An improved ?assumed enhanced displacement gradient? ring-element for finite deformation axisymmetric and torsional problems

Abstract

Analyzing axisymmetric solids under torsional loading the 3d(imensional) problem can always be reduced by one dimension, since the displacement field and the rotation field are independent of the cylindrical (angle) co-ordinate Θ, respectively. For this purpose a four-node ring-element for finite deformation axisymmetric and torsional problems was recently developed and is now going to be up-dated. The original assumption of the enhanced displacement gradient H̃=αi⊗Gi is expanded in two steps according to Simo, Armero and Taylor and to Glaser and Armero, respectively: firstly in defining the additional unknowns (parameters) αi as objects in the material configuration and pushing forward H̃ by (1+U⊗Grad) ∣ξ=0—this provides ‘objectivity’—and secondly in replacing αi⊗Gi by Gi⊗αi. Numerical results of three classical benchmarks, the in-plane torsion test, the copper rod impact and the thermomechanical localization of a rectangular strip are presented. Copyright © 2001 John Wiley & Sons, Ltd.