Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells

Cengiz Polat

doi:doi:10.11648/j.mma.20170206.11

| Peer-Reviewed

Geometrically Nonlinear Behavior of Axisymmetric Thin Spherical Shells

Cengiz Polat

Published in Mathematical Modelling and Applications (Volume 2, Issue 6)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	Mathematical Modelling and Applications (Volume 2, Issue 6)
DOI	10.11648/j.mma.20170206.11
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

[1]	Zhang, J., Wang, M., Wang, W., and Tang, W. (2017). Buckling of egg-shaped shells subjected to external pressure. Thin-Walled Structures, 113, 122-128.
[2]	Kim, Y. Y., and Kim, J. G. (1996). A simple and efficient mixed finite element for axisymmetric shell analysis. International journal for numerical methods in engineering, 39 (11), 1903-1914.
[3]	Rao, L. B., and Rao, C. K. (2011). Fundamental buckling of annular plates with elastically restrained guided edges against translation. Mechanics based design of structures and machines, 39 (4), 409-419.
[4]	Moslehi, M. H., and Batmani, H. (2017). Using the finite element method to analysis of free vibration of thin isotropic oblate spheroidal shell. Applied Research Journal, 3 (6), 198-204.
[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.
[11]	Bathe, K. J., and Saunders, H. (1984). Finite element procedures in engineering analysis.
[12]	Felippa, C. A. and Haugen, B. (2005). A unified formulation of small strain corotational finite elements: I. Theory. Computer Methods in Applied Mechanics and Engineering, Vol. 194, pp. 2285-2335.
[13]	De Borst, R., Crisfield, M. A., Remmers, J. J., and Verhoosel, C. V. (2012). Nonlinear finite element analysis of solids and structures. John Wiley and Sons.
[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.
[17]	Guidi, M., Fregolent, A., and Ruta, G. (2017). Curvature effects on the eigen properties of axisymmetric thin shells. Thin-Walled Structures, 119, 224-234.
[18]	Zienkiewicz, O. C., Taylor, R. L., (2000). The Finite Element Method, Fifth edition, Elsevier Editions.
[19]	Polat, C. and Calayır, Y. (2010). Nonlinear static and dynamic analysis of shells of revolution. Mechanics Research Communications, Vol. 37 (2), pp. 205-209.

Cite This Article

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

Copy | Download

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

Copy | Download

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

Author Information

Cengiz Polat

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

Download PDF

Sections

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

Copy | Download

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

Copy | Download

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