The general solution and reduction to diagonal form of a system of equations of linear isotropic elasticity

摘要

A simple representation is obtained of the general solution of the Lame system of equations for an isotropic material in the form of a linear combination of the first derivatives of the three functions satisfying three independent wave or harmonic (in the static case) equations. In the two-dimensional case of plane deformation, the found solution directly implies the Kolosov-Muskhelishvili representation of the displacements by two analytic functions of a complex variable. A formula for generation of new solutions is given.