Two problems for a half-strip with stiffeners: Exact solutions

In the paper, we give examples of exact solutions to two boundary value problems for plates stiffened by ribs in the form of explicit expansions in Papkovich–Fadle eigenfunctions. It is assumed that the stiffeners work only in tension-compression, and their flexural rigidity is equal to zero. The unknown expansion coefficients are determined in simple closed form with the help of biorthogonal functions. As an illustration of the method, solutions to even-symmetric boundary value problems are only considered. The final formulas describing the exact solutions are simple and can easily be used in engineering practice.