A finite-element approach in stream-tube method for solving fluid and solid mechanics problems Amine Ammar, Jean-Robert Clermont * Laboratoire de Rh eologie, UMR 5520 CNRS, Universit e Joseph-Fourier, Institut National Polytechnique de Grenoble, Domaine Universitaire, BP 53, 38041 Grenoble Cedex 9, France Available online 10 May 2004 Abstract This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Domain transformation; Variational formulation; Finite elements; Elasticity; Fluid flow 1. Introduction In the recent years, significant progress has been made on computational possibilities for solid and fluid mechanics problems. The methods generally involve primary unknowns directly related to the kinematics and the pressure. In contrast to these approaches, the so-called ‘‘stream-tube method’’ (STM) (Clermont, 1988; B ereaux and Clermont, 1995) uses a reference computational domain X  where the streamlines are parallel and straight. The unknown to be considered is the unknown transformation between the reference domain X  and the physical domain X. The main purpose of this paper is to present, with the aid of variational concepts defined for finite-element problems (e.g. Zienkiewicz, 1977), theoretical information to help in finding numerical approximate solu- tions in the fields of solid and fluid mechanics, with the stream-tube method (STM). The transformation between X  and X, assumed to be one-to-one, implies that the streamlines define simply-connected regions. Mechanics Research Communications 32 (2005) 65–73 www.elsevier.com/locate/mechrescom MECHANICS RESEARCH COMMUNICATIONS * Corresponding author. Tel.: +33-4-76825292; fax: +33-4-76825164. E-mail addresses: ammar@ujf-grenoble.fr (A. Ammar), clermont@ujf-grenoble.fr (J.-R. Clermont). 0093-6413/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechrescom.2004.04.002 http://www.DownloadEbook.ir http://www.GigaPaper.ir Contact Us: Info@DownloadPaper.ir http://www.DownloadPaper.ir http://www.DownloadBooks.ir http://www.DownloadEbooks.ir http://www.FindPdf.ir http://www.DownloadMaghale.ir http://www.DownloadEbook.ir http://www.DownloadEbook.ir http://www.GigaPaper.ir Contact Us: Info@DownloadPaper.ir http://www.DownloadPaper.ir http://www.DownloadBooks.ir http://www.DownloadEbooks.ir http://www.FindPdf.ir http://www.DownloadMaghale.ir http://www.DownloadEbook.ir