Fourier series method for plane elastic problems of polygonal domain Original Research Article

This study employs the Fourier series method based on the edge function approach to solve the plane elastic problem of polygonal domain described by Navier equations. The analytical solutions serve as a set of fundamental solutions for each edge. Superposing the solution function and matching the prescribed boundary conditions in each edge allows the solving of the unknown variables and the analysis of the problem. An extra corner function and regularization technique is utilized to enhance convergence rate. Only one element is required to analyze which polygon domain is convex, however, by dividing a non-convex shape into several convex shapes, the proposed method can be extended to irregular geometrical shape. Numerical examples demonstrate the merits of the developed scheme, as well as its efficiency and accuracy.