Nonhomogeneous boundary value problem for a clamped rectangle: Exact solution

This paper presents an exact solution to the nonhomogeneous boundary value problem of the theory of elasticity for a clamped rectangle. First, a solution to the nonhomogeneous problem for an infinite strip with clamped sides is constructed. Then, a solution for the rectangle is added to this solution, with the help of which the boundary conditions at the ends are satisfied. To solve the nonhomogeneous problem in the clamped strip, Papkovich's generalized orthogonality relation is used. The solution in the rectangle is represented in the form of series in Papkovich–Fadle eigenfunctions, the coefficients of which are determined by simple formulas. The final formulas are simple and can easily be used in engineering.