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SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS

Year 2015, Volume: 7 Issue: 1, 68 - 85, 01.03.2015

Ali İ. Karakaş Ayse T. Daloğlu

https://doi.org/10.24107/ijeas.251240

Abstract

Harmonic solid ring finite elements are commonly used in the analysis of axisymmetric structures subjected to non-axisymmetric as well as axisymmetric loadings. Depending on the material and/or geometrical properties of axisymmetric problems the finite element analysis may produce erroneous solutions due to approximations assumed in the formulation. Volumetric and shear locking are the some troublesome behaviors of some finite elements. In this study, finite element formulations of 4-noded (Ring4) and 9-noded (Ring9) ring elements are developed considering constant and linear shear locking effect for the element types, respectively, by incorporating selectively reduced integration technique. A computer program is coded in Matlab for the purpose and the performances of both elements are explored in terms of locking issue as well as accuracy. For this purpose several axisymmetric problems are solved such as hollow thick cylinder and circular plate problems. Numerical results indicate that while Ring9 does not suffer from volumetric locking for high values of Poisson’s ratios Ring4 suffers. Besides, while Ring4 with full integration displays shear locking effects Ring4 with selectively reduced integration eliminates the locking. The finite element formulations areexplained in detail and the results of numerical examples are presented comparatively in graphical and tabular formats

Keywords

shear and volumetric locking harmonic solid ring element selectively reduced integration

References

  • [1] Felippa, A.C., IFEM Lecture Notes, Department of Aerospace Engineering Sciences, University of Colorado at Boulder, 2011.
  • [2] Bell, R.W., Houlsby, G.T. and Burd, H.J., Suitability of three-dimensional finite elements for modelling material incompressibility using exact integration, Communications in Numer. Methods in Eng, 9(4), 313-329, 1993.
  • [3] Oñate, E., Rojek, J., Taylor, R.L., Zienkiewicz, O.C., Finite calculus formulation for incompressible solids using linear triangles and tetrahedral, Int. J. Numer. Methods in Eng., 59(11), 1473-1500, 2004.
  • [4] Bart V., Volumetric locking in finite elements, Bachelor Final Project, Eindhoven University of Technology, Department of Mechanical Engineering, 2008.
  • [5] Korhan, Ö. and Ayse, T.D., Elastik zemine oturan kalın plaklar için kayma kilitlenmesiz bir sonlu eleman modeli. İMO Teknik Dergi, 346, 5341-5358, 2011.
  • [6] Pugh, E.D.L., Hinton, E. And Zienkiewichz, O.C., A study of quadrilateral plate bending elements with reduced integration, Int. J. Numer. Methods in Eng., 12(7), 1059-1079, 2005.
  • [7] Alves de Sousa, R.J., Natal Jorge, R.M., Fontes Valente, R.A. and Cesar de Sa, J.M.A., A new volumetric and shear locking-free 3D enhanced strain element, Eng.Computations, 20(7), 896-925, 2003.
  • [8] Malkus, D.S., Hughes, T.J.R., Mixed finite element methods - reduced and selective integration techniques: a unification of concepts, Comp. Methods in Appl. Mech. Eng. 15(1), 63-81, 1978.
  • [9] Lee, P.S. and Bathe, K.J., On the asymptotic behavior of shell structures and the evaluation of finite element solutions, Comp. and Struct., 80, 235-255, 2002.
  • [10] Cook, R.,D., Malkus, D.,S. and Plesha, M.,E., Concepts and Applications of Finite Element Analysis, 3rd Edition, Wiley & Sons, USA, 1989.
  • [11] Ali, İ.Karakaş, Static and Dynamic Analyses of Axisymmetric Structures Using Harmonic Solid Ring Finite Element Modeling, Master dissertation. Karadeniz Technical University, Turkey, 2012.
  • [12] Benasciutti, D., De Bona, F. and Munteanu, M.Gh., Numerical analysis-theory and application, In: Awrejcewicz J. editor, University of Udine, 2011.
  • [13] Bathe, K.J., Finite Element Procedures, Prentice-Hall, USA, 1996.
  • [14] Bhatti MA. Advanced Topics in Finite Element Analysis of Structures: with Mathematica and Matlab Computations, USA: John Wiley&Sons, 2006.
  • [15] Halil, K., Spectral Analysis Program of Structures: SAPOS User Manual, Delft University of Technology, Netherlands, 79-90, 2009.
  • [16] Timoshenko, S. and Goodier, J.N., Theory of Elasticity, McGraw-Hill, New York,1951.
  • [17] Ugural, A.C., Stresses in Plates and Shells, McGraw-Hill, USA, 1981.

