A Fourier series method for polygonal domains: Large element computation for plates

An efficient approach using the Fourier series for boundary value problems on polygonal domains was developed. The method is applied to (1) a reduced wave equation and the potential problems, (2) the classical plate bending problems, and (3) the bending problems of elastic plates considering transverse shear. For a problem with convex domain, which is treated as a large element, the Levy-type solution for an infinite strip can be obtained first. Then, the problem can be solved by superimposing the solution functions and matching the Fourier harmonics of the prescribed boundary conditions. For a non-convex domain, the domain can be cut into a few convex elements and connected back together using the continuity condition. Since the number of elements is much smaller than that of most existing methods, time is saved in both setting up the input data and solving the problem. To demonstrate its accuracy and effectiveness, several examples are presented and compared with the available results. These include a heat conduction problem, a mode 3 crack problem, a plate bending problem, and the bending problem of a stiffened plate.