Abstract:

Assumption made in the mathematical model for large deflection of microscopic incompressible  saturated poroelastic beam is that fluid in pores can only flow in the direction of a deformed axis. Based on this model, nonlinear quasi-tatic bending of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable,  with a suddenly applied nonconservative concentrated transverse load at its free end, is investigated with the Galerkin  truncation method. The curves of deflections and bending moments of the beam skeleton are shown with respect to time and the beam axis. Numerical results show that, for small loads, there is little difference between results for the nonconservative  and conservative concentrated load and between large nonlinear and small linear deflection models. For large loads, results of large nonlinear deflection model are smaller than those of small linear deflection model. Results for the nonconservative loads are larger than those for conservative loads. The difference increases with load. Further, when a concentrated load is suddenly applied, deformation of the beam skeleton does not instantly occur. Deflection of the poroelastic beam increases and finally converges to a stationary state in which the poroelastic beam skeleton takes the entire external load.

Key words: theory of porous media； saturated poroelastic beam； large deflection； nonconservative load；Galerkin truncation method