Generalization of Plate Finite Elements to Shells

TLDR: In this paper, a technique for finding the finite-element equations (including geometric nonlinearity) for a curved shell using Marguerre's strain-displacement relations is described.

Abstract: A technique is described for finding the finite-element equations (including geometric nonlinearity) for a curved shell using Marguerre’s strain-displacement relations. Both the displacements and the shell geometry are interpolated by arbitrary plate functions. Strain-energy tensors are developed which yield the stiffness equations through application of an energy principle. An automated method for explicitly generating the stiffness terms is presented, and applied to give several third and fifth order triangular elements of nonconstant curvature. Applicability is analyzed for both shallow and deep shells, and numerical results are given for a shallow conoid problem.