轴向扩散不可压饱和多孔弹性梁的拟静态弯曲  

QUASI-STATIC BENDING OF INCOMPRESSIBLE SATURATED POROELASTIC BEAMS WITH THE AXIAL 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》2007年第4期393-398,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(No.10272070);上海市重点学科建设项目(No.Y0103)资助

摘　　要：建立了横观各向同性不可压饱和多孔弹性梁拟静态弯曲的数学模型,并给出了一般的求解方法。作为例子,研究了端部不同渗透条件对梁中点承受突加常集中载荷作用的饱和多孔悬臂梁拟静态弯曲的影响,给出了挠度和孔隙流体压力等效力偶沿梁轴线的分布以及随时间的响应曲线。结果表面:端部渗透条件对饱和多孔弹性梁的弯曲行为有显著的影响,梁的弯曲挠度既可随时间单调递增、亦可单调递减,其性态依赖于梁端部的渗透条件。同时发现不同于经典单相弹性梁,由于孔隙流体压力的作用,不承受载荷作用的梁段亦发生弯曲,并且Man-del-Cryer效应亦存在于不可压饱和多孔弹性梁的拟静态响应中,这些结果有助于揭示传热管道、植物根茎等力学行为的机理。A mathematical model for the quasi-static bending of an incompressible saturated porous beam is established and solved. As examples, the bendings of cantilever beams subjected to a concentrated step load in the middle of the beam are investigated, while different diffusion couditions are prescribed at the beam ends. The deflections, the bending moments of the solid skeleton and the equivalent couples of the pore pressures are shown schematically. It is shown that the behavior of the saturated poroelastic beams depends greatly on the diffusion conditions at the beam ends, whose deflection may increase or decrease monotonously with time with different end diffusion condition. Different from the classical singlephase beam theory, a poroelastic beam may also take place deflection due to the presence of pore pressure, even if there is no external load acted on the beam. Furthermore, it is found that the Mandel-Cryer effect also exists in incompressible saturated poroelastic beams. These results are helpful for recognizing the deformation mechanisms of plant roots and heat transfer ducts.

关 键 词：饱和多孔介质理论 多孔弹性梁的拟静态弯曲 变量分离法 Mandel—Cryer效应 

分 类 号：O343[理学—固体力学]