Abstract
We present a simple methodology to design curved shell finite elements based on Nzengwa-Tagne’s shell equations. The element has three degrees of freedom at each node. The displacements field of the element satisfies the exact requirement of rigid body modes in a ‘shifted-Lagrange’ polynomial basis. The element is based on independent strain assumption insofar as it is allowed by the compatibility equations. The element developed herein is first validated on analysis of benchmark problems involving a standard shell with simply supported edges. Examples illustrating the accuracy improvement are included in the analysis. It showed that reasonably accurate results were obtained even when using fewer elements compared to other shell elements. The element is then used to analyse spherical roof structures. The distribution of the various components of deflection is obtained. Furthermore, the effect of introducing concentrated load on a cylindrical clamped ends structure is investigated. It is found that the CSFE3-sh element considered is a very good candidate for the analysis of general shell structures in engineering practice in which the ratio h/R ranges between 1/1000 and 2/5.
References
[1] Raju G., Babu K.H., Nagaraju N.S., Chand K.K., Design and analysis of Stress on Thick Walled Cylinder with and without Holes Int. J. Eng. Research and Appl. 2015, 5, 75-83.Search in Google Scholar
[2] Kim D.N., Bathe K.J., A triangular six-node shell element, Computers and Structures, 2009, 87, 1451-1460.10.1016/j.compstruc.2009.05.002Search in Google Scholar
[3] Lahcene Fortas L.B., Merzouki T., Formulation of a new fnite element based on assumed strains for membrane structures, Int. J. Adv. Str. Eng, 2019, 11, S9-S19.10.1007/s40091-019-00251-9Search in Google Scholar
[4] Carrera E., Valvano S., Filippi M., Classical, higher-order, zigzag and variable kinematic shell elements for the analysis of composite multilayered structures, Euro. J. Mech./A Solids, 2018, 72, 97-110.10.1016/j.euromechsol.2018.04.015Search in Google Scholar
[5] Harursampath D., Keshava Kumar S., Carrera E., Cinefra M., Valvano S., Modal analysis of delaminated plates and shell using Carrera Unified Formulation-MITC9 shell element, Mech. Adv. Mat. Struc. 2018, 8, 681-697. 8510.1080/15376494.2017.1302024Search in Google Scholar
[6] Huang L.H., Li G., A 4-node plane parameterized element based on quadrilateral area coordinate, Eng. Mech., 2014, 31, 15-21.Search in Google Scholar
[7] Taylor R.L., Piltner R., A systematic construction of B-BAR functions for linear and non-linear mixed-enhanced fnite elements for plane elasticity problems, Int. J. Numer. Meth. Eng, 1999, 5, 615-635.10.1002/(SICI)1097-0207(19990220)44:5<615::AID-NME518>3.0.CO;2-USearch in Google Scholar
[8] Chen X.M., Cen S., Long Y.Q., Yaob Z.H., Membrane elements insensitive to distortion using the quadrilateral area coordinate method, Comp. Struct., 2004, 82(1), 35-54.10.1016/j.compstruc.2003.08.004Search in Google Scholar
[9] Wang C., Qi Z., Zhang X., Hu P., Quadrilateral 4-node quasicon-forming plane element with internal parameters., Chin. J. Theor. Appl. Mech., 2014, 6, 971-976.Search in Google Scholar
[10] Xia Y., Zheng G., Hu P., Incompatible modeswith Cartesian coordinates and application in quadrilateral fnite element formulation., Comput. Appl. Math., 2017, 2, 859-875.10.1007/s40314-015-0262-zSearch in Google Scholar
[11] Cen S., Zhou M.J., Fu X.R., An unsymmetric 4-node, 8-DOF plane membrane element perfectly breaking through MacNeal’s theorem., Int. J. Numer. Meth. Eng., 2015, 7, 469-500.10.1002/nme.4899Search in Google Scholar
[12] Kugler S., Fotiu P.A., Murin J., A highly efficicient membrane finite element with drilling degrees of freedom, Acta Mech., 2010, 3-4, 323-348.10.1007/s00707-009-0279-8Search in Google Scholar
[13] Cen S., Zhou M.J., Fu X.R., A 4-node hybrid stress-function (HSF) plane element with drilling degrees of freedom less sensitive to severe mesh distortions, Comput. Struct., 2011, 5-6, 517-528.10.1016/j.compstruc.2010.12.010Search in Google Scholar
[14] Hammady F., Zouari W., Ayad R., Quadrilateral membrane finite elements with rotational DOFs for the analysis of geometrically linear and nonlinear plane problems., Comput. Struct., 2016, 173, 139-149.10.1016/j.compstruc.2016.06.004Search in Google Scholar
[15] Grafton P.E., Strome D.R., Analysis of axisymmetric shells by the direct stiffness method, AIAA, 1963, 1.10, 2342-2347.10.2514/3.2064Search in Google Scholar
