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This and the next 2 images are from:
M. Bischoff (1), W. A. Wall (2), K.-U. Bletzinger (1) and E. Ramm (3)
(1) Lehrstuhl fuer Statik, TU Muenchen, Muenchen, Germany
(2) Lehrstuhl fuer Numerische Mechanik, TU Muenchen, Garching, Germany
(3) Institut fuer Baustatik, Universitaet Stuttgart, Stuttgart, Germany
“Models and finite elements for thin-walled structures”, Chapter 3 in Encyclopedia of Computational Mechanics, Edited by Erwin Stein, Rene de Borst and Thomas J.R. Hughes. Volume 2: Solids, Structures and Coupled Problems, John Wiley & Sons, 2004
PARTIAL ABSTRACT/INTRODUCTION: This paper concentrates on the mathematical modeling of nonlinear mechanics of thin-walled structures in view of associated finite element formulations. This means that we will primarily focus on formulations for structural models as prerequisite for derivation of finite elements, rather than specific ‘elementology’. The main emphasis is put on shells, including the special case of flat plates, turning into shells anyway in the nonlinear regime. The derivations are kept as general as possible, including thick and layered shells (laminated or sandwich structures), as well as anisotropic and inhomogeneous materials from the outset. Throughout Section 4.4, we will specify the corresponding restrictions and assumptions to obtain the classical 5-parameter shell formulation predominantly used for standard shell problems in the context of finite element analysis. In most part of the text, we restrict ourselves to static problems within the framework of geometrically nonlinear elasticity, neglecting time dependence and inertia effects. The extension into the materially nonlinear area is a straightforward procedure. It is believed that this does not mean a too strong restriction in view of the underlying motivation. It is a well cultivated tradition to let review articles start with the remark that a complete overview of existing methods and appropriate literature is utterly impossible. The multitude of existing concepts, methods, and implementations, as well as scientific papers, text books, and yet other review articles would effectively prohibit an exhaustive overview…
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