A method of analyzing the stability and post-buckling behavior of corrugated arches is proposed. It involves solving a nonlinear system of first-order differential equations with the method of incremental loading. The boundary-value problem for increments is solved with the discrete-orthogonalization method. The results obtained show that the behavior of corrugated arches is essentially different from that of circular arches
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References
A. N. Dinnik, Stability of Arches [in Russian], Gostekhizdat, Moscow–Leningrad (1946).
S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk, 16, No. 3, 171–174 (1961).
E. I. Grigolyuk and V. I. Shalashilin, Problems of Nonlinear Deformation: Parameter Continuation Method in Nonlinear Problems of Solid Mechanics [in Russian], Nauka, Moscow (1988).
Ya. M. Grigorenko, Isotropic and Anisotropic Layered Shells of Revolution with Variable Stiffness [in Russian], Naukova Dumka, Kyiv (1973).
V. I. Gulyaev, V. A. Bazhenov, and E. A. Gotsulyak, Stability of Nonlinear Mechanical Systems [in Russian], Vyshcha Shkola, Lviv (1982).
N. P. Semenyuk, N. B. Zhukova, and V. V. Ostapchuk, “Stability of corrugated composite noncircular cylindrical shells under external pressure,” Int. Appl. Mech., 43, No. 12, 1380–1389 (2007).
N. P. Semenyuk, V. M. Trach, and N. B. Zhukova, “Incremental analysis of the nonlinear behavior of thin shells,” Int. Appl. Mech., 44, No. 9, 1025–1031 (2008).
S. P. Timoshenko, Theory of Elastic Stability, McGraw-Hill, New York (1936).
I. Yu. Babich, N. B. Zhukova, N. P. Semenyuk, and V. M. Trach, “Stability of circumferentially corrugated shells under hydrostatic pressure,” Int. Appl. Mech., 46, No. 9, 1001–1009 (2010).
A. V. Boriseiko, N. P. Semenyuk, and V. M. Trach, “Canonical equations in the geometrically nonlinear theory of thin anisotropic shells,” Int. Appl. Mech., 46, No. 2, 165–174 (2010).
M. Bresse, Cours de Mechanique, P.1, Imprimeur-Libraire du Bureau des Longitudes, Mallet-Bashelier, Paris (1859).
G. H. Bryan, “Application of the energy test to the collapse of a thin long pipe under external pressure,” Proc. Cambridge Philos. Soc., 6, 287–292 (1888).
E. Hurlbrink, “Festigkeits-Berechnung von rohrenartigen Korpern, die unter ausserem Drucke stehen,” Schiffbau, 9, No. 14, 517–523 (1907/1908).
M. Levy, “Memoire sur un nouveau cas integrable du probleme de l’elastique et l’une de ses aplications”, J. Math. Pures et Appliquees (Lionville Journal),” Series 3, Paris, 10, 5–42 (1884).
E. Riks, “An incremental approach to the solution of snapping and buckling problems,” Int. J. Solids Struct., 15, No. 7, 529–551 (1979).
N. P. Semenyuk, V. M. Trach, and V. V. Ostapchuk, “Nonlinear axisymmetric deformation of anisotropic spherical shells,” Int. Appl. Mech., 45, No. 10, 1101–1111 (2009).
C. J. Wang, “Buckling and postbuckling of segmented tubes under external pressure,” Int. J. Non-Linear Mech., No. 3, 551–556 (2005).
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Translated from Prikladnaya Mekhanika, Vol. 49, No. 2, pp. 90–99, March–April 2013.
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Semenyuk, N.P. Stability of Corrugated Arches under External Pressure. Int Appl Mech 49, 211–219 (2013). https://doi.org/10.1007/s10778-013-0561-2
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DOI: https://doi.org/10.1007/s10778-013-0561-2