{"title":"Efficiency of the Strain Based Approach Formulation for Plate Bending Analysis","authors":"Djamal Hamadi, Sifeddine Abderrahmani, Toufik Maalem, Oussama Temami","volume":92,"journal":"International Journal of Materials and Metallurgical Engineering","pagesStart":1408,"pagesEnd":1413,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9999026","abstract":"
In recent years many finite elements have been
\r\ndeveloped for plate bending analysis. The formulated elements are
\r\nbased on the strain based approach. This approach leads to the
\r\nrepresentation of the displacements by higher order polynomial terms
\r\nwithout the need for the introduction of additional internal and
\r\nunnecessary degrees of freedom. Good convergence can also be
\r\nobtained when the results are compared with those obtained from the
\r\ncorresponding displacement based elements, having the same total
\r\nnumber of degrees of freedom. Furthermore, the plate bending
\r\nelements are free from any shear locking since they converge to the
\r\nKirchhoff solution for thin plates contrarily for the corresponding
\r\ndisplacement based elements. In this paper the efficiency of the strain
\r\nbased approach compared to well known displacement formulation is
\r\npresented. The results obtained by a new formulated plate bending
\r\nelement based on the strain approach and Kirchhoff theory are
\r\ncompared with some others elements. The good convergence of the
\r\nnew formulated element is confirmed.<\/p>\r\n","references":"[1] O. C. Zienkiewicz and R.L. Taylor, \"The finite element method in solid\r\nand fluid mechanics, dynamics and nonlinearity\", Vol. II, (Mc Graw\r\nHill, New York, 1991).\r\n[2] R.H. Gallagher, \"Introduction to the finite elements\" .Printice-Hall, Inc.,\r\nEnglewood Cliffs, (New Jersey, USA, 1975).\r\n[3] Belarbi M.T. and Maalem T., On improved rectangular finite element for\r\nplane linear elasticity analysis, Revue europ\u00e9enne des \u00e9l\u00e9ments finis,\r\nVol. 14, N\u00b0 8, 2005.\r\n[4] Djoudi M.S. and Bahai H., A shallow shell finite element for the linear\r\nand nonlinear analysis of cylindrical shells. Engineering structures (25):\r\n769- 778, 2003.\r\n[5] Djoudi M.S. and Bahai H., A cylindrical strain-based shell element for\r\nvibration analysis of shell structures. Finite Elements in Analysis and\r\nDesign, 40: 1947-1961.\r\n[6] Belarbi M.T. and Maalem T., On improved rectangular finite element for\r\nplane linear elasticity analysis, Revue europ\u00e9enne des \u00e9l\u00e9ments finis,\r\nVol. 14, N\u00b0 8, 2005.\r\n[7] D. Hamadi, M. Mellas, R. Chebili and M. Nouaouria, \"An efficient\r\nquadrilateral membrane element for civil engineering analysis\u201d, World\r\nJournal of Engineering, Vol. 4 No.1, 2007, pp. 54 -65.\r\n[8] Belounar L. and Guenfoud M.., A new rectangular finite element based\r\non the strain approach for plate bending, Thin-Walled Structures 43\r\n(2005) 47- 63.\r\n[9] Hamadi D., Derbane S. and Ounis A., \"Formulation of A new plate\r\nbending finite element based on the strain approach, international\r\nconference on applied and computational mathematics October 2012\r\nAnkara.\r\n[10] Batoz JL, Dahtt G. Mode\u00b4lisation des structures par e\u00b4le\u00b4ments finies.\r\nPoutres et plaques, vol. 2. Paris: Hermes; 199.\r\n[11] Belarbi M.T. et Charif A., D\u00e9veloppement d'un nouvel\r\n\u00e9l\u00e9menthexa\u00e9drique simple bas\u00e9 sur le mod\u00e8le en d\u00e9formation pour\r\nl\u2019\u00e9tude des plaques minces et \u00e9paisses, Revue Europ\u00e9enne des \u00e9l\u00e9ments\r\nfinis, Vol. 8, N\u00b0 2, pp. 135-157, 1999.\r\n[12] D. Hamadi, \"Analysis of structures by non-conforming finite\r\nelements\",PhD Thesis, Civil engineering department, Biskra University,\r\nAlgeria,2006, pp. 130.\r\n[13] A. Adini. and R.W. Clough., \"Analysis of plate bending by the finite\r\nelement method\u201d, Report to the Nat. Sci. Found., U.S.A., G 7337, 1961.\r\n[14] Timoshenko S, Woinowsky-Krieger S. Theory of plates and shells.\r\nLondon: McGraw-Hill; 1959.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 92, 2014"}