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| Large Deflection Analysis of a Saturated Poroelastic Timoshenko Beam |
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Abstract 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 step constant transverse 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 shown in figures. 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 , 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 be employed when the slenderness ratio of the beam .
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Received: 21 February 2011
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Corresponding Authors:
Yang Xiao
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2012, Vol. 33 