Nonlinear Mathematical Model for Large Deflection of Incompressible Saturated Poroelastic Beams

YANG Xiao; WANG Chen

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(12): 1417-1424

YANG Xiao, WANG Chen. Nonlinear Mathematical Model for Large Deflection of Incompressible Saturated Poroelastic Beams[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1417-1424.

Citation:

YANG Xiao, WANG Chen. Nonlinear Mathematical Model for Large Deflection of Incompressible Saturated Poroelastic Beams[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1417-1424.

Citation:

YANG Xiao, WANG Chen. Nonlinear Mathematical Model for Large Deflection of Incompressible Saturated Poroelastic Beams[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1417-1424.

PDF( 2103 KB)

Nonlinear Mathematical Model for Large Deflection of Incompressible Saturated Poroelastic Beams

YANG Xiao¹,
WANG Chen²

1.
Department of Civil Engineering, Shanghai University, Shanghai 200072, P. R. China;

Received Date: 2006-08-17
Rev Recd Date: 2007-11-05
Publish Date: 2007-12-15

Abstract

Abstract

Nonlinear governing equations were established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, was examined with the Galerkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure were shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam were compared, and the differences between them are revealed. It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory, and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.
- theory of porous medium,
- poroelastic beam,
- large deflection,
- axial diffusion,
- Galerkin truncation method

FullText(HTML)

References(15)

References

[1]	Ehlers W, Markert B. On the viscoelastic behaviour of fluid-saturated porous materials[J].Granular Matter,2000,2(3):153-161. doi: 10.1007/s100359900037
[2]	Schanz M, Cheng A H D. Transient wave propagation in a one-dimensional poroelastic column[J].Acta Mechanica,2000,145(1):1-18. doi: 10.1007/BF01453641
[3]	Leclaire P, Horoshenkov K V. Transverse vibrations of a thin rectangular porous plate saturated by a fluid[J].J Sound Vibration,2001,247(1):1-18. doi: 10.1006/jsvi.2001.3656
[4]	Theodorakopoulos D D, Beskos D E. Flexural vibrations of poroelastic plates[J].Acta Mechanica,1994,103(1/4):191-203. doi: 10.1007/BF01180226
[5]	Brsan M.On the theory of elastic shells made from a material with voids[J].Internat J Solids and Structures,2006,43(10):3106-3123. doi: 10.1016/j.ijsolstr.2005.05.028
[6]	Nowinski J L, Davis C F.The flexural and torsion of bones viewed as anisotropic poroelastic bodies[J].Internat J Engrg Sci,1972,10(12): 1063-1079. doi: 10.1016/0020-7225(72)90026-2
[7]	Zhang D, Cowin S C.Oscillatory bending of a poroelastic beam[J].J Mech Phys Solids,1994,42(10):1575-1599. doi: 10.1016/0022-5096(94)90088-4
[8]	Li L P, Schulgasser K, Cederbaum G. Theory of poroelastic beams with axial diffusion[J].J Mech Phys Solids,1995,43(12):2023-2042. doi: 10.1016/0022-5096(95)00056-O
[9]	Li L P, Schulgasser K, Cederbaum G. Large deflection analysis of poroelastic beams[J].Internat J Non-Linear Mech,1998,33(1):1-14. doi: 10.1016/S0020-7462(97)00003-6
[10]	Cederbaum G, Schulgasser K,Li L P. Interesting behavior patterns of poroelastic beams and columns[J].Internat J Solids Structures,1998,35(34): 4931-4943. doi: 10.1016/S0020-7683(98)00102-4
[11]	Li L P, Cederbaum G, Schulgasser K. A Finite element model for poroelastic beams with axial diffusion[J].Computers and Structures,1999,73(6):595-608. doi: 10.1016/S0045-7949(98)00226-0
[12]	杨骁,李丽. 不可压饱和多孔弹性梁、杆动力响应的数学模型[J]. 固体力学学报, 2006,27(2):159-166.
[13]	de Boer R, Didwania A K. Saturated elastic porous solids: incompressible, compressible and hybrid Binary models[J].Transport in Porous Media,2001,45(3):425-445.
[14]	de Boer R.Theory of Porous Media: Highlights in the Historical Development and Current State[M].Berlin, Heidelberg: Springer-Verlag, 2000.
[15]	Gere J M, Timoshenko S P.Mechanics of Materials[M].second edition. New York: Van Nostrand Reinhold, 1984.