|تعداد مشاهده مقاله||108,056,899|
|تعداد دریافت فایل اصل مقاله||84,476,903|
Impact of Integration on Straining Modes and Shear-Locking for Plane Stress Finite Elements
|Civil Engineering Infrastructures Journal|
|مقاله 11، دوره 51، شماره 2، اسفند 2018، صفحه 425-443 اصل مقاله (1.59 M)|
|نوع مقاله: Research Papers|
|شناسه دیجیتال (DOI): 10.7508/ceij.2018.02.011|
|Mehdi Ghassemieh* 1؛ Behrouz Badrkhani Ajaei2|
|1Professor, School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran.|
|2Department of Civil Engineering, Boğazi&ccedil;i University, Istanbul, Turkey.|
|Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectangular as well as square element. It is shown that method of integration has no effect on the straining modes, but it influences the eigenvalues of the bending modes. This effect is intensified by increasing the element aspect ratio, confirming the occurrence of shear locking.|
|Finite Elements؛ Plane Stress؛ Reduced Integration؛ Shear Locking؛ Straining Modes|
Adam, C., Bouabdallah, S., Zarroug, M. and Maitournam, H. (2014). “Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams”, Computer Methods in Applied Mechanics and Engineering, 279, 1-28.
Adam, C., Bouabdallah, S., Zarroug, M. and Maitournam, H. (2015). “Improved numerical integration for locking treatment in isogeometric structural elements. Part II: Plates and shells”, Computer Methods in Applied Mechanics and Engineering, 284, 106-137.
Arnold, D. and Brezzi, F. (1997). “Locking-free Finite Element methods for shells”, Mathematics of Computation of the American Mathematical Society, 66(217), 1-14.
Bathe, K.J. (2014). Finite Element Procedures, 2nd Edition, K.J. Bathe, Watertown, MA, USA.
Bletzinger, K.U., Bischoff, M. and Ramm, E. (2000). “A unified approach for shear-locking-free triangular and rectangular shell Finite Elements”, Computers and Structures, 75(3), 321-334.
da Veiga, L. B., Lovadina, C., and Reali, A. (2012). “Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods”, Computer Methods in Applied Mechanics and Engineering, 241, 38-51.
Fallah, N., Parayandeh-Shahrestany, A. and Golkoubi, H. (2017). “A Finite Volume formulation for the elasto-plastic analysis of rectangular Mindlin-Reissner plates, a non-layered approach”, Civil Engineering Infrastructures Journal, 50(2), 293-310.
Garcia-Vallejo, D., Mikkola, A.M. and Escalona, J.L. (2007). “A new locking-free shear deformable Finite Element based on absolute nodal coordinates”, Nonlinear Dynamics, 50(1-2), 249-264.
Javidinejad, A. (2012). “FEA practical illustration of mesh-quality-results differences between structured mesh and unstructured mesh”, ISRN Mechanical Engineering, Volume 2012, Article ID 168941, 7 pages, doi:10.5402/2012/168941.
Kanok‐Nukulchai, W., Barry, W., Saran‐Yasoontorn, K. and Bouillard, P. H. (2001). “On elimination of shear locking in the element‐free Galerkin method”, International Journal for Numerical Methods in Engineering, 52(7), 705-725.
Kreyszig, E. (2011). Advanced engineering mathematics, 10th Edition, John Wiley & Sons, New Jersey, USA.
Liu, G.R. and Quek, S.S. (2014). The Finite Element method, A practical course, 2nd Edition, Butterworth–Heinemann, Oxford, UK.
Logan, D.L. (2012). A first course in the Finite Element method, 5th Edition, Global Engineering, Stamford, CT, USA.
Nguyen-Thanh, N., Rabczuk, T., Nguyen-Xuan, H. and Bordas, S.P. (2008). “A smoothed Finite Element method for shell analysis”, Computer Methods in Applied Mechanics and Engineering, 198(2), 165-177.
Nguyen-Xuan, H., Liu, G.R., Thai-Hoang, C.A. and Nguyen-Thoi, T. (2010). “An edge-based smoothed Finite Element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates”, Computer Methods in Applied Mechanics and Engineering, 199(9-12), 471-489.
Pagani, M., Reese, S. and Perego, U. (2014). “Computationally efficient explicit nonlinear analyses using reduced integration-based solid-shell Finite Elements”, Computer Methods in Applied Mechanics and Engineering, 268, 141-159.
Pawsey, S.F. and Clough, R.W. (1971). “Improved numerical integration of thick shell Finite Elements”, International Journal for Numerical Methods in Engineering, 3(4), 575-586.
Pugh, E.D.L., Hinton, E. and Zienkiewicz, O.C. (1978). “A study of quadrilateral plate bending elements with reduced integration”, International Journal for Numerical Methods in Engineering, 12(7), 1059-1079.
Reddy, J.N. (1997). “On locking-free shear deformable beam Finite Elements”, Computer Methods in Applied Mechanics and Engineering, 149(1-4), 113-132.
Reddy, J.N. (2006). An introduction to the Finite Element method, 3rd Edition, McGraw Hill, New Jersey, USA.
Rezaiee-Pajand, M. and Yaghoobi, M. (2012). “Formulating an effective generalized four-sided element”, European Journal of Mechanics-A/Solids, 36, 141-155.
Rezaiee-Pajand, M. and Yaghoobi, M. (2013). “A free of parasitic shear strain formulation for plane element”, Research in Civil and Environmental Engineering, 1, 1-27.
Rezaiee-Pajand, M. and Yaghoobi, M. (2014). “A robust triangular membrane element”, Latin American Journal of Solids and Structures, 11(14), 2648-2671.
Rezaiee-Pajand, M. and Yaghoobi, M. (2015). “Two new quadrilateral elements based on strain states”, Civil Engineering Infrastructures Journal, 48(1), 133-156.
Rezaiee-Pajand, M. and Yaghoobi, M. (2017). “A hybrid stress plane element with strain field”, Civil Engineering Infrastructures Journal, 50(2), 255-75.
van Rossum, G. and Drake, F.L. (2010). “The Python Language Reference”, Python Software Foundation, from https://docs.python.org/release/2.7/reference/index.html
Videla, L., Baloa, T., Griffiths, D. V. and Cerrolaza, M. (2007). “Exact integration of the stiffness matrix of an 8-node plane elastic Finite Element by symbolic computation”, Numerical Methods for Partial Differential Equations, 24(1), 249-261.
Walentyski, R.A. (2008). “On exact integration within an isoparametric tetragonal Finite Element”, International Conference of Numerical Analysis and Applied Mathematics, AIP Conference Proceedings, 936, 582-585.
Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971). “Reduced integration technique in general analysis of plates and shells”, International Journal for Numerical Methods in Engineering, 3(2), 275-290.
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