Stresses Owing to Internal Pressure in Solid Propellant Rocket Grains

An analysis was made of the stresses and displacements in an elastic solid propellant grain perforated internally by a star shaped configuration, bonded peripherally to an elastic motor case, and loaded internally by pressure normal to the perforation. The analysis was performed under the assumption of plane strain using conformal mapping and the complex variable method of N. I. Muskhelishvili. The effects on stress concentration at the star tip owing to changes in star tip radius of curvature and web thickness of the grain were studied. The analysis was made specifically for a four-pointed, star shaped internal perforation but can be generalized to an n-pointed configuration.