An investigation into the approximation problems in thin shell finite elements.

Despite large amounts of numerical and theoretical work on the finite element method one application, that of shells, is still not adequately understood. Shell elements are significantly less efficient than elements for other applications. Not surprisingly, the curvature function is the primary contributor to the inefficiencies and therefore most of the thesis is concerned with it. Numerous curved beam formulations are studied for an initial numerical assessment of the problem. From an examination of the results and element strain expressions it is possible to identify how curvatures are responsible for the poor accuracy. More rigorous mathematical investigations follow and finally methods of improving the performance of elements with curvature are considered.