Article
MSC:
49D37,
49M37,
73T05,
74A55,
74M15,
74S05 | MR 0640138 | Zbl 0495.73094 | DOI: 10.21136/AM.1982.103943
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Keywords:
elastic perfectly plastic; Hencky’s law; extension of Haar-Kármán principle; case of unilateral contact on boundary; piecewise constant triangular elements; convergence; any regular family of triangulations; simplification; approximate problem with bounded contact zone; nonlinear
elastic perfectly plastic; Hencky’s law; extension of Haar-Kármán principle; case of unilateral contact on boundary; piecewise constant triangular elements; convergence; any regular family of triangulations; simplification; approximate problem with bounded contact zone; nonlinear
Summary:
If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Kármán principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.
References:
[1a] J. Haslinger I. Hlaváček: Contact between elastic bodies. I. Continuous problems. Apl. mat. 25 (1980), 324-347. MR 0590487
[1b] J. Haslinger I. Hlaváček: Contact between elastic bodies. II. Finite element analysis. Apl. mat. 26 (1981), 263-290. MR 0623506
[1c] J. Haslinger I. Hlaváček: Contact between elastic bodies. III. Dual finite element analysis. Apl. mat. 26 (1981), 321-344. MR 0631752
[2] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique. Paris, Dunod 1972. MR 0464857
[3] B. Mercier: Sur la théorie et l'analyse numérique de problèmes de plasticité. Thésis, Université Paris VI, 1977. MR 0502686
[4] I. Hlaváček J. Nečas: Mathematical theory of elastic and elasto-plastic solids. Elsevier, Amsterdam 1981.
[5] P.-M. Suquet: Existence and regularity of solutions for plasticity problems. Proc. IUTAM Congress in Evanston - 1978.
[6] J. Céa: Optimisation, théorie et algorithmes. Dunod, Paris 1971. MR 0298892
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