Integro-differential equations the second boundary value problem of linear elasticity theory. Message 1. Homogeneous isotropic body

Abstract

The system of equations of the second boundary value problem of the linear theory of elasticity for homogeneous isotropic bodies is reduced to two separate integro-differential equations of Fredholm type, which allowed to apply for their research the theorem of Fredholm. The spectral radii of the corresponding operators are determined and the existence and uniqueness of the solution of the second boundary value problem are proved. It is also established that the decision of the second integro-differential equation can be found by successive approximations and presented convergent with a geometric rate close to Neumann. The method application is illustrated on the example of calculation of residual stresses in a quenched cylinder.

Keywords

• second boundary-value problem
• homogeneous isotropic body
• integro-differential equation
• spectral radius
• successive approximation