ENGINEERING RESEARCH

A method of numerical solution was developed for obtaining the stresses, strains, and displacements in a solid propellant grain of finite length subject to loadings of pressure, cure and thermal shrinkage, and axial acceleration. Although the method is applicable to any solid of revolution, the development was restricted to a propellant grain in the form of hollow, right, circular cylinder bonded at the outer periphery to a rigid motor case. The ends of the grain were treated for both bonded and free conditions. The analysis was limited to materials which are homogeneous, isotropic, elastic, and undergo small deformations. Results were obtained in dimensionless form which can be expressed in terms of only three independent variables - Poisson's ratio and the length-to-diameter and the inner-to-outer diameter ratios of the grain. The effect of these variables on the stress strain, and displacement distributions in the propellant grain was examined. he Rayleigh-Ritz method was employed in conjunction with the principle of minimum potential energy to obtain expressions for the displacements in a propellant grain in the form of a hollow, right circular cylinder bonded at the outer periphery to a rigid motor case and subjected to cure shrinkage.