Theoretical Formulation of Finite-Element Methods in Linear-Elastic Analysis of General Shells∗

A systematic classification of the variational functional whose stationarity conditions (Euler equations) can be used alternately to solve for the various unknowns in a boundary-value problem in linear-shell theory is made. The application of these alternate variational principles to a finite-element assembly of a shell and thus, the development of the properties of an individual discrete element are studied in detail. A classification of the finite-element methods, formulated from the variational principles by systematically relaxing the continuity requirements at the interelement boundaries of adjoining discrete elements is made.