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Equilibrium Stability of Nonlinearly Elastic Cylindrical Tube with Distributed Dislocations Under Axial Compression

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Advances in Linear and Nonlinear Continuum and Structural Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 198))

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Abstract

The problem of equilibrium stability of a nonlinearly elastic hollow circular cylinder under axial compression is considered. The cylinder contains continuously distributed edge dislocations specified by the tensor field of the dislocation density. The distribution of dislocations is axisymmetric. The unperturbed state is described by a system of nonlinear ordinary differential equations. In the study of stability, the bifurcation method is used to search for equilibrium positions that differ little from the unperturbed state. The critical values of the longitudinal force for thin-walled and thick-walled cylinders made of a compressible semi-linear material (John’s model), at which the equilibrium bifurcation occurs, are determined. The buckling modes are investigated. The effect of dislocations on the loss of stability is analyzed.

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Acknowledgements

The reported study was funded by the Russian Science Foundation, project number 23-21-00123, https://rscf.ru/en/project/23-21-00123/.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics, and Computer Science of Southern Federal University, Milchakova Str. 8a, Rostov-on-Don, 344090, Russia

    Evgeniya V. Goloveshkina

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  1. Evgeniya V. Goloveshkina
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Correspondence to Evgeniya V. Goloveshkina .

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Editors and Affiliations

  1. Institute of Mechanics, University of Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. DICAAR, Edificio A, Università di Cagliari, CAGLIARI, Cagliari, Italy

    Victor Eremeyev

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Goloveshkina, E.V. (2023). Equilibrium Stability of Nonlinearly Elastic Cylindrical Tube with Distributed Dislocations Under Axial Compression. In: Altenbach, H., Eremeyev, V. (eds) Advances in Linear and Nonlinear Continuum and Structural Mechanics. Advanced Structured Materials, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-031-43210-1_11

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