Abstract
We obtain elasticity equations of higher (in the general case, infinite) order than the equations of the classical theory. In contrast to the numerous known versions of the nonclassical theory (Cosserat, nonsymmetric, microstructure, micropolar, multipolar, and gradient), which also result in higher-order equations and contain elasticity relations for traditional and couple stresses with a large number of elastic constants, our theory, regardless of the order of the equations, contains only one additional constant, which can be expressed in terms of the microstructure parameter of the medium. The basic equations of the generalized theory are presented for one-, two-, and three-dimensional problems; these equations take into account the stress gradients and can be written in terms of generalized stresses, strains, and displacements. A boundary value problem that does not require the introduction of couple stresses is stated for the generalized theory of elasticity.
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Original Russian Text © V.V. Vasil’ev, S.A. Lurie, 2015, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2015, No. 4, pp. 16–27.
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Vasil’ev, V.V., Lurie, S.A. Generalized theory of elasticity. Mech. Solids 50, 379–388 (2015). https://doi.org/10.3103/S0025654415040032
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DOI: https://doi.org/10.3103/S0025654415040032