An Efficient Strain Based Cylindrical Shell Finite Element

Document Type : Research Paper


Civil Engineering Department, University of Biskra, BP 145 RP, 07000 Biskra, Algeria


The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additional rotational degree of freedom. The resulting element has 24 degrees of freedom, six essential external degrees of freedom at each of the four nodes and thus, avoiding the difficulties associatedwithinternal degrees of freedom (the three translations and three rotations) and the displacement functions of the developed element satisfy the exact representation of the rigid body motion and constant strains (in so far as this allowed by compatibility equations). Numerical experiments analysis have been conducted to assess accuracy and reliability of the present element, this resulting element with the added degree of freedom is found to be numerically more efficient in practical problems than the corresponding Ashwell element [4].


[1] Belarbi M.T. , Bourezane M., 2005, On improved sabir triangular element with drilling rotation, Revue Européenne de Genie Civil 9: 1151-1175.
[2] Belarbi M.T., 2000, Developpement de Nouvel Element Fini Base Sur le Modele en Deformation, Application Lineaire et Non Lineaire, Phd Thesis, University of Constantine, Algeria.
[3] Bourezane M., 2006, Utililisation of the Strain Model in the Analysis of the Structures, Phd Thesis, University of Biskra, Algeria.
[4] Ashwell D.G., Sabir A.B., 1972, A new cylindrical shell finite element based on simple independent strain functions, International Journal of Mechanical Sciences 14: 171-183.
[5] Lindberg G.M., Olson M.D., Cowper G.R., 1969, New Development in the Finite Element Analysis of Shells, Structures and Materials Laboratory National Aeronautical Establishment, National Research Council of Canada.
[6] Yang T.Y., 1973, High order rectangular shallow shell finite element, Journal of Engineering Mechanics 99: 157-181.
[7] Dawe D.J., 1975, High order triangular finite element for shell analysis, International Journal of Solids Structures 11: 1097-1110.
[8] Hrennlkoff A., Tezcan S.S, 1968, Analysis of cylindrical shells by the finite element method, Sympoium on Problems of Interdependence of Design and Construction of Large Span Shells, Lenigrad.
[9] Zienkiewicz O.C., Cheng Y.K., 1967, The Finite Element in Structural and Continuum Mechanics, Mc Graw Hill, Book Co, London.
[10] Clough R.W., Johnson R.G., 1968, A finite element approximation for the analysis of thin shells, International Journal for Solids and Structures 4: 43-60.
[11] Carr A.J., 1967, A Refined Finite Element Analysis of Thin Shell Structures Including Dynamic Loadings, Phd Thesis, University of California, Berekely.
[12] Bogner F.K., Fox R.L., Schmit L.A., 1967, A cylindrical shell discrete element, AIAA Journal 5: 745-750.
[13] Cantin G., Clouth R.W., 1968, A curved cylindrical shell Finite Element, AIAA Journal 6: 1057-1062.
[14] Olson M.D., Lindberg G.M., 1968, Vibration analysis of cantilevered curved plates usisng a new cylindrical shell finite element, Proceedings of the Second Conference on Matrix Methods in Structural Mechanics ,Wright- Patterson AFB, Ohio.
[15] Ashwell D.G., Sabir A.B., 1971, Limitations of certain curved finite elements when applied to arches, International Journal of Mechanical Sciences 13: 133-139.
[16] Ashwell D.G., Sabir A.B., Roberts T.M., 1971, Further studies in the application of curved elements to circular arches, International Journal of Mechanical Sciences 13(6): 507-517.
[17] Sabir A.B., Lock A.C., 1972, A curved cylindrical shell finite element, International Journal of Mechanical Sciences 14(2): 125-135.
[18] Sabir A.B., Sfendji A., 1995, Triangular and rectangular plane elasticity finite elements, Thin Walled Structures 21(3): 225-232.
[19] Sabir A.B., Moussa A.I. , 1997, Analysis of fluted conical shell roofs using the finite element method, Computer and Structures 64 (1-4): 239-251.
[20] Sabir A.B., Salhi H.Y., 1986, A strain based finite element for general plane elasticity problems in polar coordinates, Research Mechanica 19: 1-6.
[21] Sabir A.B., 1983, Strain based finite elements for the analysis of cylinders with holes and normally intersecting cylinders, Nuclear Engineering and Design North-Holland 76: 111-120.
[22] Sabir A.B., Ashwell D.G., 1969, A stiffness matrix for shallow shell finite elements, International Journal of Mechanical Science 11: 269-279.
[23] Sabir A.B., Ramadani F., 1985, A shallow shell finite element for general shell analysis, Proceedings of the 2nd International Conference on Variational Methods in Engineering.
[24] Sabir A.B., 1983, A new class of finite elements for plane elasticity problems, CAFEM 7th, International Conference on Structural Mechanics in Reactor Technology,Chicago.
[25] Trinh V.D., Abed-Meriam F., Comberscure A., 2011, Assumed strain solid- shell formulation “SHB6’’ for the six node prismatic, Journal of Mechanical Science and Technology 25(9): 2345-2364.
[26] Mousa A.I., EINaggar M.H., 2007, Shallow spherical shell rectangular finite element for analysis of cross shaped shell roof, Electronic Journal of Structural Engineering 7: 41-51.
[27] Rebiai C., Belounar L., 2013, A new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis, Archives of Civil and Mechanical Engineering 13: 72-81.
[28] Djoudi M.S., Bahi H., 2003, A shallow shell finite element for the linear and nonlinear analysis of cylindrical shells, Engineering Structures 25(6):769-778.
[29] Sabir A.B., Djoudi M.S., 1995, Shallow shell finite element for the large deflection geometrically nonlinear analysis of shells and plates, Thin Wall Structures 21: 253-267.
[30] Timoshenko S., Woinoisky-Kreiger S., 1959, Theory of Plates and Shells, Mc Graw-Hill, New York.
[31] Charchafchi T.A., Sabir A.B., 1982, Curved Rectangular and General Quadrilateral Shell Element for Cylindrical Shells,The Mathematics of Finite Element and Applications , Whiteman Academic Press.
[32] Cantin G., 1970, Rigid body motions in curved finite elements, AIAA Journal 8: 1252-1255.
[33] Bull J.W., 1984, The strain approach to the development of thin cylindrical shell finite element, Computer and Structures 2(3): 195-205.
[34] Batoz J.L., Dhatt G., 1992, Modélisation des Structures par Eléments Finis, Coques, Eds Hermès, Paris.
[35] MacNeal R. H., Harder R. L., 1985, A proposed standard set of problems to test finite element accuracy, Finite Elements in Analysis and Design 1: 3-20.