Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells

Cengiz Polat

doi:doi:10.11648/j.mma.20170206.11

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Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells

Cengiz Polat

Received: 28 September 2017 Accepted: 7 November 2017 Published: 5 December 2017

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Abstract

This article presents a geometrically nonlinear formulation of a two node axisymmetric shell element. The geometrically nonlinear formulation is based on the Total Lagrangian approach and the material behavior is assumed to be linearly elastic. The spherical arc-length procedure is used to obtain the pre-buckling, buckling and post-buckling deformation path. Some numerical examples are solved to demonstrate geometrically nonlinear behavior of elastic thin spherical shells subjected to various loads.

DOI	10.11648/j.mma.20170206.11
Published in	Mathematical Modelling and Applications (Volume 2, Issue 6, December 2017)
Page(s)	57-62
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Axisymmetric Shell Element, Buckling Behavior, Total Lagrangian Approach

References

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[5]	Jiammeepreecha, W., Chucheepsakul, S., and Huang, T. (2014). Nonlinear static analysis of an axisymmetric shell storage container in spherical polar coordinates with constraint volume. Engineering Structures, 68, 111-120.
[6]	Btachut, J. (2005). Buckling of shallow spherical caps subjected to external pressure. Journal of applied mechanics, 72 (5), 803-806.
[7]	Yang, L., Luo, Y., Qiu, T., Yang, M., Zhou, G., and Xie, G. (2014). An analytical method for the buckling analysis of cylindrical shells with non-axisymmetric thickness variations under external pressure. Thin-Walled Structures, 85, 431-440.
[8]	Sumirin, S., Nuroji, N., and Besari, S. (2015). Snap-Through Buckling Problem of Spherical Shell Structure. International Journal of Science and Engineering, 8 (1), 54-59.
[9]	Bagchi, A. (2012). Linear and nonlinear buckling of thin shells of revolution. Trends in Applied Sciences Research, 7 (3), 196.
[10]	Polat C., and Calayır Y., (2012). Post buckling behavior of a spherical cap subjected to various ring loads, 10th International Congress on Advances in Civil Engineering, Ankara, Turkey.
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[14]	Feng, Y. T., Perić, D., and Owen, D. R. J. (1996). A new criterion for determination of initial loading parameter in arc-length methods. Computers and structures, 58 (3), 479-485.
[15]	de Souza Neto, E. A., and Feng, Y. T. (1999). On the determination of the path direction for arc-length methods in the presence of bifurcations and snap-backs'. Computer methods in applied mechanics and engineering, 179 (1), 81-89.
[16]	Cui, X. Y., Wang, G., and Li, G. Y. (2016). A nodal integration axisymmetric thin shell model using linear interpolation. Applied Mathematical Modelling, 40 (4), 2720-2742.
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Cengiz Polat. (2017). Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells. Mathematical Modelling and Applications, 2(6), 57-62. https://doi.org/10.11648/j.mma.20170206.11

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ACS Style

Cengiz Polat. Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells. Math. Model. Appl. 2017, 2(6), 57-62. doi: 10.11648/j.mma.20170206.11

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AMA Style

Cengiz Polat. Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells. Math Model Appl. 2017;2(6):57-62. doi: 10.11648/j.mma.20170206.11

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@article{10.11648/j.mma.20170206.11,
  author = {Cengiz Polat},
  title = {Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {6},
  pages = {57-62},
  doi = {10.11648/j.mma.20170206.11},
  url = {https://doi.org/10.11648/j.mma.20170206.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170206.11},
  abstract = {This article presents a geometrically nonlinear formulation of a two node axisymmetric shell element. The geometrically nonlinear formulation is based on the Total Lagrangian approach and the material behavior is assumed to be linearly elastic. The spherical arc-length procedure is used to obtain the pre-buckling, buckling and post-buckling deformation path. Some numerical examples are solved to demonstrate geometrically nonlinear behavior of elastic thin spherical shells subjected to various loads.},
 year = {2017}
}

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TY  - JOUR
T1  - Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells
AU  - Cengiz Polat
Y1  - 2017/12/05
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170206.11
DO  - 10.11648/j.mma.20170206.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 57
EP  - 62
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170206.11
AB  - This article presents a geometrically nonlinear formulation of a two node axisymmetric shell element. The geometrically nonlinear formulation is based on the Total Lagrangian approach and the material behavior is assumed to be linearly elastic. The spherical arc-length procedure is used to obtain the pre-buckling, buckling and post-buckling deformation path. Some numerical examples are solved to demonstrate geometrically nonlinear behavior of elastic thin spherical shells subjected to various loads.
VL  - 2
IS  - 6
ER  -

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Author Information

Cengiz Polat

Technical Vocational School, F?rat University, Elazig, Turkey

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Plain Text BibTeX RIS

APA Style

Cengiz Polat. (2017). Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells. Mathematical Modelling and Applications, 2(6), 57-62. https://doi.org/10.11648/j.mma.20170206.11

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ACS Style

Cengiz Polat. Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells. Math. Model. Appl. 2017, 2(6), 57-62. doi: 10.11648/j.mma.20170206.11

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AMA Style

Cengiz Polat. Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells. Math Model Appl. 2017;2(6):57-62. doi: 10.11648/j.mma.20170206.11

Copy | Download

@article{10.11648/j.mma.20170206.11,
  author = {Cengiz Polat},
  title = {Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {6},
  pages = {57-62},
  doi = {10.11648/j.mma.20170206.11},
  url = {https://doi.org/10.11648/j.mma.20170206.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170206.11},
  abstract = {This article presents a geometrically nonlinear formulation of a two node axisymmetric shell element. The geometrically nonlinear formulation is based on the Total Lagrangian approach and the material behavior is assumed to be linearly elastic. The spherical arc-length procedure is used to obtain the pre-buckling, buckling and post-buckling deformation path. Some numerical examples are solved to demonstrate geometrically nonlinear behavior of elastic thin spherical shells subjected to various loads.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells
AU  - Cengiz Polat
Y1  - 2017/12/05
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170206.11
DO  - 10.11648/j.mma.20170206.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 57
EP  - 62
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170206.11
AB  - This article presents a geometrically nonlinear formulation of a two node axisymmetric shell element. The geometrically nonlinear formulation is based on the Total Lagrangian approach and the material behavior is assumed to be linearly elastic. The spherical arc-length procedure is used to obtain the pre-buckling, buckling and post-buckling deformation path. Some numerical examples are solved to demonstrate geometrically nonlinear behavior of elastic thin spherical shells subjected to various loads.
VL  - 2
IS  - 6
ER  -

Copy | Download