Equations of cylindrical bending of orthotropic plates with arbitrary conditions on their front surfaces

Based on approximations of solutions of elasticity theory equations by Legendre polynomial segments, differential equations for bending of orthotropic plates are constructed. In contrast to equations constructed with the use of kinematic and force hypotheses, the order of these differential equations is independent of the type of conditions on front surfaces. The matrices of the constructed equations depend on the type of boundary conditions. An analytical solution is given for the system of equations in the case with normal and shear stresses being specified on the upper and lower front surfaces.