In a century of computers and developed numerical methods there are very actual the analytical solutions of boundary value problems of the elasticity and elasto-plasticity theories. In this monograph a uniform original approach is offered: the formulation and analytical solution of problems of static and dynamic theories of elasticity and elasto-plasticity for isotropic solid in displacements. This approach was successfully tested on a number of well-known solutions obtained by Kirsch, Lame and others. Besides, there are formulated and proved two theorems about components of displacement for plane and 3-D problems of linear elasticity for isotropic solid.

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