Conditions of equivalence of effects for the solid body from incompressible material

Abstract

Polemicizing with the existing opinion that modern numerical methods allow to solve practically any problem of mechanics, it should be noted that analytical and experimental methods still are relevant, and a complex of methods leads to development of mechanics of a deformable solid body. At present one of the most important directions of development of mechanics of a deformable solid body is creation of the approaches that allow to combine organically great computing opportunities of modern supercomputers with experimental methods of the material and design research. In engineering practice at production of designs and products incompressible materials are widely used. Assessment of their durability requires detailed studying of deflected mode caused by action of various loadings and forces. For a solid body from incompressible material, using the resolving equations set of mechanics of a deformable solid body, at action of the compelled deformations of a general view, volume and superficial forces conditions of equivalence are established. It is shown that the known solutions are special cases of the established equivalence conditions. The efficiency of the analytical solution of a three-dimensional task on the rotating disk from incompressible material is shown by the method of equivalence of effects.