饱和多孔弹性Timoshenko梁的大挠度分析

LARGE DEFLECTION ANALYSIS OF A SATURATED POROELASTIC TIMOSHENKO BEAM

基于微观不可压饱和多孔介质理论和弹性梁的大挠度变形假设,考虑梁剪切变形效应,在梁轴线不可伸长和孔隙流体仅沿轴向扩散的限定下,建立了饱和多孔弹性Timoshenko梁大挠度弯曲变形的非线性数学模型.在此基础上,利用Galerkin截断法,研究了两端可渗透简支饱和多孔Timoshenko梁在突加均布横向载荷作用下的拟静态弯曲,给出了饱和多孔Timoshenko梁弯曲变形时固相挠度、弯矩和孔隙流体压力等效力偶等随时间的响应.比较了饱和多孔Timoshenko梁非线性大挠度和线性小挠度理论以及饱和多孔Euler-Bernoulli梁非线性大挠度理论的结果,揭示了他们间的差异,指出当无量纲载荷参数q>10时,应采用饱和多孔Timoshenko梁或Euler-Bernoulli梁的大挠度数学模型进行分析,特别的,当梁长细比λ<30时,应采用饱和多孔Timoshenko梁大挠度数学模型进行分析.

Based on the theory of microscopic incompressible saturated porous media and the hypothesis of large deflection deformation of the elastic beam,with the effect of shear deformation of the beam,a nonlinear mathematical model is presented for large deflection bending of saturated poroelastic Timoshenko beams under constraints of the inextensibility of the axial line and the diffusion of the pore fluid only in the axial direction of beams.Then,the nonlinear quasi-static bending of a simply supported saturated poroelastic Timoshenko beam with two ends permeable,subjected to a uniform transverse step load,is investigated with the Galerkin truncation method.The curves of deflections,bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are given.The results of the nonlinear large deflection and the linear small deflection theories of the saturated poroelastic Timoshenko beam as well as the nonlinear large deflection theory of the saturated poroelastic Euler-Bernoulli beam are compared,and the differences among them are revealed.It is shown that,when the dimensionless load parameter q10,the nonlinear large deflection mathematical model of the saturated poroelastic Timoshenko beam or Euler-Bernoulli beam should be employed for analysis of the bending of the saturated poroelastic beams,and especially,the large deflection mathematical model of the saturated poroelastic Timoshenko beam should be employed when the slenderness ratio of the beam λ30.