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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?
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