Some Solutions of the Theory of Elasticity for a Rectangle
The article presents ready-made formulas describing solutions to boundary value problems of the theory of elasticity in a rectangle in which two opposite sides are free and normal or tangential stresses are given on the other two sides. All cases of symmetry with respect to the central axes are considered. The solutions are represented as series in Papkovich–Fadle eigenfunctions. The series coefficients are determined from simple closed formulas as Fourier integrals of given boundary functions. An example of comparing the exact solution with the solution obtained on the basis of the beam theory is given for a sufficiently narrow rectangle.