饱和不可压多孔弹性板在面内扩散下的动力弯曲理论  

A DYNAMIC BENDING MODEL OF INCOMPRESSIBLE SATURATED POROELASTIC PLATES WITH IN-PLANE DIFFUSION

作　　者：何录武[1] 杨骁[2] 

机构地区：[1]华东理工大学机械与动力工程学院,上海200237 [2]上海大学土木工程系,上海市应用数学和力学研究所,上海200444

出　　处：《固体力学学报》2008年第2期121-128,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10272070);上海市浦江人才计划(07pj14073)资助

摘　　要：根据多孔介质理论,在Kirchhoff假定和小变形前提下,针对流体的面内扩散情形,建立了饱和不可压多孔弹性板动力弯曲的数学模型.然后,利用Fourier展开法研究分析了阶梯载荷作用下四边简支透水矩形多孔弹性板的拟静定和动力弯曲响应,考察了不同参数下多孔弹性板的挠度、孔隙流体压力等效弯矩和固相有效应力等效弯矩的变化规律和特征.同时,通过基于Biot三维固结理论所建立的动力弯曲模型,比较了可压与不可压情况下其结果的差异.Based on the theory of porous media, with the hypothesis of Kirchhoff and small deformation, a dynamic bending mathematical model of incompressible saturated poroelastic plates with in-plane diffusion is established. The dynamic and quasi-static bending responses of a rectangular incompressible saturated poroelastic plate with simply-support at the four permeable edges, subjected to a step load, are investigated by the Fourier series method. Numerical results reveal the dynamical behaviors of the equiva- lent moment of the pore pressure and effective stress moment in the incompressible saturated poroelastic plates. Finally, the difference between the compressible （based on the Biot＇s theory） and incompressible saturated poroelastic plate is discussed, which is usually negligible when the compressibility of solid and fluid are very small.

关 键 词：多孔介质理论 饱和不可压多孔弹性板 动力弯曲 拟静定弯曲 BIOT理论 

分 类 号：O357.3[理学—流体力学] TU323.3[理学—力学]