pressure, stresses and strains, are compared to an approximate analytical solution that incorporates the assumptions of simple beam theory. The applicability of the approximate beam-bending solution is investigated by comparing it to FEA simulations of beams with various aspect ratios. For “beams” with large width-to-height ratios, the Poisson effect causes vertical deflections that cannot be neglected. It is suggested that a theory of plate bending is needed in the case of poroelastic media with large width-to-height ratios. Nevertheless, use of the approximate solution yields very small errors over the range of width-to-height ratios (viz., 1–4) explored with FEA.

- Wang, Z. H., Jean Hervé Prévost, and O. Coussy, 2008:
**Bending of Fluid-Saturated Linear Poroelastic Beams with Compressible Constituents**. *International Journal for Numerical and Analytical Methods in Geomechanics*, **33(4)**, doi:10.1002/nag.722 425-447

[ Abstract ]Analytical solutions are presented for fluid-saturated linear poroelastic beams under pure bending. The
stress-free boundary condition at the lateral surfaces is satisfied in the St Venant’s sense and the Beltrami–
Michell compatibility conditions are resolved rigorously, rendering the flexure of the beams analytically tractable. Two sets of formulations are derived based on the coupled and uncoupled diffusion equations respectively. The analytical solutions are compared with three-dimensional finite element simulations.
Both sets of analytical formulations are capable of capturing exactly both the initial (undrained) and the
steady-state (fully drained) deflection of the beams. However, the analytical solutions are found to be
deficient during the transient phase. The cause for the deficiency of the transient analytical solutions is
discussed. The accuracy of the analytical solutions improves as Poisson’s ratio and the compressibility of
the constituents of the porous beam increase, where the St Venant’s edge effect at the lateral surfaces is
mitigated.

Direct link to page: http://cmi.princeton.edu/bibliography/results.php?author=3544