I am a doing a research on analysis of hyperbolic paraboloid shell using levy type soluton which will be validated later by using ansys. Levy type method as suggested by apeland and popov is being used. Since its a eight order differential equation with boundary value problem having a problem in solving boundary condition. Can anyone suggest an easier method to solve the boundary conditions? or can anyone explain the method to use the tables given by Apeland and Popov?

P.S. Already tried spilines method.