Abstract Based on the three dimensional theory of incompressible saturated porous media, first, a one-dimensional mathematical model for quasi-static bending of the transversely isotropic saturated poroelastic Timoshenko cantilever beam is established with assumptions of deformation of the classical single phase Timoshenko beam and the movement of pore fluid only in the axial direction of the poroelastic beam, and the corresponding boundary conditions are presented. Secondly, the quasi-static bending of the saturated poroelastic Timoshenko cantilever beams with different end permeability conditions, subjected to a step load at its free end, is analyzed by the Laplace transform and its numerical inverse transform. The variations of the deflections, bending moments of the poroelastic beam and the equivalent couples of the pore fluid pressure against the time are shown in figures and are compared with those of the saturated poroelastic Euler-Bernoulli cantilever beam. The effect of the slenderness ratio of the beam is examined. It is shown that the interaction coefficient between the solid skeleton and pore fluid plays a role as viscidity, and the quasi-static deflections of the saturated poroelastic beams possess the creep behavior. Furthermore, the influence of the end permeability conditions on the bending behavior is great, and the Mandel-Cryer phenomenon also occurs in the quasi-static deformations of the saturated poroelastic Timoshenko cantilever beam.
2011, Vol. 32 
