Quadrilateral Isoparametric Shear Deformable Shell Element for Use in Soil-Structure Interaction Problems
Publication: International Journal of Geomechanics
Volume 7, Issue 1
Abstract
In the finite-element analysis of soil-structure interaction problems, shell elements are important to model structural components such as tunnel linings or sheet pile walls. In this paper the development, implementation, and testing of a curved quadrilateral isoparametric shear deformable shell element are presented. An overriding concern in the analysis of soil-structure interaction problems is the compatibility of the shell elements with the solid elements used to model the soil. Many recent publications on shell elements deal with the elements in a purely structural context and therefore do not require the compatibility with solid elements. The development of the shell element presented here forms an extension of a new approach to curved Mindlin and axisymmetric shell elements introduced by Day and Potts in 1990. There are no generally accepted benchmarking marking problems for the use of shell elements in three-dimensional geotechnical engineering problems. Consequently, the performance of the shell element is first assessed by analyzing standard structural benchmarking problems. It is found that the new element performs well compared to other elements used in a purely structural context. Further, it is demonstrated that the same element that is used to analyze curved shells can be used to analyze flat plates without the requirement of a different formulation. Finally, the performance of the new shell element is compared with a closed form solution in the analysis of a deep tunnel.
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References
Ahmad, S., Irons, B. M., and Zienkiewicz, O. C. (1970). “Analysis of thick and thin shell structures by curved finite elements.” Int. J. Numer. Methods Eng., 2(3), 419–451.
Augarde, C. E., and Burd, H. J. (2001). “Three-dimensional finite element analysis of lined tunnels.” Int. J. Numer. Analyt. Meth. Geomech., 25(3), 243–262.
Belytschko, T., Stolarski, H., Liu, W. G., Carpenter, N., and Ong, J. S.-J. (1985). “Stress projection for membrane and shear locking in shell finite elements.” Comput. Methods Appl. Mech. Eng., 51(1–3), 221–258.
Crisfield, M. A. (1986). Finite element and solution procedures for structural analysis, Vol. 1, Pineridge Press, Swansea, U.K.
Day, R. A. (1990). “Finite element analysis of sheet pile retaining walls.” Ph.D. thesis, Imperial College, Univ. of London, London.
Day, R. A., and Potts, D. M. (1990). “Curved Mindlin beam and axi-symmetric shell elements—A new approach.” Int. J. Numer. Methods Eng., 30(7), 1263–1274.
Einstein, H. H., and Schwartz, C. (1979). “Simplified methods for tunnel design.” J. Geotech. Engrg. Div., 105, 499–518.
Hinton, E., and Huang, H. C. (1986). “A family of quadrilateral Mindlin plate elements with substitute shear strain fields.” Comput. Struct., 23(3), 409–431.
Hughes, T. J. R., and Brezzi, F. (1989). “On drilling degrees of freedom.” Comput. Methods Appl. Mech. Eng., 72(1), 105–121.
Jaamei, S., Frey, F., and Jetteur, P. (1989). “Nonlinear thin shell finite element with six degrees of freedom per node.” Comput. Methods Appl. Mech. Eng., 75(1–3), p. 251–266.
Kamoulakos, A. (1988). “Understanding and improving the reduced integration of Mindlin shell elements.” Int. J. Numer. Methods Eng., 26(9), 2009–2029.
Kanok-Nukulchai, W. (1979). “A simple and efficient finite element for general shell analysis” Int. J. Numer. Methods Eng., 14(2), 179–200.
Kraus, H. (1967). Thin elastic shells, Wiley, New York.
Liu, J., Riggs, H. R., and Tessler, A. (2000). “A four-node, shear deformable shell element developed via explicit Kirchhoff constraints.” Int. J. Numer. Methods Eng., 49(8), 1065–1086.
Love, A. E. H. (1888). “On the small free vibrations and deformations of thin elastic shells.” Philos. Trans. R. Soc. London, 179, 491–546.
Love, A. E. H. (1944). A treatise on the mathematical theory of elasticity, 4th Ed., Dover, New York.
MacNeal, R. H., and Harder, R. L. (1985). “A proposed standard set of problems to test finite element accuracy.” Finite Elem. Anal. Design, 1(1), 3–20.
Naghdi, P. M. (1957). “On the theory of thin elastic shells.” Q. Appl. Math., 14(4), 369–380.
Pawsey, S. F., and Clough, R. W. (1971). “Improved numerical integration of thick shell finite elements.” Int. J. Numer. Methods Eng., 3(4), 575–586.
Phaal, R., and Calladine, C. R. (1992). “A simple class of finite elements for plate and shell problems. II: An element for thin shell with only translational degrees of freedom.” Int. J. Numer. Methods Eng., 35(5), 979–996.
Prathap, G., and Ramesh Babu, C. (1986). “An isoparametric quadratic thick curved beam element.” Int. J. Numer. Methods Eng., 23(9), 1583–1600.
Reissner, E. (1952). “Stress strain relations in the theory of thin elastic shells.” J. Math. Phys. (Cambridge, Mass.), 31(2), 109–119.
Schroeder, F. C. (2003). “The influence of bored piles on existing tunnels.” Ph.D. thesis, Imperial College, Univ. of London, London.
Scordelis, A. C. (1971). “Analysis of cylindrical shells and folded plates.” Concrete thin shells, American Concrete Institute Publication No. SP-28, Detroit, 207–236.
Scordelis, A. C., and Lo, K. S. (1969). “Computer analysis of cylindrical shells.” J. Am. Concr. Inst., 61(5), 539–561.
Timoshenko, S., and Woinowsky-Krieger, S. (1959). Theory of plates and shells, 2nd Ed., McGraw-Hill, New York.
Yang, H. T. Y., Saigal, S., Masud, A., and Kapania, R. K. (2000). “A survey of recent shell finite elements.” Int. J. Numer. Methods Eng., 47(1–3), 101–127.
Zhang, Y. X., Cheung, Y. K., and Chen, W. J. (2000). “Two refined non-conforming quadrilateral flat shell elements.” Int. J. Numer. Methods Eng., 49(3), 355–382.
Zienkiewicz, O. C., Bauer, J., Morgan, K., and Onate, E. (1977). “A simple and efficient element for axi-symmetric shells.” Int. J. Numer. Methods Eng., 11(10), 1545–1558.
Zienkiewicz, O. C., and Taylor, R. L. (1991). The finite element method, Vol. 2, 4th Ed., McGraw-Hill, London.
Zienkiewicz, O. C., Taylor, R. L., and Too, J. M. (1971). “Reduced integration technique in general analysis of plates and shells.” Int. J. Numer. Methods Eng., 3(2), 275–290.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 7 • Issue 1 • January 2007
Pages: 44 - 52
Copyright
© 2007 ASCE.
History
Received: Dec 9, 2004
Accepted: Jan 26, 2006
Published online: Jan 1, 2007
Published in print: Jan 2007
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