A method of boundary states in a solution to the first fundamental problem of the theory of anisotropic elasticity with mass forces

D. A. Ivanychev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 66 (2020), pp. 96-111

Résumé

The purpose of this work is to determine the stress-strain state of the anisotropic bodies of revolution exposed to axisymmetric surface and mass forces. The problem is solved using the method of boundary states. A theory for the construction of space bases of the inner and boundary states conjugated with isomorphism is developed. Determination of the internal state is reduced to a study of isomorphic boundary state. The elastic state components are represented as Fourier series with quadrature coefficients. In the first fundamental problem of mechanics, determination of the elastic state is reduced to the solution of an infinite system of algebraic equations. A particularity of this solution is that the pattern of the determined elastic field satisfies both the conditions specified at the boundary and inside the body. A rigorous solution to a test problem for a circular cylinder, as well as a solution to the problem with inhomogeneous boundary conditions is presented. An elastic field is found in the problem for the non-canonical body of revolution exposed to mass forces and zero boundary conditions. The explicit and indirect indicators of problem solution convergence and a graphical visualization of results are shown.

Détail

Keywords: boundary state method, anisotropy, boundary value problems, state space, first fundamental problem.
Mots-clés : mass forces