The Strain-Energy Expression for Thin Elastic Shells

A strain-energy expression is derived for thin isotropic elastic shells in terms of the displacements of the middle surface of the shell. This expression is confined to small-deflection theory, and the condition of plane stress previously used in the theory of thin shells is retained. A simplified expression is also obtained by the introduction of the Kirchhoff-Love hypothesis, and the relative merits of these two expressions are discussed. The strain-energy expression is applied to the thin circular cylinder, and the result is compared with various strain-energy expressions developed by previous authors.