The boundary value problem of the theory of elasticity in a rectangle: An exact solution

An exact solution is constructed for the boundary value problem of the theory of elasticity in a rectangle, in which two opposite (horizontal) sides are free, and normal stresses are given on the other two (the ends of the rectangle) (even-symmetric deformation relative to the central axes). The solution is constructed in the form of expansions in Papkovich–Fadle eigenfunctions. The expansion coefficients are determined by simple closed formulas.