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

• Published in: Applied mathematics and mechanics 2007-12, Vol.28 (12), p.1587-1595
• Main Author: 杨骁 王琛
• Format: Article
• Language: English
• Subjects: Cantilever beams; Computational fluid dynamics; Deflection; Fluid flow; Fluid pressure; Mathematical models; Nonlinearity; Porosity; 多孔渗水介质; 大偏转; 弹性板; 轴向扩展; 非线性数学模型
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-007-1205-3

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.