Finite element analysis of tension structures

Abstract

A new iterative scheme is proposed for finite element analysis of wrinkling or tension structures. The scheme is based upon the observation that there exists an invariant relationship, due to the uniaxial tensile stress state of wrinkling, between some of the strain components referred to the local frame aligned with wrinkling in a region where wrinkling occurs. This enables us to update the stress state and the internal forces correctly taking into account the existence of wrinkling. This scheme is to be applicable to an anisotropic membrane as well as an isotropic membrane. Moreover, we categorize wrinkling criteria into three types, discuss the effectiveness or the difficulties of each criterion. For the static analysis, the finite element implementation of the scheme is straightforward and simple, and only minor modifications of the existing total Lagrangian finite element codes for membranes are needed. The validity of the scheme is demonstrated via numerical examples for the torsion of a membrane and the quasi-static inflation of an automotive airbag, both made of isotropic or anisotropic elastic membranes. The examples suggest that the present iterative scheme has a good convergence characteristic even for a large loading step. For the dynamic analysis, we also implement the scheme into a dynamic finite element analysis, which is based on a Total Lagrangian formulation. The application of the scheme for dynamic analysis is very simple as for static analysis. We demonstrate the validity of the scheme through the example of the inflation of a circular airbag of which a fabric is modeled as an orthotropic material. An explicit central difference scheme is used to integrate the resulting nonlinear discrete equations of motion. Nagtegaal‘s contact algorithm is used to prevent the penetration of two contacting surfaces: the back plane of an airbag and a rigid plane representing a steering wheel. Moreover we also discuss the contact-impact characteristics for a...