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Analysis of a mixed finite element method for elasto-plastic plates


Authors: F. Brezzi, C. Johnson and B. Mercier
Journal: Math. Comp. 31 (1977), 809-817
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1977-0443373-1
MathSciNet review: 0443373
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Abstract: We consider a mixed finite element method for finding approximations of the displacement and moments in a thin elastic-perfectly plastic plate. Under some weak assumptions concerning the regularity of the exact solution, we prove an error estimate for the moments.


References [Enhancements On Off] (What's this?)

  • [1] F. BREZZI & P. A. RAVIART, "Mixed finite element methods for 4th order problems," Topics in Numerical Analysis. III, J. MILLER (Editor), Academic Press, New York, 1976.
  • [2] J. BÄCKLUND, "Mixed finite element analysis of elasto-plastic plates in bending," Arch. Mech., v. 24, 1972, pp. 319-335.
  • [3] I. EKELAND & R. TEMAM, Analyse Convexe et Problèmes Variationnels, Dunod, Paris, 1973. MR 0463993 (57:3931a)
  • [4] K. HELLAN, "An analysis of elastic plates in flexure by a simplified finite element method," Acta Polytech. Scand. Ci. Ser., v. 46, 1967.
  • [5] L. R. HERRMANN, "Finite element bending analysis for plates," J. Engr. Mech. Div. ASCE, EM5, a3, 1967, pp. 49-83.
  • [6] C. JOHNSON, "On the convergence of some mixed finite element methods for plate bending problems," Numer. Math., v. 21, 1973, pp. 43-62. MR 0388807 (52:9641)
  • [7] C. JOHNSON, "Existence theorems for plasticity problems," J. Math. Pures Appl., v. 55, 1976, pp. 431-444. MR 0438867 (55:11773)
  • [8] C. JOHNSON, "A mixed finite element method for plasticity with hardening," SIAM J. Numer. Anal. (To appear.) MR 0489265 (58:8711)
  • [9] V. A. KONDRAT'EV, "Boundary value problems for elliptic equations in domains with conical or angular points," Trudy Moskov. Mat. Obšč., v. 16, 1967, pp. 209-292. (Russian) MR 37 #1777. MR 0226187 (37:1777)
  • [10] C. E. MASSONNET & M. A. SAVE, Plastic Analysis and Design of Plates, Shells and Disks, North-Holland, Amsterdam, 1972.
  • [11] B. MERCIER, Sur la Théorie et l'Analyse Numérique de Problèmes de Plasticité, Thèse, Paris, 1977.
  • [12] R. T. ROCKAFELLAR, Convex Analysis, Princeton Univ. Press, Princeton, N. J., 1970. MR 43 #445. MR 0274683 (43:445)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0443373-1
Article copyright: © Copyright 1977 American Mathematical Society

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