Mechanics of Composite Materials

, Volume 55, Issue 3, pp 349–362 | Cite as

Stability of Functionally Graded Circular Cylindrical Shells under Combined Loading

  • S. A. BоchkarevEmail author
  • S. V. Lekomtsev

The stability of loaded circular cylindrical shells made of functionally graded materials and flowed round by a supersonic gas stream is investigated. The effective temperature-dependent properties of the material examined vary across the shell thickness according to a power law. The temperature distribution along its radial coordinate is determined by solving the one-dimensional heat conduction equation. The aerodynamic pressure is evaluated using the quasi-static aerodynamic theory. The behavior of the elastic structure is described by the classical shell theory based on Kirchhoff–Love hypotheses. The geometric and physical relationships, along with the equations of motions, are reduced to a system of eight ordinary differential equations in new unknowns. The boundary-value problem formulated is solved by the Godunov orthogonal sweep method, and the differential equations are integrated using the Runge–Kutta method. The behavior of circular cylindrical shells clamped at both its ends is analyzed at different volume fractions of the functionally graded material. Impact of various combinations of mechanical, thermal, and aerodynamic loads on the boundaries of elastic, thermoelastic, and aeroelastic stability of the shells is evaluated.


functionally graded material supersonic gas flow cylindrical shell thermal load Godunov orthogonal sweep method stability 


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Authors and Affiliations

  1. 1.Institute of Mechanics of Continuous Media, UrB of the Russian Academy of SciencesPermRussia

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