Derivation of a poroelastic elliptic membrane shell model
Derivation of a poroelastic elliptic membrane shell model
复制标题
多孔弹性椭圆膜壳模型的推导
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
J. Tambača
中科院分区：
文献类型：
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作者：
A. Mikelić;J. Tambača
本文对多孔弹性椭圆膜壳的模型进行了推导。三维壳域中的流动和变形由准静态线性孔隙弹性毕奥方程描述。我们考虑壳厚趋于零时的极限，并寻找极限方程。利用Ciarlet、Lods、Miara等人在开创性文章中发展的技术以及Marciniak-Czochra、Mikelić和Tambača对多孔弹性板和弯曲多孔弹性壳方程的严格推导的最新结果，我们给出了线性多孔弹性椭圆膜壳模型的严格推导。重新标度后，相应的速度场和压力场在范数下接近，应力在范数下接近。我们注意到弯曲情况下的主要区别：（i）不再是重新标度的总应力除以标度参数，而是重新标度的总应力本身收敛;（ii）相同的评论适用于孔隙流体压力;（iii）重新标度位移的垂直分量的收敛性恶化。上述差异的结果是有效模型在空间中保持二阶。在球膜壳的情况下，我们证实了泰伯从文献中的结果。
ABSTRACT A derivation of the model for a poroelastic elliptic membrane shell is undertaken. The flow and deformation in a three-dimensional shell domain is described by the quasi-static Biot equations of linear poroelasticity. We consider the limit when the shell thickness goes to zero and look for the limit equations. Using the technique developed in the seminal articles by Ciarlet, Lods, Miara et al.and the recent results on the rigorous derivation of the equations for poroelastic plates and flexural poroelastic shells by Marciniak-Czochra, Mikelić, and Tambača, we present a rigorous derivation of the linear poroelastic elliptic membrane shell model. After rescaling, the corresponding velocity and the pressure field are close in the norm and the stresses in norm. We note the major difference with respect to the flexural case: (i) it is not anymore the rescaled total stress divided by the scaling parameter, but the rescaled total stress itself which converges ; (ii) the same comment applies to the pore fluid pressure; and (iii) there is a deterioration of the convergence for the vertical component of the rescaled displacement. Consequence of the above differences is that the effective model remains of the 2nd order in space. In the case of a spherical membrane shell, we confirm the results by Taber from the literature.