不可压饱和多孔弹性梁的大挠度非线性数学模型

Nonlinear Mathematical Model for Large Deflection of Incompressible Saturated Poroelastic Beams

在孔隙流体仅存在沿梁轴线方向扩散的假定下,建立了微观不可压饱和多孔弹性梁大挠度问题的非线性数学模型.利用Galerkin截断法,研究了固定端不可渗透、自由端可渗透的饱和多孔弹性悬臂梁在自由端突加集中载荷作用下的非线性弯曲,得到了梁骨架的挠度、弯矩以及孔隙流体压力等效力偶等的时间响应和沿轴线的分布.比较了大挠度非线性和小挠度线性理论的结果,揭示了两者间的差异.研究发现大挠度理论的结果小于相应的小挠度理论结果,并且,大挠度理论的结果趋于其稳态值的时间小于相应的小挠度理论结果趋于其稳态值的时间.

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 impemleable and free end permeable, subjected to a suddenly applied constant concenmated 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, aad the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.