The Theory of Simple Elastic Shells

At present the shell theory find out new branches of applications. Biological membranes, thin polymeric films and thin structures made from shape memory materials may be pointed out as examples . In addition, the manufacturing technology of shells leads to significant changes of the material properties. As a result the conventional variants of the shell theory, based on the derivation of the basic equations from the 3D-theory of elasticity, cannot be used. The effective elastic moduli of the shell must be found directly for the shell structure. That means that we have to use the direct method for the formulation of the shell theory. The main idea of the direct approach is the introduction of a 2D-continuum with some physical properties. The basic laws of mechanics and thermodynamics are applied directly to this 2D-continuum. The main advantage of the direct approach is the possibility to obtain quite strict equations.