FINITE-ELEMENT FORMULATION OF HYPERELASTIC PLANE FRAMES SUBJECTED TO NONCONSERVATIVE LOADS

A finite element formulation for finite deformation static analysis of plane hyperelastic frames subjected to nonconservative loads is prese nted. A rubber-like material is considered for which the behaviour in tension and in compression differs substantially. A new proposal for t he strain energy function of rubber at uniaxial stress state is given, convenient for the present deformation analysis. The finite element f ormulation is based on a new variational principle of the Hu-Washizu t ype where exact nonlinear kinematic equations of one-dimensional finit e-strain beam theory are taken into account. The contribution of the s hear deformations to the total potential energy and the initial curvat ure of the beam are neglected. The functional of the variational princ iple is expressed in terms of only one function, the rotation of the c ross-section of the beam. Thus only one function needs to be approxima ted in the functional in the finite element implementation of the vari ational principle. The outstanding accuracy and high efficiency of the method are illustrated by numerical examples. The application of the present method for the analysis of hyperelastic frames subjected to st atic nonconservative forces is shown, and some results for critical lo ads for the dynamic instabilities in the form of flutter are given.