Asymmetric Bending of Polar Orthotropic Circular Plates

The asymmetric bending of polar orthotropic circular plates using the finite element method is explored. The plate bending model consists of one-dimensional circular and annular ring segments using a Fourier series approach to model the problem asymmetries. Using displacement functions, which are the exact solutions of the plate bending equation, the stiffness coefficients corresponding to the 0th, 1st, and nth harmonics are presented in closed form. These stiffness coefficients, which can be readily coded into any special or general purpose structural analysis computer program, represent the exact solution to any structural model consisting of nodal displacements and forces. An example is considered which compares the mathematical formulation using this technique to the classical solution.