Previous |  Up |  Next

Article

Keywords:
Haar-Kármán principle; basic boundary value problems; piecewise linear stress fields; composite triangles; torsion problem
Summary:
Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.
References:
[1] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique. Paris, Dunod 1972. MR 0464857
[2] B. Mercier: Sur la théorie et l'analyse numérique de problèmes de plasticité. Thesis, Université Paris VI, 1977. MR 0502686
[3] P. Suquet: Existence and regularity of solutions for plasticity problems. (Preprint). Proc. IUTAM Congress in Evanston - 1978.
[4] R. Falk B. Mercier: Estimation d'erreur en élastoplasticité. C. R. Acad. Sc. Paris, 282, A, (1976), 645-648. MR 0426575
[5] R. Falk B. Mercier: Error estimates for elasto-plastic problems. R.A.I.R.O. Anal. Numer., 11 (1977), 135-144. MR 0449119
[6] V. B. Watwood B. J. Hartz: An equilibrium stress field model for finite element solution of two-dimensionalelastostatic problems. Inter. J. Solids Structures 4, (1968), 857-873.
[7] C. Johnson B. Mercier: Some equilibrium finite element methods for two-dimensional elasticity problems. Numer. Math. 30 (1978), 103-116. DOI 10.1007/BF01403910 | MR 0483904
[8] J. Céa: Optimisation, théorie et algorithmes. Dunod, Paris 1971. MR 0298892
[9] F. Brezzi W. W. Hager P. A. Raviart: Error estimates for the finite element solution of variational inequalities. Part I. Primal Theory. Numer. Math. 28, (1977), 431 - 443. DOI 10.1007/BF01404345 | MR 0448949
[10] M. Křížek: An equilibrium finite element method in three-dimensional elasticity. Apl. Mat. 27 (1982). MR 0640139
[11] P. A. Raviart J. M. Thomas: A mixed finite element method for 2-nd order elliptic problems. Math. Aspects of Fin. El. Meth. Rome 1975, Springer-Verlag 1977, 292-315. MR 0483555
[12] H. Brezis K. Stampacchia: Sur la regularité de la solution d'inéquations elliptiques. Bull. Soc. Math. France 96, (1968), 153-180. MR 0239302
Partner of
EuDML logo