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Journal of Applied Mechanics and Technical Physics

, Volume 50, Issue 6, pp 1044–1048 | Cite as

Analysis of bifurcation bending modes of arches and panels

  • L. I. Shkutin
Article
  • 38 Downloads

Abstract

This paper reports the results of numerical analysis of the bifurcation solutions of nonlinear boundary-value problems of plane bending of elastic arches and panels. Problems are formulated for a system of six nonlinear ordinary differential equations of the first order with independent fields of finite displacements and rotations. Two loading versions (by follower and conservative pressures) and two versions of boundary conditions (rigid clamping and pinning) are considered. In the case of clamped arches and panels, the set of solutions consists of symmetric and asymmetric bending modes which exist only for positive values of the load parameter. In the case of pinning, the set of solutions includes symmetric and asymmetrical modes which correspond to positive, negative, and zero values of the parameter. In both problems, the phase relations between the state parameter and the load parameter are bifurcated, ambiguous, have isolated branches, and admit a catastrophe — a finite jump from the fundamental equilibrium mode to a buckled mode.

Key words

arches panels nonlinear bend buckling stability numerical analysis 

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References

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    É. I. Grigolyuk and V. I. Shalashilin, Problems of Nonlinear Deformation: The Parameter Continuation Method in Nonlinear Problems of Solid-State Mechanics [in Russian], Nauka, Moscow (1988).Google Scholar
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    L. Shkutin, “Numerical analysis of the bifurcation forms of bending of arches,” J. Appl. Mech. Tech. Phys., 42, No. 4, 310–315 (2001).CrossRefGoogle Scholar

Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Institute of Computational Modeling, Siberian DivisionRussian Academy of SciencesKrasnoyarskRussia

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