Two-Surface Approach to the Derivation of Anisotropic Shallow-Shell Theory Equations—Part 1: Transverse Loading

Abstract

The governing differential equations describing the behaviour of thin, elastic shallow shells having anisotropic material properties and subjected to transverse loading are formulated on the basis of the two-surface shell theory. Apart from its elegance, when compared to existing derivations, the present approach also has clear didactic advantages. The latter include a qualitative study of the shell equations, the elucidation of the meanings of the various quantities in the governing expressions in simple, physical terms, and, finally, the identification of the invariant terms in the field equations in an explicit manner. These advantages stem from the use, in the present scheme, of the two-surface notion of separable bending and stretching effects, and of the Gaussian curvature change as the prime kinematic variable.