On the Direct Kinematic Theory of Thin Elastic Shells

Abstract

<p> This thesis consists of a rigorous development of the direct kinematic, small-displacement theory of thin elastic shells. The theory is developed, so as to facilitate a derivation of the equations of compatibility of middle-surface strains. These equations are developed by the kinematic approach and it is shown that this produces a more coherent relation of such equations to the general theory of shells, as no special techniques are required. The equations of compatibility are developed again by the formal Saint-Venant method; this development serves to substantiate the validity of the kinematic approach. At the same time, it provides many useful identities which are then employed as transformation relations, in order to compare the various forms of compatibility equations, as developed by other authors. A general comparison of kinematic shell theory with other nonkinematic methods is undertaken, and appended to the main discussion.</p>