Abstract

A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress isotropic behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperelastic law is considered for the elastic part while for the plastic part a von Mises yield function with non‐linear isotropic hardening is adopted. The element is an extension of a previous similar rotation‐free triangle element based upon an updated Lagrangian formulation with hypoelastic constitutive law. The element termed BST (for basic shell triangle) has been implemented in an explicit (hydro‐) code adequate to simulate sheet‐stamping processes and in an implicit static/dynamic code. Several examples are shown to assess the performance of the present formulation.

Abstract

A methodology for the geometrically nonlinear analysis of orthotropic shells using a rotation-free shell triangular element is developed. The method is based on the computation of the strain and stress fields in the principal fiber orientation of the material. Details of the definition of the fiber orientation in a mesh of triangles and of the general formulation of the orthotropic rotation-free element are given. The accuracy of the formulation is demonstrated in examples of application.

Abstract

The simulation of the contact within shells, with all of its different facets, represents still an open challenge in Computational Mechanics. Despite the effort spent in the development of techniques for the simulation of general contact problems, an all-seasons algorithm applicable to complex shell contact problems is yet to be developed. This work focuses on the solution of the contact between thin shells by using a technique derived from the particle finite element method together with a rotation-free shell triangle. The key concept is to define a discretization of the contact domain (CD) by constructing a finite element mesh of four-noded tetrahedra that describes the potential contact volume. The problem is completed by using an assumed-strain approach to define an elastic contact strain over the CD.

Abstract

This paper is confined to the study of thin shells. The aim is to summarize the different theories used and to examine the assumptions upon which each of them is based. The intention is to show when it is more suitable to use a particular approximation and to indicate the errors it introduces. Beginning with the general deep shell theory, some simplifications are introduced to obtain the shallow shell theories. The special implications of this theory for the finite element method are also examined. Finally the particular case of flat elements is discussed.

Abstract

The problem related to the derivation of conforming deep shell finite elements is examined in the light of the thin shell theory and using the classical Loves strain energy formulation. A family of quadrangular finite elements allowing for variable curvature is developed. It is shown how an exact conformity of the displacements can be ensured in a large number of cases.

Various static and dynamic applications are used to illustrate the advantages of these elements.