@Carl Love Thank you so much. You answer is very helpful and impressive.
There are still some questions I don't understand. If I want to get the exact answer as
1. If I want to get the exact answer as Equation (23) in the reference. What should I do for the input in Maple. I read the help file,but I still can't the useful information (My major is Civil Engineering,so such an equation is a little bit difficult for me).
2. The left side of Equation (23) is Laplace form. How to solve the equation and get the function Φ? For the Airy's stress function Φ consists of two parts, one is the general solution and the other is particular solution. Normally, the general solution component is the red part below. And the other is particular solution.
Thank you for your time and comments.