Tapered Plane Stress Annular Sector Finite Element

The annular sector finite element has four nodes, each node with four kinematic degrees-of-freedom. The stiffness matrix and other properties of the element are derived in a very simple manner through the use of an algorithm for the integration in closed form of congruently transformed matrices. Based on the results of the numerical examples, the performance of the element is considered very satisfactory. Convergence of the finite element solution is slightly slower for plane problems in which the thickness is nonuniform. The element presented herein is particularly suitable for the analysis of plane stress problems of curved variable thickness domains formulated in polar coordinate system. Such problems are often encountered in the stress analysis of machine components such as turbine and supercharger units which contain disks of variable thickness.