Short Communication
Mechanics of Solids

Integro-differential equations of the second boundary value problem of linear elasticity theory. Communication 2. Inhomogeneous anisotropic body

V. V. Struzhanov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation

Abstract: In communication 1, the integro-differential equations of the second boundary value problem of the theory of elasticity for a homogeneous isotropic body were considered. The results obtained are extended to boundary value problems for the general case of an inhomogeneous anisotropic body. It is shown that the integro-differential equations found are also Fredholm type equations. The existence and uniqueness of their solution is proved, the conditions under which the solution can be found by the method of successive approximations are determined. An example of calculating the residual stresses in an inhomogeneous quenched cylinder is given.

Keywords: second boundary-value problem, inhomogeneous anisotropic body, integro-differential equation, spectral radius, successive approximation, second kind Fredholm equations, iteration convergence.

UDC: 539.3

MSC: 74C10

Received: July 30, 2019
Revised: January 27, 2020
Accepted: February 10, 2020
First online: March 12, 2020

DOI: 10.14498/vsgtu1730

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