简支饱和多孔弹性梁的非线性弯曲

基于饱和多孔介质理论和弹性梁的大挠度弯曲假设,在多孔弹性梁轴线不可伸长,孔隙流体仅沿轴向方向扩散的限制下,建立了微观不可压饱和多孔弹性梁大挠度拟静态响应的一维非线性数学模型.在此基础上,利用Galerkin截断法,分析了两端可渗透的简支多孔弹性梁在突加横向均布载荷作用下的非线性弯曲,给出了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶随时间的响应曲线.数值结果表明:当载荷较小时,大挠度非线性与小挠度线性理论的结果相差很小,而当载荷较大时,非线性大挠度理论的结果小于相应线性小挠度理论的结果,并且这种差异随着载荷的增大而增大.同时,在载荷突加于梁上时,多孔弹性梁骨架起初不变形,孔隙流体压力等效力偶由零突增为非零,其值与外载荷保持平衡.随着时间的增加,梁的挠度增加,等效力偶逐渐减小为零,最终多孔梁骨架承担全部的外载荷.

Nonlinear Bending of Simply Supported Saturated Poroelastic Beam

Based on the theory of porous media and the hypothesis of large deflection of slender beams,one dimensional nonlinear mathematical model was presented for quasi-static large deflection of incompressible fluid saturated poroelastic beams under constraint that the axis line of poroelastic beam doesn't elongate and the diffusion of pore fluid is only in the axial direction of the deformed beams.The nonlinear bending of a simply supported poroelastic beam with two ends permeable,subjected to a suddenly applied constant transverse load,was examined with Galerkin truncation method.The curves of deflections and bending moments of beam skeleton and the equivalent couples of pore fluid pressures were shown in figures.It shows that there are little differences between the results of large deflection and small deflection theories when the load is small,and the results of nonlinear large deflection theory are smaller than those of linear small deflection theory when the load is large.The differences between them become more evident as the load increases.Furthermore,at the time when the load is suddenly applied to the poroelastic beam,the deformation of beam skeleton does not occur instantaneously,and the equivalent couple of pore fluid pressure increases suddenly from zero to a value,which keeps equilibrium of the poroelastic beam with external load.With the time increasing,the deformation of the poroelastic beam increases,and the equivalent couple decreases generally to zero,and finally the poroelastic beam skeleton takes the external load wholly.