The method of boundary states in the solution of the second fundamental problem of the theory of anisotropic elasticity with mass forces

D. A. Ivanychev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 61 (2019), pp. 45-60

Résumé

The aim of the paper is to assess the stress-strain state of anisotropic bodies of revolution with specified displacements of the boundary points and acting mass forces. The problem solution is intended to develop the method of boundary states. A theory is elaborated for constructing a basis of the internal state space, including displacements, strains, and stresses within the body, and a basis of the boundary state space, including forces at the boundary, displacements of the boundary points, and mass forces. The bases are formed using a general solution of the boundary value problem for a transversely-isotropic body of revolution and a method for creating basis vectors of displacement, which is similar to the one usually employed in problems dealing with stress conditions caused by non-conservative mass forces. The internal area and the boundaries are conjugated by isomorphism. This property allows one to reduce the analysis of the whole body state to the analysis of its boundary state. The characteristics of the stress-strain state are presented using the Fourier series. Eventually, a determination of the stress-strain state is reduced to solving an infinite system of algebraic equations. The paper proposes a solution to the second fundamental problem of a circular plane cylinder made of rock, as well as the relevant steps of the study and conclusions. The obtained results are visualized graphically.

Détail

Keywords: boundary state method, anisotropy, boundary value problems, the second fundamental problem, state space, anisotropic cylinder.
Mots-clés : mass forces

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