A nonlinear mathematical model for large deflection of incompressible saturated poroelastic beams  

作　　者：杨骁 王琛 

机构地区：[1]Department of Civil Engineering,Shanghai University [2]Shanghai Institute of Applied Mathematics and Mechanics

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第12期1587-1595,共9页应用数学和力学（英文版）

基　　金：the National Natural Science Foundation of China(No.10272070);Shanghai Leading Academic Discipline Project(No.Y0103)

摘　　要：Nonlinear governing equations are 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 flee end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Gaierkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are 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.Nonlinear governing equations are 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 flee end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Gaierkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are 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.

关 键 词：theory of porous media poroelastic beam large deflection axial diffusion Galerkin truncation method 

分 类 号：O357.3[理学—流体力学]