Mixed plane problems of linearized mechanics of solids. Exact solutions

This article is devoted to the analysis of the exact solutions for the mixed plane problems of the linearized solid mechanics as applied to the statics, dynamics and stability loss problems and fracture mechanics problems. Above mentioned exact solutions were obtained in universal form for the compressible and incompressible elastic and plastic solids taking into account the representations of the stresses and displacements of the linearized solid mechanics by the analytical functions of the complex variables. The methods of the theory of functions of complex variables in particularly the methods of the Riemann-Gilbert problem and Keldysh-Sedov formula are used. When the initial (residual) stresses tend to zero the above mentioned exact solutions of the linearized solid mechanics transform into the corresponding exact solutions of the classical linear solid mechanics based on the complex representations of Muskhelishvili, Lekhnitski and Galin.