Finite element analysis of the in-plane behaviour of annular disks

In-plane analysis of annular disks using the finite element method is presented. A semi-analytical, one-dimensional finite element model is developed using a Fourier series approach to account for the circumferential behaviour. Using displacement functions which are exact solutions of the two dimensional elasticity plane stress problem, the shape functions, stiffness matrices and mass matrices corresponding to the 0th, 1st and nth harmonics are derived. To show the utility of this new element, example probelms have been solved and compared with the exact solution. The present element can be readily coded into any general purpose finite element program