Non-Classical Theories of Beams, Plates and Shells (A Review)

The article is an analytical review and is devoted to the problem of constructing non-classical theories of beams, plates and shells, the demand for which is associated with the emergence of new structural materials with properties that do not fully correspond to the hypotheses adopted in constructing classical theories. The presentation is based on the analysis of the problem of reducing the order of elasticity theory equations for thin-walled structural elements and the mathematical and physical methods used for this purpose. The main attention is paid to the correctness and energy consistency of these methods. The presentation is illustrated by examples of specific theories.