轴向扩散下简支饱和多孔弹性梁的大挠度分析  

LARGE DEFLECTION ANALYSIS OF SIMPLY SUPPORTED SATURATED POROELASTIC BEAM

作　　者：杨骁[1] 李丽[1] 

机构地区：[1]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3期313-317,共5页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10272070);上海市重点学科建设项目(Y0103)资助

摘　　要：基于多孔介质理论和弹性梁的大挠度理论,并考虑轴向变形,在孔隙流体仅沿轴向扩散的假设下,建立了微观不可压饱和多孔弹性梁大挠度弯曲变形的一维非线性数学模型.在此基础上,忽略饱和多孔弹性梁的轴向应变,并利用Galerkin截断法,研究了两端可渗透的简支饱和多孔弹性梁在突加横向均布载荷作用下的拟静态弯曲,给出了饱和多孔梁弯曲时挠度、弯矩和轴力以及孔隙流体压力等效力偶等沿轴线的分布曲线.揭示了大挠度非线性和小挠度线性模型的结果差异,指出大挠度非线性模型的结果小于相应小挠度线性模型的结果,并且这种差异随着载荷的增大而增大.计算表明:当无量纲载荷参数q>5时,应该采用大挠度非线性数学模型进行研究.Based on the theory of porous media and the large deflection theory of slender beams, with consideration of the effect of axial strain, a one-dimensional nonlinear mathematical model is presented for large deflection bending of an incompressible fluid-saturated poroelastic beam with assuming that the pore fluid diffuses only in the axial direction. Then, the quasi-static nonlinear bending of a simply supported saturated poroelastic beam with two ends permeable, subjected to a suddenly applied constant transverse load, is examined with the Galerkin truncation method. The distribution laws of deflections, bending moments, axial force and the equivalent couples of the pore fluid pressure along the beam are shown numerically. Comparing the results obtained from the large deflection analysis with those from the small deflection theory, it is found that the results of the former are smaller than those of the latter, which implies that the large deflection model should be employed, when the dimensionless load parameter q is larger than five.

关 键 词：多孔介质 饱和多孔弹性梁 大挠度 轴向扩散 Galerkin截断法 

分 类 号：O343[理学—固体力学]