Fourier differential quadrature method for irregular thin plate bending problems on Winkler foundation

This paper describes Fourier differential quadrature method (FDQM). It is the combination of the Fourier spectral method and differential quadrature method (DQM) in barycentric form as a numerical method for solving problems for thin plates resting on Winkler foundations with irregular domains. The solution is decomposed into a polynomial particular solution for the inhomogeneous equation and the general solution for the homogeneous equation. In the solution procedure, the arbitrary distributed loading is first approximated by the Chebyshev polynomials and thus, the desired polynomial particular solution is obtained. For the latter, we use Fourier series expansion and determine the Fourier coefficients from the boundary conditions. Furthermore, the complex boundary conditions on irregular domains can be solved with DQM directly. Finally, numerical experiments are carried out to demonstrate the flexibility, high efficiency and accuracy of our method for irregular domains.