Year 2015, Volume: 7 Issue: 1, 68 - 85, 01.03.2015

Ali İ. Karakaş Ayse T. Daloğlu

https://doi.org/10.24107/ijeas.251240

Abstract

References

  • [1] Felippa, A.C., IFEM Lecture Notes, Department of Aerospace Engineering Sciences, University of Colorado at Boulder, 2011.
  • [2] Bell, R.W., Houlsby, G.T. and Burd, H.J., Suitability of three-dimensional finite elements for modelling material incompressibility using exact integration, Communications in Numer. Methods in Eng, 9(4), 313-329, 1993.
  • [3] Oñate, E., Rojek, J., Taylor, R.L., Zienkiewicz, O.C., Finite calculus formulation for incompressible solids using linear triangles and tetrahedral, Int. J. Numer. Methods in Eng., 59(11), 1473-1500, 2004.
  • [4] Bart V., Volumetric locking in finite elements, Bachelor Final Project, Eindhoven University of Technology, Department of Mechanical Engineering, 2008.
  • [5] Korhan, Ö. and Ayse, T.D., Elastik zemine oturan kalın plaklar için kayma kilitlenmesiz bir sonlu eleman modeli. İMO Teknik Dergi, 346, 5341-5358, 2011.
  • [6] Pugh, E.D.L., Hinton, E. And Zienkiewichz, O.C., A study of quadrilateral plate bending elements with reduced integration, Int. J. Numer. Methods in Eng., 12(7), 1059-1079, 2005.
  • [7] Alves de Sousa, R.J., Natal Jorge, R.M., Fontes Valente, R.A. and Cesar de Sa, J.M.A., A new volumetric and shear locking-free 3D enhanced strain element, Eng.Computations, 20(7), 896-925, 2003.
  • [8] Malkus, D.S., Hughes, T.J.R., Mixed finite element methods - reduced and selective integration techniques: a unification of concepts, Comp. Methods in Appl. Mech. Eng. 15(1), 63-81, 1978.
  • [9] Lee, P.S. and Bathe, K.J., On the asymptotic behavior of shell structures and the evaluation of finite element solutions, Comp. and Struct., 80, 235-255, 2002.
  • [10] Cook, R.,D., Malkus, D.,S. and Plesha, M.,E., Concepts and Applications of Finite Element Analysis, 3rd Edition, Wiley & Sons, USA, 1989.
  • [11] Ali, İ.Karakaş, Static and Dynamic Analyses of Axisymmetric Structures Using Harmonic Solid Ring Finite Element Modeling, Master dissertation. Karadeniz Technical University, Turkey, 2012.
  • [12] Benasciutti, D., De Bona, F. and Munteanu, M.Gh., Numerical analysis-theory and application, In: Awrejcewicz J. editor, University of Udine, 2011.
  • [13] Bathe, K.J., Finite Element Procedures, Prentice-Hall, USA, 1996.
  • [14] Bhatti MA. Advanced Topics in Finite Element Analysis of Structures: with Mathematica and Matlab Computations, USA: John Wiley&Sons, 2006.
  • [15] Halil, K., Spectral Analysis Program of Structures: SAPOS User Manual, Delft University of Technology, Netherlands, 79-90, 2009.
  • [16] Timoshenko, S. and Goodier, J.N., Theory of Elasticity, McGraw-Hill, New York,1951.
  • [17] Ugural, A.C., Stresses in Plates and Shells, McGraw-Hill, USA, 1981.
There are 17 citations in total.

Details

Other ID JA66DR86FK
Journal Section Articles
Authors

Ali İ. Karakaş This is me

Ayse T. Daloğlu This is me

Publication Date March 1, 2015
Published in Issue Year 2015 Volume: 7 Issue: 1

Cite

APA Karakaş, A. İ., & Daloğlu, A. T. (2015). SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS. International Journal of Engineering and Applied Sciences, 7(1), 68-85. https://doi.org/10.24107/ijeas.251240
AMA Karakaş Aİ, Daloğlu AT. SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS. IJEAS. March 2015;7(1):68-85. doi:10.24107/ijeas.251240
Chicago Karakaş, Ali İ., and Ayse T. Daloğlu. “SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS”. International Journal of Engineering and Applied Sciences 7, no. 1 (March 2015): 68-85. https://doi.org/10.24107/ijeas.251240.
EndNote Karakaş Aİ, Daloğlu AT (March 1, 2015) SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS. International Journal of Engineering and Applied Sciences 7 1 68–85.
IEEE A. İ. Karakaş and A. T. Daloğlu, “SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS”, IJEAS, vol. 7, no. 1, pp. 68–85, 2015, doi: 10.24107/ijeas.251240.
ISNAD Karakaş, Ali İ. - Daloğlu, Ayse T. “SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS”. International Journal of Engineering and Applied Sciences 7/1 (March 2015), 68-85. https://doi.org/10.24107/ijeas.251240.
JAMA Karakaş Aİ, Daloğlu AT. SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS. IJEAS. 2015;7:68–85.
MLA Karakaş, Ali İ. and Ayse T. Daloğlu. “SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS”. International Journal of Engineering and Applied Sciences, vol. 7, no. 1, 2015, pp. 68-85, doi:10.24107/ijeas.251240.
Vancouver Karakaş Aİ, Daloğlu AT. SHEAR AND VOLUMETRIC LOCKING EFFECT ON THE PERFORMANCE OF HARMONIC SOLID RING FINITE ELEMENTS. IJEAS. 2015;7(1):68-85.

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