A total Lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part I. Two‐dimensional problems: Shell and plate structures

Published in Int. Journal for Numerical Methods in Engineering Vol. 20 (12), pp. 2253-2281, 1984
doi: 10.1002/nme.1620201208

Abstract

A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co‐ordinate system, based on the shell principal curvature directions, for the evaluation of strains and stresses. A series of examples of nonlinear analysis of shell and plate structures is given.