A Comparative Study between Displacement and Strain Based Formulated Finite Elements Applied to the Analysis of Thin Shell Structures
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
A Comparative Study between Displacement and Strain Based Formulated Finite Elements Applied to the Analysis of Thin Shell Structures

Authors: Djamal Hamadi, Oussama Temami, Abdallah Zatar, Sifeddine Abderrahmani

Abstract:

The analysis and design of thin shell structures is a topic of interest in a variety of engineering applications. In structural mechanics problems the analyst seeks to determine the distribution of stresses throughout the structure to be designed. It is also necessary to calculate the displacements of certain points of the structure to ensure that specified allowable values are not exceeded. In this paper a comparative study between displacement and strain based finite elements applied to the analysis of some thin shell structures is presented. The results obtained from some examples show the efficiency and the performance of the strain based approach compared to the well known displacement formulation.

Keywords: Displacement formulation, Finite elements, Strain based approach, Shell structures.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094239

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2642

References:


[1] Grafton, P.E and Strome, D.R. "Analysis of axsymmetric shells by the direct stiffness method" AIAA.Vol 1.10, 1963, PP2342-2347.
[2] Jones, R.E and Strome, D.R "Direct stiffness method analysis of shells of revolution utilizing curved elements "AIAA J., Vol. 4, 1966, PP1519-1525.
[3] Brebbia, C and Connor, j.j. "Stiffness matrix for shallow rectangular shell element" J. Eng. Mech. Div. ASCE 93 EMS, 1967, PP43-65.
[4] Cantin, G. and Clough, R.W. "A curved cylindrical shell finite element". AIAA Journal, vol 6, 1968, PP1057-1062.
[5] Sabir, A.B. and lock, A.C "A curved cylindrical shell finite element". Int. J. Mech. Sci.14, 1972, P125.
[6] Ashweil,D.G., Sabir,A.B. and Roberts,T.M. "Further studies in the application of curved finite elements ta circular arches”, Int. J. Mech. Sci., vol. 13, 1971, pp. 507-517.
[7] Sabir, A.B. "Stiffness matrices for general deformation (out of plane and in plane) of curved beam members based on independent strain functions”, The Math. of Finite Elements and Applications II, Academic Press, 34, 1975, pp. 411–421.
[8] Ashwell,D.G. and Sabir,A.B. "A new cylindrical shell finite element based on simple independent strain functions”, Int. J. Mech. Sci., vol. 14, 1972, pp. 171-183.
[9] Sabir,A.B. and Charchafchi,T.A, "Curved rectangular and general quadrilateral shell element for cylindrical shells” The math. of finite elements and applications IV, Âcademic Press, 1982, pp. 231-239.
[10] Ashwell,D.G. and Sabir,A.B. "Diffusion of concentrated loads into thin cylindrical shells”, The math. of finite elements and appl. III, Academic Press, 33, 1979, pp. 379-389.
[11] Sabir,A.B. "Strain based finite elements for the analysis of cylinders with holes and normally intersecting cylinders”, Nuclear Engg and Design, 76, 1983, pp. 111-120.
[12] Sabir,A.B. and Ramadhani,F. "A shallow shell finite element for general shell analysis”, Proc. 2nd Int. Conf. on variational methods in eng., Univ. of Southampton, 1985 pp. 5-3 to 5-13.
[13] Sabir,A.B.”Strain—based shallow spherical shell element”, Proc. Int. Conf. on the mathematics of finite elements and appl., Brunel Univ., 1987.
[14] Djoudi M.S. & Sabir A.B., Finite element analysis of singly and doubly curved dams of constant or variable thickness. Thin-walled structures (21): 279- 289, 1995.
[15] Sabir A.B. & Moussa A.I., Finite element analysis of cylindrical-conical storage tanks using strain-based elements. Structural Engineering Review (8) 4: 367-374. 1996.
[16] Belarbi M.T. et Charif A., Développement d'un nouvel élément hexaédrique simple basé sur le modèle en déformation pour l’étude des plaques minces et épaisses, Revue Européenne des éléments finis, Vol. 8, N° 2, pp. 135-157, 1999.
[17] Assan A.E., Analysis of multiple stiffened barrel shell structures by strain-based finite elements. Thin-walled structures (35): 233-253, 1999.
[18] Djoudi M.S. & Bahai H., A shallow shell finite element for the linear and nonlinear analysis of cylindrical shells. Engineering structures (25): 769- 778, 2003.
[19] Djoudi M.S. & Bahai H., A cylindrical strain-based shell element for vibration analysis of shell structures. Finite Elements in Analysis and Design, 40: 1947-1961. 2004.
[20] Djoudi M.S. & Bahai H., Strain- based finite element for the vibration of cylindrical panels with openings. Thin-walled structures (42): 575-588, 2004.
[21] D. Hamadi, R. Chebili and M. Mellas: Numerical and Experimental Investigation of an Elliptical Paraboloid Shell Model. Computer Technology and Application, 6 Vol. 2 No 4 April 2011, pages 324-328, Editor David Publishing Company, ISSN: 1934-7332 (Print), ISSN: 1934-7340 (Online). Website: www.davidpublishing.com
[22] D. Hamadi, M. Mellas, R. Chebili and M. S. Nouaouria, "An efficient quadrilateral membrane element for civil engineering analysis”, World Journal of Engineering, Vol 4 N°. 1, 2007, pp 54-65.
[23] A. Adini. and R.W. Clough., "Analysis of plate bending by the finite element method”, Report to the Nat. Sci. Found., U.S.A., G 7337, 1961.
[24] R.J. Melosh, "Basis of derivation of matrices for the direct stiffness method”, J.AIAA Vol. 1 N7, 1963, pp. 1631-1637.
[25] Dhatt G ,and Touzot G; "une présentation de la méthode des éliment finis ", Eds Maloine, Paris,1984.
[26] Fraeijis de veubeke B ;"Les connexions cinématiques co-déformables des élements de coques plans" , Univ de Liège,1974.
[27] Belarbi M.T. et Charif A., Développement d'un nouvel élément hexaédrique simple basé sur le modèle en déformation pour l’étude des plaques minces et épaisses, Revue Européenne des éléments finis, Vol. 8, N° 2, pp. 135-157, 1999.
[28] D. Hamadi, "Analysis of structures by non-conforming finite elements", PhD Thesis, Civil engineering department, Biskra University, Algeria, 2006, pp. 130.
[29] F.E Hazim,"Finite element analysis of shell structures"; University of Wales College of Cardiff, Phd Thesis 1989.
[30] A.I. Mousa and M.H. El Naggar." Shallow Spherical Shell Rectangular Finite Element for Analysis of Cross Shaped Shell Roof ", Electronic Journal of Structural Engineering, 7(2007).
[31] Batoz J.L. et Dhatt G., Modélisation des structures par éléments finis, Vol. 3 : coques, Eds Hermès, Paris, 1992.
[32] M.T. Belarbi , "Développement de nouveaux éléments finis bases sur le modèle en déformation. Application linéaire et non linéaire”.Thèse de Doctorat d’état, Université de Constantine, Algérie, 2000.Scordelis
[33] Schnobrich,W.C. "Stresses in gable roof H.P. Shells", Bull. Int. Assoc. for shells and spatial structures, 1977.
[34] A.C. Scordelis A.C. and Lo K.S.,Computer analysis of cylindrical shells, J. Amer. Concrete Institute Vol. 61, pp. 539-561, 1969. Journal of Structural Engineering, 7(2007).