Approximate Finite-Element Method of Stress Analysis of Non-Axisymmetric Configurations.

Abstract A finite-element method of analysis is developed for structural configurations which are derived from axisymmetric geometries but contain definite non-axisymmetric features in the circumferential direction. The purpose of the present analysis is to develop a method which will take into consideration the fact that the stress and strain conditions in these geometires will be related to the corresponding axisymmetric solution. To analyze these structures, the geometry is divided into several segments in the r - θ plane. The axisymmetric displacements are obtained for each segment by solving a related axisymmetric configuration. A perturbation analysis is then performed to match the solutions at certain points between the segments and obtain the perturbation displacements for the total structure. The total displacement is then the axisymmetric displacement plus the perturbation displacement. The stresses and strains are then calculated at any desired point once the total displacements are known. The method is applied to a number of examples to illustrate the accuracy of the method. The results for these examples are presented and discussed. Some of these examples illustrate the difference between the present approach and the well known substructural analysis and it is shown that the present method is much more accurate.