A total lagrangian formulation for the geometrically non-linear analysis of shells

Published in Flexible Shells, Hinton E. y Owen D.R.J. (Eds.), Pineridge Press, 1984

Abstract

The analysis of structures subjected to large displacements by means of the finite element method has attracted the attention of many researchers in recent years and different publications have been reported in the literature [1-8] In this work the authors suggest an alternative finite element formulation for the analysis of shells process of the structure is defined via a total Lagrangian approach. Stresses and strain over the shell surface are defined using a local set of Cartesian axes based on the principal curvature directions of the shell middle surface. This allows to obtain useful explicit expressions of the finite element matrices in a simple manner. Additionally, normal to the midsurface before deformation are assumed to remain straight but not necessarily to the midsurface after deformation, thus allowing for shear deformation effects. Finally, it is worth pointing out that no restrictions are made on the magnitude of the curvatures. This is of special interest for the analysis of non-shallow shells using a small number of elements. The formulation uses two dimensional finite elements for the analysis of 3-D shells. The discretization over the shell thickness is eliminates using what is usually known as “degenerated element technique” [2,4]. This allows for a substantial reduction in the number of variables and eliminates the possibility of ill-conditions of the element matrices which takes place when using 3-D elements and the thickness of the shell is small. In the first part of this work the formulation for 3-D shells is presented. Then a series of examples of shells undergoing large displacements are presented.