Abstract
For h-type adaptive finite element method, the local mesh refinement introduces irregular nodes and destroys the standard continuity between elements. The reference nodes of the irregular are used to interpolate element coordinates and displacements. The improved shape functions, of which the conventional shape functions are a particular case, are presented to guarantee the continuity. No changes but the shape functions are needed when the method is applied in finite element programs. The computational results show the features of the method: higher accuracy, simplicity, fewer degrees of freedom and less computation effort.
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References
A. K. Noor and S. N. Atluri, Advances and trends in computational structural mechanics, AIAA Journal, 25 (1987), 977–995.
L. Demkowicz, J. T. Oden, W. Rachowicz and O. Hardy, Toward a universal h-p adaptive finite element strategy, Part 1: Constrained approximation and data structure, Comput. Methods Appl. Mech. Engng., 77 (1989), 79–112.
J. T. Oden, L. Demkowicz, W. Rachowicz and T. A. Westermann, Toward a universal h-p adaptive finite element strategy, Part 2: A posteriori error estimation, Comput. Methods Appl. Mech. Engng., 77 (1989), 113–180.
D. W. Kelly, J. P. DE S. R. Gago and O. C. Zienkiewicz, A posteriori error analysis and adaptive processes in the finite element method, Part I: Error analysis, Int. J. Num. Meth. Engng., 19 (1983), 1593–1619.
J. P. DE S. R. Gago, D. W. Kelly and O. C. Zienkiewicz, A posteriori error analysis and adaptive processes in the finite element method, Part II: Adaptive mesh refinement, Int. J. Num. Meth. Engng., 19 (1983), 1621–1656.
R. E. Bank and A. Werser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comput., 44 (1985), 283–301.
I. Babuska and A. Miller, A feedback finite element method with a posteriori error estimation: Part I: The finite element method and some basic properties of the a posteriori error estimator, Comput. Methods Appl. Mech. Engng., 61 (1987), 1–40.
W. C. Rheinboldt and CH. K. Mesztenyi, On a data structure for adaptive finite element mesh refinement, ACM Trans., Math. Software, 6 (1980), 166–187.
L. Demkowicz and J. T. Oden, A review of local mesh refinement techniques and corresponding data structures in h-type adaptive finite element methods, TICOM Rept. 88–02, the Texas Institute for Computational Mechanics, the University of Texas at Austin, Texas 78–12 (1983).
Fan Tianyou, Fundamental of Fracture Mechanics, 1st Ed, Jiangsu Science and Technology Publisher (1978), (in Chinese)
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Project supported by the National Natural Science Foundation of China
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Xing, X., Daosheng, L., Qinghua, D. et al. An h-type adaptive finite element. Appl Math Mech 17, 507–513 (1996). https://doi.org/10.1007/BF00119747
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DOI: https://doi.org/10.1007/BF00119747