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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping, Z. Bittnar
Chapter 1

On the Finite Element Analysis of Shells and their Full Interaction with Navier-Stokes Fluid Flows

K.J. Bathe+, J.F. Hiller+ and H. Zhang*

+Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
*ADINA R&D, Inc., Watertown, Massachusetts, United States of America

Full Bibliographic Reference for this chapter
K.J. Bathe, J.F. Hiller, H. Zhang, "On the Finite Element Analysis of Shells and their Full Interaction with Navier-Stokes Fluid Flows", in B.H.V. Topping, Z. Bittnar, (Editors), "Computational Structures Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 1, pp 1-31, 2002. doi:10.4203/csets.7.1
Keywords: shell structures, Navier-Stokes fluids, fluid flows with structural interactions.

The objective in this paper is to present an overview of some of our latest research and developments in the finite element analysis of shells, Navier-Stokes fluid flows and the full interaction of these flows with general shell structures.

In the area of shell analysis, we have studied some generic physical behaviours of shells with specific emphasis on boundary and internal layers as the thickness of the shell decreases. Furthermore, we have studied how best to evaluate general finite element schemes when considering the variety of shell behaviours. To demonstrate the developments, a membrane-dominated problem and a bending-dominated problem have been solved. When proper care is taken in meshing boundary and internal layers, optimal convergence rates to the reference solutions are observed with the MITC4 shell element.

In the area of fluid flow analysis, we are developing a new solution approach - a flow-condition-based interpolation, FCBI, finite element scheme - to solve high Reynolds number incompressible fluid flows. This scheme has a number of advantages as discussed and demonstrated in the paper, including that conservation of mass and momentum is satisfied locally and no artificial parameter is used for stabilization. The procedure has been developed for the solution of fluid flows fully coupled with shells and other structures. The capability is illustrated by the solution of some example problems.

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