ABSTRACT
Being loaded by normal pressure, the plane elements of thin-walled structures experience bending that is described by the classical plate theory. Within the framework of this theory, the problem of bending is reduced to the biharmonic boundary problem and was partially studied. This chapter devotes to exact solutions of some classical problems of the plate theory in Cartesian and polar coordinates. For special boundary conditions, the problem admits solutions in trigonometric series. The first solution of such a type was constructed by A. Navier in 1820 for a simply supported rectangular plate. For particular problems of the theory of orthotropic plates, solutions in the form of trigonometric series can be found elsewhere. In application to the method of homogeneous solutions they can be used to construct particular solutions of nonhomogeneous biharmonic equation or to reduce nonhomogeneous boundary conditions to homogeneous ones.
