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References
Ashwell, D.G. and Sabir, A.B., (1972). A new cylindrical shell finite element based on simple independent strain functions. Int. J. Mech. Sci., 14, 171–183.
Belytschko, T., Liu, W.K., Ong, J.S.-J. (1984a). A consistent control of spurious singular modes in the 9-node Lagrange element for the Laplace and Mindlin plate equations. Comput. Meths. Appl. Mech. Eng., 44, 269–295.
Belytschko, T., Ong, J.S.-J., Liu, W.K., Kennedy, J.M. (1984b). Hourglass control in linear and non-linear problems, Comput. Meths. Appl. Mech. Eng., 43, 251–276.
Belytschko, T., Stolarski, H., Carpenter, N. (1984c). A C° triangular plate element with one-point quadrature. Int. J.Num. Meths. Eng., 20, 787–802.
Belytschko, T., Stolarski, H., Liu, W.K., Carpenter, N., Ong, J.S.-J. (1985). Stress projection for membrane and shear locking in shell finite elements. Comput. Methods Appl. Mech. Eng., 51, 221–258.
Cook, R.D. (1972). Two hybrid elements for analysis of thick and thin sandwich plates. Int. J.Num. Meths. Eng., 5, 277.
Cook, R.D., Malkus, D.S., Plesha, M.E. (1989). Concepts and Applications of Finite Element Analysis. 3rd edition, John Wiley & Sons, New York.
Cook, R.D., Malkus, D.S., Plesha, M.E., Witt, R.J. (2002). Concepts and Applications of Finite Element Analysis. 4th edition, John Wiley & Sons, New York.
Flugge, W. (1960). Stresses in Shells. Springer, New York.
Hibbit, Karlson & Sorensen, Inc. (2001). Abaqus, Theory Manual, Pawtucket, RI, USA
Hu, H-C. (1981). The Variational Principles in Elasticity and its Application. Scientific Publisher, Beijing.
Hughes, T.J.R. (1987). The Finite Element Method. Prentice-Hall, Englewood-Cliffs, NJ.
Hughes, T.J.R. and Hinton, E. (1986). Finite Element Methods for Plate and Shell Structures. Pineridge, Swansea, UK.
Koiter,W.T. (1960). A consistent first approximation in general theory of thin elastic shells. In Theory of Thin Elastic Shells, First IUTAM Symp. (Edited by W.T. Koiter), pp 12–33. North-Holland, Amsterdam.
Lindberg, G.M., Olson, M.D., Cowper, G.R. (1969). New developments in the finite element analysis of shells. Qart. Bull. Div. Mech. Eng. Natl. Aeronautical Establishment, 4, 1–99.
Liu, Y., Shi, G., Tang, L. (1984). Quasi-conforming elements for thick/thin beam and plate bending problems. J. DIT, 22, 3, 79–85.
Lu, H. and Liu, Y. (1981). Quasi-conforming element technique applied to double curvature shallow shells. J. DIT, 20, 1.
MacNeal, H.R. and Harder, R.L. (1985). A proposed standard set of problems to test finite element accuracy. Finite Elements Anal. Design, 1, 3–20. North-Holland.
Morley, L.S.D and Morris, A.J. (1978). Conflict between finite elements and shell theory, Royal Aircraft Establishment Report. London.
Sanders, J.L. (1959). An improved first approximation theory of thin shells. NASA Report24.
Scordelis, A.C. and Lo, K.S. (1969) Computer analysis of cylindrical shells. J. Am. Concrete Inst.; 61:539–561.
Shi, G. and Voyiadjis, G.Z. (1990). A simple C0 quadrilateral thick/thin shell element based on the refined shell theory and the assumed strain fields. Int. J. Solids Struct., 27, 3, 283–298.
Shi, G. and Voyiadjis, G.Z. (1991a). Geometrically nonlinear analysis of plates by assumed strain element with explicit tangent stiffness. Comput. Struct., 41, 757–763.
Shi, G. and Voyiadjis, G.Z. (1991b). Simple and efficient shear flexible two node arch/beam and four node cylindrical shell/plate finite element. Int. J. Num. Meth. Eng., 31, 759–776.
Simo, J.C.; Fox, D.D. and Rifai, M.S. (1989a). On a stress resultant geometrically exact shell model. Comp. Meth. Appl. Mech. Eng., 73, 53–92, North-Holland.
Simo, J.C.; Fox, D.D. and Rifai, M.S. (1989b). On a stress resultant geometrically exact shell model. Part II: The linear theory. Comp Meth. Appl. Mech. Eng., 73, 53–92, North-Holland.
Stolarski, H. and Belytschko, T. (1981). Reduced integration for shallow-shell facet elements. New Concepts in Finite Element Analysis, Eds. T.J.R. Hughes, et. al., ASME, New York 179–194.
Stolarski, H. and Belytschko, T. (1982). Membrane locking and reduced integration for curved elements. J. Appl. Mech. 49, 172–177.
Tang, L., Chen, W. and Liu, Y. (1980). Quasi-conforming elements for finite element analysis. J. DIT, 19, 2.
Tang, L., Chen, W. and Liu, Y. (1983). String net function applications and quasi conforming technique. In Hybrid and Mixed Finite Element Methods, Wiley, New York
Timoshenko, S.P. and Woinowsky-Krieger, S. (1959). Theory of Plates. McGraw-Hill, Inc., New York.
Zienkiewicz, O.C. (1971). The Finite Element in Engineering Science. McGraw-Hill, London.
Zienkiewicz, O.C. (1978). The Finite Element Method, McGraw-Hill, New York.
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Voyiadjis, G.Z., Woelke, P. (2008). Shell Element Based on the Refined Theory of Thick Spherical Shells. In: Elasto-Plastic and Damage Analysis of Plates and Shells. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79351-9_3
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