Efficiency of High-Order Elements in Large-Deformation Problems of Geomechanics
Publication: International Journal of Geomechanics
Volume 15, Issue 6
Abstract
This paper investigates the application of high-order elements within the framework of the arbitrary Lagrangian-Eulerian method for the analysis of elastoplastic problems involving large deformations. The governing equations of the method as well as its important aspects such as the nodal stress recovery and the remapping of state variables are discussed. The efficiency and accuracy of 6-, 10-, 15-, and 21-noded triangular elements are compared for the analysis of two geotechnical engineering problems, namely, the behavior of an undrained layer of soil under a strip footing subjected to large deformations and the soil behavior in a biaxial test. The use of high-order elements is shown to increase the accuracy of the numerical results and to significantly decrease the computational time required to achieve a specific level of accuracy. For problems considered in this study, the 21-noded elements outperform other triangular elements.
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Acknowledgments
This project received support from the Australian Research Council Discovery Project Program DP110101033. The authors are grateful for this support.
References
Babuska, I., Szabo, B. A., and Katz, I. N. (1981). “The -version of the finite element method.” SIAM J. Numer. Anal., 18(3), 515–545.
Benson, D. J. (1989). “An efficient, accurate, simple ALE method for nonlinear finite element programs.” Comput. Methods Appl. Mech. Eng., 72(3), 305–350.
De Borst, R., and Vermeer, P. A. (1984). “Possibilities and limitations of finite elements for limit analysis.” Géotechnique, 34(2), 199–210.
de Lyra Nogueira, C., de Azevedo, R. F., and Zornberg, J. G. (2009). “Coupled analyses of excavations in saturated soil.” Int. J. Geomech., 73–81.
Dunavant, D. A. (1985). “High degree efficient symmetrical Gaussian quadrature rules for the triangle.” Int. J. Numer. Methods Eng., 21(6), 1129–1148.
Ergatoudis, I., Irons, B. M., and Zienkiewicz, O. C. (1968). “Curved, isoparametric, ‘quadrilateral’ elements for finite element analysis.” Int. J. Solids Struct., 4(1), 31–42.
Griffiths, D. V., Huang, J., and Schiermeyer, R. P. (2009). “Elastic stiffness of straight-sided triangular finite elements by analytical and numerical integration.” Commun. Numer. Methods Eng., 25(3), 247–262.
Kardani, M., Nazem, M., Abbo, A. J., Sheng, D., and Sloan, S. W. (2012). “Refined -adaptive finite element procedure for large deformation geotechnical problems.” Comput. Mech., 49(1), 21–33.
Karlsrud, K., and Andresen, L. (2005). “Loads on braced excavations in soft clay.” Int. J. Geomech., 107–113.
Laursen, M. E., and Gellert, M. (1978). “Some criteria for numerically integrated matrices and quadrature formulas for triangles.” Int. J. Numer. Methods Eng., 12(1), 67–76.
Nazem, M., Carter, J. P., Sheng, D., and Sloan, S. W. (2009). “Alternative stress-integration schemes for large-deformation problems of solid mechanics.” Finite Elem. Anal. Des., 45(12), 934–943.
Nazem, M., Kardani, M., Carter, J. P., and Sloan, S. W. (2013). “On the application of high-order elements in large deformation problems of geomechanics.” Proc., 3rd Int. Symp. on Computational Geomechanics (ComGeo III), G. Pande and S. Pietruszczak, eds., International Centre for Computational Engineering, Rhodes, Greece, 284–291.
Nazem, M., Sheng, D., and Carter, J. P. (2006). “Stress integration and mesh refinement for large deformation in geomechanics.” Int. J. Numer. Methods Eng., 65(7), 1002–1027.
Nazem, M., Sheng, D., Carter, J. P., and Sloan, S. W. (2008). “Arbitrary Lagrangian–Eulerian method for large-strain consolidation problems.” Int. J. Numer. Anal. Methods Geomech., 32(9), 1023–1050.
Ramesh, S. S., Wang, C. M., Reddy, J. N., and Ang, K. K. (2008). “Computation of stress resultants in plate bending problems using higher-order triangular elements.” Eng. Struct., 30(10), 2687–2706.
Rathod, H. T., Nagaraja, K. V., Kesavulu Naidu, V., and Venkatesudu, B. (2008). “The use of parabolic arcs in matching curved boundaries by point transformations for some higher order triangular elements.” Finite Elem. Anal. Des., 44(15), 920–932.
Sheng, D., Sloan, S. W., and Yu, H. S. (2000). “Aspects of finite element implementation of critical state models.” Comput. Mech., 26(2), 185–196.
Sloan, S. W. (1986). “An algorithm for profile and wavefront reduction of sparse matrices.” Int. J. Numer. Methods Eng., 23(2), 239–251.
Sloan, S. W. (1989). “A FORTRAN program for profile and wavefront reduction.” Int. J. Numer. Methods Eng., 28(11), 2651–2679.
Sloan, S. W., and Randolph, M. F. (1982). “Numerical prediction of collapse loads using the finite element methods.” Int. J. Numer. Anal. Methods Geomech., 6(1), 47–76.
SNAC 2014 [Computer software]. Callaghan, NSW, Australia, Univ. of Newcastle.
Zienkiewicz, O. C., and Zhu, J. Z. (1992). “The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique.” Int. J. Numer. Methods Eng., 33(7), 1331–1364.
Zienkiewicz, O. C., Zhu, J. Z., and Wu, J. (1993). “Superconvergent patch recovery techniques—Some further tests.” Commun. Numer. Methods Eng., 9(3), 251–258.
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© 2014 American Society of Civil Engineers.
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Received: Apr 1, 2014
Accepted: Oct 15, 2014
Published online: Nov 10, 2014
Published in print: Dec 1, 2015
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