A mixed finite element for shell model with free edge boundary conditions. I: The mixed variational formulation. II: The numerical scheme
type: Item
instance of: scholarly article
title: A mixed finite element for shell model with free edge boundary conditions. I: The mixed variational formulation. II: The numerical scheme
zbMATH Open document ID: 0852.73059
DOI: 10.1016/0045-7825(94)00676-E
author: Philippe Destuynder
author: M. Salaun
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1996-11-24T00:00:00Z
review text: After a very brief recall on general shell theory, we construct a mixed variational formulation based on the introduction of a new unknown: the rotation of the normal to the medium surface. In Koiter shell theory (for instance), this rotation can be expressed with respect to the three components of the displacement field of the medium surface and their derivatives. The Lagrange multiplier corresponding to this relation (known as the Kirchhoff-Love kinematical assumption), is also introduced as an independent unknown. There are two main difficulties: one is due to the differential geometry of surfaces and is rather technical; the other is to define correctly the dual space for the Kirchhoff-Love relation. From the mixed variational formulation suggested in Part I, we construct a finite element scheme. Then, a mathematical justification concerning the error estimate is developed. The most important point is to justify two compatibility conditions between the approximation of the kinematics and the stresses. Because of the structure of the shell operator they are not obvious at all, and several restrictions on the mesh are necessary. Therefore, the classical result known in fluid mechanics for Stokes equations cannot be applied directly.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 881052
zbMATH Keywords: rotation of normal to medium surface
zbMATH Keywords: Lagrange multiplier
zbMATH Keywords: Kirchhoff-Love kinematical assumption
zbMATH Keywords: error estimate
MaRDI profile type: Publication
cites work: A formulation of general shell elements—the use of mixed interpolation of tensorial components
cites work: Q3718273
cites work: A study of three-node triangular plate bending elements
cites work: Shear and membrane locking in curved \(C^ 0\) elements
cites work: Transverse shear oscillations in four-node quadrilateral plate elements
cites work: Q4128127
cites work: Numerical Approximation of Mindlin-Reissner Plates
cites work: Q4105995
cites work: Q5538494
cites work: Some numerical aspects of mixed finite elements for bending plates
cites work: A new finite element scheme for bending plates
cites work: An analysis of a mixed finite element method for the Navier-Stokes equations
cites work: A simple and efficient finite element for plate bending
cites work: Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element
cites work: Studies in plate flexure. I: A mixed finite element formulation for Reissner-Mindlin plate theory: Uniform convergence of all higher-order spaces
cites work: Thin shell theory. New Trends and applications
cites work: A simple quadrilateral shell element
cites work: Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates
cites work: Q4206464
cites work: Q4192429
description: scientific article; zbMATH DE number 881052