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On the contact problem in elastostatics. (English) Zbl 0621.73127
Unilateral problems in structural analysis, Proc. 2nd Meet., Ravello/Italy 1983, CISM Courses Lect. 288, 81-118 (1985).
[For the entire collection see Zbl 0581.00018.]
Within the framework of the theory of small displacements the author presents a survey of various algorithms for solving of a class of elastic unilateral problems with friction (quasi-static Signorini-like problem with friction).
However, the formulation of the problem itself is not complete since the initial condition was not taken into account. Moreover the numerical procedures developed by Oden and his coworkers have not been discussed at all. A proper variational formulation of quasi-static and dynamic Signorini problems with friction has been proposed by the reviewer in 1987 [see the volume: Non-Smooth Mechanics and Applications, ed. by J. J. Moreau and P. D. Panagiotopoulos, Springer-Verlag, CISM Courses and Lectures, 1988 (in print)]. The reader is also advised to the paper by J. T. Oden and T. L. Lin, Comput. Methods Appl. Mech. Eng. 57, 297-367 (1986; Zbl 0582.73113; Zbl 0591.73141).
Despite its incompleteness the paper will be of interest to researchers working on unilateral problems of elasticity.
Reviewer: J.J.Telega

MSC:
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics