Stress Analysis of Translational Shells

by James A. Mandel,
Paul J. Brennan,

Serial Information: Journal of the Engineering Mechanics Division, 1968, Vol. 94, Issue 5, Pg. 1109-1126

Document Type: Journal Paper


A set of governing simultaneous partial differential equations describing the bending and membrane stress conditions in any translational shell are derived in this study. By employing a curvilinear coordinate system in the middle surface of the shell in the direction of the principal generators of the surface, the necessity of making the shallow shell assumptions is eliminated, thus the derived set of equations is equally valid for deep as well as shallow translational shells. However, the curvilinear coordinate system used is not, in general, orthogonal and the governing set of partial differential equations have variable coefficients. A finite difference solution is performed for the set of partial differential equations for a particular case - a fixed-edge hyperbolic paraboloid. The numerical solution was checked for discretization and round off error and found to be satisfactory. A small scale structural test program was instituted to verify the assumptions made in the derivation of the governing partial differential equations, and to further check the numerical solutions. Agreement between the test results and numerical solution was, in general, good and in many cases was within 10%.

Subject Headings: Stress analysis | Differential equations | Numerical methods | Bending (structural) | Membranes | Affirmative action | Paraboloid | Verification

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