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Solution of the Non-Linear Differential Equations for Finite Bending of a Thin-Walled Tube by Parameter Differentiation
Published online by Cambridge University Press: 07 June 2016
Summary
The method of parameter differentiation is applied to the solution of the non-linear, two-point, ordinary differential equations resulting from an analysis of the finite bending of a thin-walled tube. Starting from a given set of solutions of the differential equations for a particular value of the curvature parameter α, solutions for a range of values of α can be obtained by this method non-iteratively. Very close agreement was obtained with solutions using iterative numerical methods.
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- Copyright © Royal Aeronautical Society. 1974
References
1
Perrone, N, Kao, R, A general nonlinear relaxation iteration technique for solving nonlinear problems in mechanics. Journal of Applied Mechanics, Transactions ASME, Vol 38, Series E, Number 2, pp 371-376, June 1971.CrossRefGoogle Scholar
2
Thurston, G A, Newton’s Method applied to problems in nonlinear mechanics. Journal of Applied Mechanics, Transactions ASME, Vol 87, Series E, pp 383-388, June 1965.Google Scholar
3
Reissner, E, Weinitschke, H J, Finite pure bending of circular cylindrical tubes. Quarterly of Applied Mathematics, Vol 20, No 4, pp 305-312, January 1963.Google Scholar
4
Reissner, E, Weinitschke, H J, Corrections to Reference 3. Quarterly of Applied Mathematics, Vol 23, No 4, pp 368, January 1966.Google Scholar
5
Rubbert, P E, Landahl, M T, Solution of nonlinear flow problems through parameter differentiation. Physics of Fluids, Vol 10, pp 831-835, 1967.Google Scholar
6
Tan, C W, Di Bano, R, A study of the Falkner-Skan problem with mass transfer. AIAA Journal, Vol 10, pp 923-925, 1972.CrossRefGoogle Scholar
7
Narayana, C L, Ramamoorthy, P, Compressible boundary layer equations solved by the method of parameter differentiation. AIAA Journal, Vol 10, pp 1085-1086, July 1972.Google Scholar
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