Ring-element analysis of layered orthotropic bodies

For the analysis of arbitrarily laminated circular bodies, a displacement-based ring-element is presented. The analysis is performed in a cylindrical coordinate system. The method of analysis requires the boundary conditions as well as the external forces to be pi-periodic. The element formulation accounts for a desired degree of approximation of the displacement field in the direction of the circumference. This is done by a truncated Fourier expansion of the angular dependence of the displacements in terms of trigonometric functions. Thus the Fourier expansion coefficients are the unknowns to be determined in the finite element analysis. The element chosen is an eight node isoparametric element of the serendipity family. The Fourier series show very high rate of convergence for the problems solved. The investigation shows that the computational work is remarkably reduced in relation to that of solutions obtained by traditional 3D elements. A scheme for analytical integration of the angular dependence of the stiffness matrix is given.