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Isogeometric finite element analysis of poroelasticity

Authors


Correspondence to: René de Borst, School of Engineering, University of Glasgow, Oakfield Avenue, Rankine Building, Glasgow G12 8LT, U.K.

E-mail: Rene.DeBorst@glasgow.ac.uk

SUMMARY

We present an alternative numerical approach for predicting the behaviour of a deformable fluid-saturated porous medium. The conventional finite element technology is replaced by isogeometric analysis that uses non-uniform rational B-splines. The ability of these functions to provide higher-order continuity and to exactly represent complex geometries makes isogeometric analysis a suitable candidate for accurately modeling a poroelastic medium. After some preliminaries regarding the formulation of isogeometric finite elements using Bézier extraction and a concise outline of poroelasticity theory, we describe how isogeometric finite elements can be used for a mixed formulation that results in case of a porous medium. The manuscript concludes by one-dimensional and two-dimensional examples, which demonstrate the superiority of the results of isogeometric finite element analysis in terms of the smoothness of the results compared with conventional finite element analysis and suggest that the requirement on the minimum time step for consolidation problems can be mitigated using interpolation functions that possess a higher-order continuity. Copyright © 2013 John Wiley & Sons, Ltd.

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