Find an approximate solution for the clamped circular orthotropic plate of radius "a" (see Problem 6.3) for a centrally located concentrated load. What is the ratio of maximum deflections between the orthotropic plate and the isotropic plate for the same coordinate function you have used?
Problem 6.3:
An orthotropic continuum has three planes of symmetry with respect to elastic properties. For plane stress, generalized Hooke's law for such a material is given as
(Note there are four elastic moduli.) Formulate the equations of equilibrium as well as the boundary conditions for an orthotropic plate in terms of w using rectangular coordinates. Demonstrate that your equation degenerates to the case of the isotropic plate. Use whatever results of Sec. 6.3 that are valid for this case