Shells with thickness distension

A deductive approach to shell theory is presented, within which a shell is regarded as a constrained three-dimensional continuum with special body structure: more precisely, admissible deformations are given a restricted form, presumed to be consistent with the special shape and partitionability of a shell-like body. In addition to the standard balance equations of forces and torques, an extra balance equation is derived, allowing for a description of dilatation or contraction in the thickness dimension. As an illustrative application, the free oscillations of linearly elastic plates ± in particular, thickness±distension waves ± are studied