Use of Fourier shape functions in the scaled boundary method

The scaled boundary finite element method (SBFEM) is a semi-analytical method, whose versatility, accuracy and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using Fourier shape functions in the SBFEM to form the approximation in the circumferential direction. The shape functions effectively form a Fourier series expansion in the circumferential direction, and are augmented by additional linear shape functions. The proposed method is evaluated by solving three elastostatic and steady-state heat transfer problems. The accuracy and convergence of the proposed method is demonstrated, and the performance is found to be better than using polynomial elements or using an element-free Galerkin approximation for the circumferential approximation in the scaled boundary method.