A finite element method for geometrically nonlinear large displacement problems in thin, elastic plates and shells

Abstract

A finite element method is presented for geometrically nonlinear large displacement problems in thin, elastic plates and shells of arbitrary shape and boundary conditions subject to externally applied concentrated or distributed loading. The initially flat plate or curved shell is idealized as an assemblage of flat, triangular plate, finite elements representing both membrane and flexural properties. The \u27geometrical\u27 stiffness of the resulting eighteen degree-of-freedom triangular element is derived from a purely geometrical standpoint. This stiffness in conjunction with the standard small displacement \u27elastic\u27 stiffness is used in the linear-incremental approach to obtain numerical solutions to the large displacement problem. Only stable equilibrium configurations are considered and engineering strains are assumed to remain small. Four examples are presented to demonstrate the validity and versatility of the method and to point out its deficiencies --Abstract, page ii