Paper Info
Title
Derivation of a Poroelastic Flexural Shell Model
Abstract
AbstractIn this paper we investigate the limit behavior of the solution to quasi-static Biot equations in thin poroelastic flexural shells as the thickness of the shell tends to zero and extend the results obtained for the poroelastic plate by Marciniak-Czochra and Mikelicź in [Arch. Ration. Mech. Anal., 215 (2015), pp. 1035--1062]. We choose Terzaghi's time corresponding to the shell thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure, and total poroelastic stress to the solution of the new class of shell equations. The derived bending equation is coupled with the pressure equation, and it contains the bending moment due to the variation in pore pressure across the shell thickness. The effective pressure equation is parabolic only in the normal direction. As an additional term it contains the time derivative of the middle-surface flexural strain. Derivation of the model presents an extension of the results on the derivation of classical linear elastic shells by Ciarlet and collaborators to the poroelastic shell case. The new technical points include determination of the $2\times 2$ strain matrix, independent of the vertical direction, in the limit of the rescaled strains and identification of the pressure equation. This term is not necessary to be determined in order to derive the classical flexural shell model.
Year
DOI
Venue
2016
10.1137/15M1021556
Periodicals
Keywords
Field
DocType
thin poroelastic shell,Biot's quasi-static equations,bending-flow coupling,higher order degenerate elliptic-parabolic systems,asymptotic methods
Bending moment,Flexural strength,Mathematical analysis,Bending,Time derivative,Terzaghi's principle,Linear elasticity,Poromechanics,Mathematics,Biot number
Journal
Volume
Issue
ISSN
14
1
1540-3459
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Andro Mikelic110921.66
Josip Tambaca2214.87