何录武, 聂 磊, 武凯日. 饱和不可压正交各向异性多孔弹性大挠度板的动力弯曲模型[J]. 工程力学, 2009, 26(10): 37-043.
引用本文: 何录武, 聂 磊, 武凯日. 饱和不可压正交各向异性多孔弹性大挠度板的动力弯曲模型[J]. 工程力学, 2009, 26(10): 37-043.
HE Lu-wu, NIE Lei, WU Kai-ri. A DYNAMIC BENDING MODEL FOR LARGE DEFLECTION OF INCOMPRESSIBLE SATURATED ORTHOTROPIC POROELASTIC PLATES[J]. Engineering Mechanics, 2009, 26(10): 37-043.
Citation: HE Lu-wu, NIE Lei, WU Kai-ri. A DYNAMIC BENDING MODEL FOR LARGE DEFLECTION OF INCOMPRESSIBLE SATURATED ORTHOTROPIC POROELASTIC PLATES[J]. Engineering Mechanics, 2009, 26(10): 37-043.

饱和不可压正交各向异性多孔弹性大挠度板的动力弯曲模型

A DYNAMIC BENDING MODEL FOR LARGE DEFLECTION OF INCOMPRESSIBLE SATURATED ORTHOTROPIC POROELASTIC PLATES

  • 摘要: 对于流体饱和不可压正交各向异性多孔弹性板,建立了大挠度弯曲模型,给出了相应的基本控制方程。模型中假设Kirchhoff直法线假定和线性本构关系成立,孔隙流体的运动服从Darcy定理并且仅在板平面内扩散。根据此模型,应用Galerkin截断法数值分析了四边简支透水多孔弹性矩形板在脉冲载荷作用下的非线性拟静态和动力弯曲响应。研究结果表明:大挠度弯曲模型能够反映出流体沿板厚度方向整体排水和吸水特性;当载荷增加到使所产生的挠度较大时,大挠度和小挠度弯曲模型对应结果之间的差别明显,且在拟静态响应中,大挠度弯曲模型下挠度和孔隙流体压力等效弯矩随时间的变化过程中存在有Mandel-Cryer效应,而小挠度弯曲模型下的对应结果不存在此效应。

     

    Abstract: A large deflection bending model is developed for incompressible fluid saturated orthotropic poroelastic plates, and the corresponding basic governing equations are presented. In this model, the Kirchhoff hypotheses and the linear constitutive law are employed. The Darcy’s law is used to describe the fluid flow in pores, which diffusion is in the plate-plane directions only. According to the model, the nonlinear dynamic and quasi-static bending responses of a simply-supported rectangular orthotropic poroelastic plate with permeable conditions, subjected to a step load, are studied with Galerkin truncation method. The numerical results reveal the global drain and suction processes of fluid along the thickness direction of the plate. When the loading increases and the plate deflection thusly produced is larger, the difference between the results obtained respectively by the small and larger deflection bending models is obvious, and for quasi-static bending problem, the Mandel-Cryer effect exists in the evolutions of the plate deflection and pore pressure moment resultant on the larger deflection bending model whereas this effect never appears on the small deflection bending model.

     

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