Non-classical theories of beams, plates and shells (review)

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Abstract

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

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About the authors

V. V. Vasiliev

Central Research Institute of Special Engineering

Author for correspondence.
Email: vvvas@dol.ru
Russian Federation, Khotkovo

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2. Fig. 1. Cantilever beam.

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3. Fig. 2. Layered beam.

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4. Fig. 3. Deformation of a shell consisting of layers with reinforcement angles ±φ.

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