The role of bending in the finite element analysis of thin shells

Abstract

The role of bending in the finite element analysis of problems in the linear theory of thin shells is examined through an in-depth study of the behavior of a vehicle finite element. The chosen element is the very simple combined constant strain and constant bending moment flat triangle. It emerges that this vehicle element is a superb performer and the examination of its behaviour reveals that there are two quite different roles for the bending freedoms. One role concerns inextensional bending movements which extend over the whole model. The other role concerns local rotational movements which accompany the curvature changes of inextensional bending and of edge effect. Extensive numerical comparisons of demonstration inextensional bending movements are made against solutions obtained from the classical theory for shells which are very deep and which have strongly negative Gaussian curvature. Comparison of edge effect concerns a circular cylindrical thin shell. The paper concludes by giving details of a rudimentary matrix procedure which is currently under development and which is intended for use in the preliminary assessment of thin shell finite element models.