[16] Jones R.E., Strome D.R., Direct stiffness method analysis of shells of revolution utilizing curved elements, AIAA J, 1966, 4, 1519-1525.10.2514/3.3729Search in Google Scholar
[17] Sabir A.B., Lock A.C., A curved cylindrical shell finite element, Int. J. Mech. Sci., 1972, 14, 125.10.1016/0020-7403(72)90093-8Search in Google Scholar
[18] Moharos I., Oldal I., Szekrényes A., Finite element method, Typo-tex Publishing, 2012, House.Search in Google Scholar
[19] Mousa A.I., El Naggar M.H., Shallow Spherical Shell Rectangular Finite Element for Analysis of Cross Shaped Shell Roof, Elec. J. Struct. Eng., 2007, 7.Search in Google Scholar
[20] Bathe K.J., Lee P.S., Hiller J.F., Towards improving the MITC9 shell element, Comput. Struc., 2003, 81, 477-489.10.1016/S0045-7949(02)00483-2Search in Google Scholar
[21] Chapelle, D., Bathe K.J., The finite element analysis of shells-Fundamentals, 2010, Springer Science & Business Media.10.1007/978-3-642-16408-8Search in Google Scholar
[22] Kim D.N., Bathe K.J., A 4-node 3D-shell element to model shell surface tractions and incompressible behaviour, Comput. Struct., 2008, 86, 2027-2041.10.1016/j.compstruc.2008.04.019Search in Google Scholar
[23] Bathe K.J., The finite element method, Encyclopedia of computer science and engineering, 2009, 1253-1264, Wiley & Sons,.10.1002/9780470050118.ecse159Search in Google Scholar
[24] Lee P.S., Noh H.C., Bathe K.J., Insight into 3-node triangular shell finite elements: the effects of element isotropy and mesh patterns, Comput. Struct., 2007, 85, 404-418.10.1016/j.compstruc.2006.10.006Search in Google Scholar
[25] Tornabene F., Liverani A., Caligiana G., General anisotropic doubly-curved shell theory: A differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian, J. Sound and Vibr., 2012, 331, 4848-4869.10.1016/j.jsv.2012.05.036Search in Google Scholar
[26] Zeighampour H., Tadi Beni Y., Cylindrical thin-shell model based on modified strain gradient theory, Int. J. Eng. Sci., 2014, 78, 27-47.10.1016/j.ijengsci.2014.01.004Search in Google Scholar
[27] Nzengwa R., Feumo A.G., Nkongho Anyi J., Finite Element Model for Linear Elastic Thick Shells Using Gradient Recovery Method, Math. Prob. Eng., 2017, 14, 5903503.10.1155/2017/5903503Search in Google Scholar
[28] Echter R., Oesterle B., Bischoff M., A hierarchic family of isogeo-metric shell finite elements, Comp. Meth. Appl. Mech. Eng., 2013, 254, 170-180.10.1016/j.cma.2012.10.018Search in Google Scholar
[29] Bessais L., Analyse des structures par la MEF basée sur l’approche en déformation, Génie mécanique, Université Mohamed Khider-Biskra, 2012.Search in Google Scholar
[30] Nkongho Anyi J., Nzengwa R., Amba J.C., Abbe Ngayihi C.V., Approximation of Linear Elastic Shells by Curved Triangular Finite Elements Based on Elastic Thick Shells Theory, Math. Prob. Eng., 2016, 12, 8936075.10.1155/2016/8936075Search in Google Scholar
[31] Sabir A.B., Djoudi M.S., A shallow shell Triangular Finite Element for the Analysis of spherical shells, Struct. Ana. J., 1999, 51-57.Search in Google Scholar
[32] Mousa A.I., Finite Element Analysis of groined vault cylindrical in plan, AL-Azhar Eng. J., 2001, 37-50.Search in Google Scholar
[33] Nzengwa R., Simo Tagne B.H., A two-dimensional model for linear elastic thick shells, Inter. J. Sol. Struct., 1999, 36, 5141-5176.10.1016/S0020-7683(98)00165-6Search in Google Scholar
[34] McNeal R.H., Harder R.L., Refined Four Node Membrane Element with Rotational Degrees of Freedom, Comp. Struct., 1988, 28, 75-84.10.1016/0045-7949(88)90094-6Search in Google Scholar
[35] Lindberg G.M., Olson M.D., Cowper G.R., New developments in the finite element analysis of shell, Bulletin Division of Mechanical Engineering and National Aeronautical Establishment, National Research Council of Canada, 1969.Search in Google Scholar
[36] Saigal S., Yang H.T., Masud A., Kapania R., A Survey of Recent Shell Finite Elements, Int. J. Num. Meth. Eng., 2000, 101-127.10.1002/(SICI)1097-0207(20000110/30)47:1/3<101::AID-NME763>3.0.CO;2-CSearch in Google Scholar
[37] Djoudi M.S., Strain based Finite Elements for linear and geometrically analysis of structures, College of Cardiff (G.B), University of Walles, 1990.Search in Google Scholar
[38] A documentation, Abaqus Analysis User’s Manual, 2007.Search in Google Scholar
© 2020 Joseph Nkongho Anyi et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
