A mixed formulation for general triangular isoparametric shell elements based on the degenerated solid approach

Abstract

A mixed formulation to construct general shell elements based on the degenerated solid approach is presented. This mixed formulation can be understood as a modification of the discrete potential energy of the shell in which the membrane and shear energy terms are obtained as a combination of the usual terms, i.e., directly obtained from the displacement and geometry interpolation assumptions, and membrane and shear terms obtained from assumed strain fields. This energy splitting idea was first introduced in the context of the Naghdi shell theory by Arnold and Brezzi. This mixed formulation is used to study quadratic general triangular shell elements based on the degenerated solid approach. Although considerable success has been achieved in the formulation of reliable, free of locking, general quadrilateral shell elements, the attempts of formulating general triangular shell elements have not yet produced an element that satisfies the locking free requirements. Therefore, there is a great interest in investigating new approaches, as the one discussed in this paper, that can lead to triangular elements that do not suffer from locking difficulties. We present in this paper the formulation of specific elements and their numerical assessment through the use of well established benchmark shell problems.