Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T12:53:18.305Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear Axisymmetric Deformation Model for Structures of Revolution

Published online by Cambridge University Press:  03 June 2015

Ayman Mourad  and
Jawad Zaarour
Ayman Mourad*
Affiliation:
Department of Mathematics, Lebanese University, Hadath, Lebanon
Jawad Zaarour*
Affiliation:
Jean Kutzman Laboratory, Joseph Fourier University, Grenoble, France
*
Corresponding author. Email: ayman imag@yahoo.fr
Email: jawadzaarour@hotmail.com
Get access

Abstract

An axisymmetric formulation for modeling three-dimensional deformation of structures of revolution is presented. The axisymmetric deformation model is described using the cylindrical coordinate system. Large displacement effects and material nonlinearities and anisotropy are accommodated by the formulation. Mathematical derivation of the formulation is given, and an example is presented to demonstrate the capabilities and efficiency of the technique compared to the full three-dimensional model.

Keywords

74B2074G15Modelingaxisymmetrynonlinear elasiticitylarge deformationsnumerical simulations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 4 , August 2011 , pp. 420 - 447
Copyright
Copyright © Global-Science Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational. Mech. Anal., 63 (1977), pp. 337–403.Google Scholar
[2] Bernardi, C., Dauge, M. and Maday, Y., Spectral Methods for Axisymmetric Domains, Elsevier, Paris, 1999.Google Scholar
[3] Deparis, S., Numerical Analysis of Axisymmetric Flows and Methods for Fluid-Structure Interaction Arising in Blood Flow Simulation, PhD Thesis at the Faculty of base sciences, Lausanne, 2004.Google Scholar
[4] Eftaxiopoulos, D. A. and Atkinson, C., A nonlinear, anisotropic and axisymmetric model for balloon angioplasty, Proc. R. Soc. A., 461 (2005), pp. 1097–1128.Google Scholar
[5] Ern, A. and Guermond, J. L., Eléments Finis: Théorie, Application, Mise en œuvre, Springer, Paris, 2002.Google Scholar
[6] Fung, Y. C., Biomechanics: Mechanical Properties of Living Tissues, Second Edition, Springer-Verlag, New York, 1993.Google Scholar
[7] Gallouet, E. and Herbin, R., Modelling CO2 diffusion and assimilation in a leaf with ax-isymmetric finite volumes, Int. J. Finite. Vol., 2(2) (2005), pp. 325–335.Google Scholar
[8] Gao, D. Y. and Ogden, R. W., Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem, Z. Angew. Math. Phys., 59 (2008), pp. 498–517.Google Scholar
[9] Geuzaine, C. and Remacle, J. F., Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, , 2009.Google Scholar
[10] Hao, J. and Yan, X., Exact solution of large deformation basic equations of circular membrane under central force, Appl. Math. Mech., 27(10) (2006), pp. 1333–1337.Google Scholar
[11] Hecht, F., Freefem++, Pierre and Marie Curie University, Jacques-Louis Lions Laboratory, , 2005.Google Scholar
[12] Jeon, S., Chung, C., Kim, Y., Lee, Y. and Chung, Y., Axisymmetric modeling of prestressing tendons in nuclear containment building dome, Proc. 18th Int. Conf. Struct. Mech. React. Tech., (SMiRT 18), Beijing, China, pp. 1946–1957, 2005.Google Scholar
[13] Lin, D. H. S. and Yin, F.C. P, A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus, ASME. J. Biomech. Eng. Verlag., 120 (1998), pp. 504–517.Google Scholar
[14] Mourad, A., Biard, L., Caillerie, D., Jouk, P. S., Raoult, A., Szafran, N. and Us-Son, Y., Geometrical modeling of the fibre organization in the human left ventricle, in Functional Imaging and Modeling of the Heart, Katila et al. Eds, Springer Verlag LNCS, Vol. 2230, pp. 32–38, 2001.Google Scholar
[15] Rivlin, R. S., Large elastic deformations of isotropic materials VI, further results in the theory of torsion, shear and flexure, Phil. Trans. R. Soc. Lond. A., 242 (1949), pp. 173–195.Google Scholar
[16] Robb, J. S. and Robb, R. C., The normal heart: anatomy and physiology of the structural units, Am. Heart. J., 23 (1942), pp. 455–467.Google Scholar
[17] Shanlin, C. and Zhoulian, Z., Large deformation of circular membrane under the concentrated force, Appl. Math. Mech., 24(1) (2003), pp. 28–31.Google Scholar
[18] Streeter, D. D., Gross morphology and fiber geometry of the heart, in Berne, R. M. et al. editor, Handbook of Physiology, 1 (1979), pp. 61–112.Google Scholar
[19] Suzuki, T. and Maruyama, Y., Axisymmetric model as a method to evaluate seismically isolated tunnels, Proc. 10th Japan Earthquake Engineering Symposium, pp. 2003–2008, 1998.Google Scholar
[20] Wang-Min, Z. and Tian-You, F., Axisymmetric elasticity problem of cubic quasicrystal, Chinese. Phys., 9(4) (2000), pp. 294–303.Google Scholar