Triangular finite element based on nonlinear six-parameter shell: multiple integration points verification

Abstract

This work consists of a review of a triangular Finite Element based on a six-parameter shell, constructed with initially flat elements and only the addition of stiffness associated to the drilling D.O.F. as an artificial numerical factor, and verification of the necessary amount of integration points along the thickness and the surface to perform numerical integration and achieve equilibrium. With methodology based on integration points sets combinations, with 11 surface and 10 thickness gauss points sets, this paper determines if the surface integration points set proposed by the original authors is the minimum necessary to have a good accuracy of numerical results. The present work analyses the minimum number of integration points along the thickness, not mentioned by the original authors. The results are verified based in the displacement field. A Ciarlet-Simo neo-Hookean hyperelastic material is considered in the constitutive equations. Rotations are treated by Euler-Rodrigues formula in a pure lagrangian way. The results show that the surface set of integration points suggested by the original authors is adequate and that integration along the thickness requires only 2 points to correctly represent the displacement field.