Thermal stresses in a finite solid-propellant grain

Abstract

In order to gain a fundamental understanding of actual solid propellant thermal stress problems, the geometry of the solid propellant baa been idealized as a short, circular cylinder with flat ends. It is felt that the consideration of actual curved ends would only unduly have complicated the analysis.

The method of solution for the thermal stresses in the finite cylinder, that has been presented in this thesis, utilizes an arbitrarily selected set of cylinder end-conditions. Therefore, different end conditions than the ones employed here might have been considered just as easily.

The fundamental difficulties encountered in the thermoelastic analysis of short cylinders are that firstly the problem is at least two-dimensional and secondly, it has mixed boundary conditions since displacements and/or stresses specified along at least four distinct boundaries. It is relatively simple to solve the governing differential equation by the method of separation of variables. The greatest difficulties are encountered in satisfying the various boundary conditions. As a matter of fact the method of solution for the thermal stresses that has been presented in this thesis is applicable only when the temperature distribution throughout the propellant and casing exhibits a particular variation in the axial direction, as shown by Eqs. (39) and (43). With such temperature fields, however the elastic analytic solutions that have been presented are significant since the simultaneous linear algebraic equations, for the arbitrary constants, are easily solved. It is true that, in principle, an infinite number of these arbitrary constants must be determined. From a practical point of view, however, the arbitrary constants can always be reduced to a finite number by truncating the obtained series solutions for the thermal displacements and stresses.