Linear Theory Of Elastic Shells Research Articles

On a Variational Theorem in Elasticity and Its Application to Shell Theory

After stating a variational theorem which is a further generalization of known variational theorems and which has as its Euler equations all of the field equations and the boundary conditions of classical linear three-dimensional elasticity, the remainder of the paper deals with its application to shell theory. A new characterization of the basic system of field equations and the boundary conditions of the linear theory of elastic shells is derived which includes the effect of transverse shear deformation and involves only symmetric resultants and symmetric shell-strain measures. These results are of special significance in relation to those of a number of recent investigations in shell theory under the Kirchhoff-Love hypothesis in which the boundary-value problem of shell theory is recast in terms of symmetric (but not necessarily the same) variables.

A new derivation of the general equations of elastic shells

This paper is concerned with a new derivation of the general equations of the linear theory of elastic shells under the Kirchhoff-Love hypothesis. The entire boundary-value problem of shell theory is recast in terms of new variables for the strain measures as well as the stress and couple resultants. Particular attention is paid to an exact derivation of the constitutive equations and their first approximations which meet all invariance requirements. The natural boundary conditions for stress and couple resultants and all field equations consisting of compatibility, equilibrium and the constitutive equations (or their first approximations) involve only symmetric tensors and are, moreover, remarkably free of the anti-symmetric parts of both the middle surface strains and the couple resultants.