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V.L. Kanodia, R.H. Gallagher, H.A. Mang:
"Instability Analysis of Torispherical Pressure Vessel Heads with Triangular Thin-Shell Finite Elements";
Transactions of the American Society of Mechanical Engineers, Journal of Pressure Vessel Technology, 99 (1977), 64 - 74.

The elastic instability of an internally-pressurized cylindrical tank with a torispherical head is investigated using a triangular, doubly curved, thin-shell finite element. The formulation of the finite element, which is based upon cubic displacement functions and a modified principle of potential energy, is first described. Then, the element is verified by comparing numerical results for the linear, stable analysis to alternative solutions for the same problem. The subsequent instability investigation includes the solution of the linearized problem of equilibrium bifurcation, that is, of the classical eigenvalue problem, and a general nonlinear analysis, based on tracing the nonlinear load-displacement path. The critical pressure, obtained with use of the general non-linear analysis, agrees closely with an experimental results as well as with a numerical solution stemming from an axisymmetric formulation.