Approximate Displacements of Exact Membrane Actions in a Shell Triangular Element

Abstract

Exact stress functions which satisfy the homogeneous differential equations of equilibrium for membrane actions are available from the static geometric analogue of previously derived exact displacements of inextensional bending. For finite element evaluation it is necessary to know the displacements (and rotations) caused by these membrane actions. A method of calculating approximate displacements is described which uses the principle of minimum potential energy. Results are given for specimen triangular elements with positive, zero and negative Gaussian curvatures. A listing is appended of a Fortran computer program which allows calculation of these approximate displacements, rotations and other physical quantities for other element shapes.