Structural analysis of axisymmetric solids

Abstract

N the aerospace industry, the stress analysis of complex axisymmetric structures of arbitrary shape subjected to thermal and mechanical loads is of considerable interest. Rocket nozzles and cases, solid-propellant grains, and spacecraft heat shields are practical examples of such structures. Although the governing differential equations for solids of revolution have been known for many years, closed form solutions have been obtained for only a limited number of structures; thus, the stress analyst must rely on experimental or numerical techniques. The finite difference method has been the most popular of the numerical techniques; however, for structures of composite materials and of arbitrary geometry, this procedure is difficult to apply. In the present investigation, the finite element idealization is used as the basic numerical procedure. This technique has been applied successfully in the stress analysis of many complex structures.13 In Ref. 4 impressive results were obtained in the analysis of axisymmetric shells approximated by a series of truncated cone elements. The approach, which is presented here, is similar in many respects to existing methods used in the analysis of two-dimensional stress problems.57 Recently, the finite element method was applied to the structural analysis of axisymmetric solids subjected to axisymmetric loads.8 In the present paper, the finite element method is used in the determination of stresses and displacements developed within elastic solids of revolution which are subjected to axisymmetric or nonaxisymmetr ic loads. Emphasis is placed on the application of the technique to complex aerospace structures.