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Kestřánek, Zdenĕk

Variational inequalities in plasticity with strain-hardening - Equilibrium finite element approach. (English) Zbl 0608.73040

Apl. Mat. 31, 270-281 (1986).
(From Author’s summary.) In the work the incremental finite element method is applied to find the numerical solution of the plasticity problem with strain-hardening. The stress field is approximated by equilibrium triangular elements with linear functions. The field of the strain-hardening parameter is considered to be piecewise linear. The resulting nonlinear optimization problem with constraints is solved by the Lagrange multipliers method with additional variables. A comparison of the results obtained with an experiment is given.
Reviewer: J.Lovíšek

Cited in 1 Document

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74C99 Plastic materials, materials of stress-rate and internal-variable type
49J40 Variational inequalities
49M29 Numerical methods involving duality

Keywords:

incremental finite element method; strain-hardening; equilibrium triangular elements; nonlinear optimization problem with constraints; Lagrange multipliers method; additional variables
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References:

[1] C. Johnson: On Plasticity with Hardening. J. Math. Anal. Appl., Vol. 62, 1978, pp. 325-336. · Zbl 0373.73049 · doi:10.1016/0022-247X(78)90129-4
[2] I. Hlaváček J. Nečas: Mathematical Theory of Elastic and Elasto-Plastic Bodies. Elsevier, Amsterdam, 1981.
[3] I. Hlaváček: A Finite Element Solution for Plasticity with Strain-Hardening. R.A.I.R.O. Numerical Analysis, V. 14, No. 4, 1980, pp. 347-368.
[4] Nguyen Quoc Son: Matériaux élastoplastiques écrouissable. Arch. Mech. Stos., V. 25, 1973, pp. 695-702. · Zbl 0332.73039
[5] B. Halphen, Nguyen Quoc Son: Sur les matériaux standard généralisés. J. Mécan., V. 14, 1975, pp. 39-63. · Zbl 0308.73017
[6] C. Johnson: A Mixed Finite Element Method for Plasticity Problems with Hardening. S.I.A.M. J. Numer. Anal., V. 14, 1977, pp. 575-583. · Zbl 0374.73039 · doi:10.1137/0714037
[7] Z. Kestřánek: A Finite Element Solution of Variational Inequality of Plasticity with Strain-Hardening. Thesis, Czechoslovak Academy of Sciences, 1982
[8] V. B. Watwood B. J. Hartz: An Equilibrium Stress Field Model for Finite Element Solution of Two-Dimensional Elastostatic Problems. Inter. J. Solids Structures, V. 4, 1968, pp. 857-873. · Zbl 0164.26201 · doi:10.1016/0020-7683(68)90083-8
[9] M. Avriel: Nonlinear Programming. Analysis and Methods. Prentice-Hall, New York, 1976. · Zbl 0361.90035
[10] P. S. Theocaris E. Marketos: Elastic-Plastic Analysis of Perforated Thin Strips of a Strain-Hardening Material. J. Mech. Phys. Solids, 1964, V. 12, pp. 377-390. · doi:10.1016/0022-5096(64)90033-X
[11] C. Johnson: On Finite Element Methods for Plasticity Problems. Numer. Math., V. 26, 1976, pp. 79-84. · Zbl 0355.73035 · doi:10.1007/BF01396567
[12] M. Křížek: An Equilibrium Finite Element Method in Three-Dimensional Elasticity. Apl. Mat., V. 27, No. 1, 1982.
[13] D. M. Himmelblau: Applied Nonlinear Programming. McGraw-Hill, New York, 1972. · Zbl 0241.90051
[14] M. S. Bazaraa C. M. Shetty: Nonlinear Programming. Theory and Algorithms. John Wiley and Sons, New York, 1979. · Zbl 0476.90035
[15] P. E. Gill W. Murrey: Numerical Methods for Constrained Optimization. Academic Press, London, 1974.
[16] B. M. Irons: A Frontal Solution Program for Finite Element Analysis. Intern. J. for Numer. Meth. in Eng., V. 2, 1970. · Zbl 0252.73050 · doi:10.1002/nme.1620020104
[17] K. Schittkowski: The Nonlinear Programming Method cf Wilson, Han and Powell with an Augmented Lagrangian Type Line Search Function. Part 1, 2. Numer. Math,, V. 38, No. 1, 1981. · Zbl 0534.65030 · doi:10.1007/BF01395810
[18] A. Samuelsson M. Froier: Finite Elements in Plasticity. A Variational Inequality Approach. Proc. MAFELAP 1978, Academic Press, London, 1979. · Zbl 0437.73058
[19] J. Céa: Optimisation, théorie et algorithmes. Dunod, Paris, 1971. · Zbl 0211.17402
[20] O. L. Mangasarian: Nonlinear Programming 3, 4. Academic Press, New York, 1978, 1981.
[21] Z. Kestřánek: Variational Inequalities in Plasticity - Dual Finite Element Approach. Proc. MAFELAP 1984, Academic Press, London, 1984.
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