04007881

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04007881 Marini, L.D. Numerical approximation and error estimates for elastic-plastic torsion problems in multiply connected domains. Unilateral problems in structural analysis, Proc. 2nd Meet., Ravello/Italy 1983, CISM Courses Lect. 288, 119-142 (1985). 1985 EN conforming finite elements piecewise linear approximation ideal plasticity elastic-plastic torsion rods multiply connected sections two obstacle minimization problem implicit variational problems Zbl 0581.00018 Zbl 0346.49003 [For the entire collection see Zbl 0581.00018.] The main objective of this paper is the numerical analysis of a classical problem of ideal plasticity: the elastic-plastic torsion of rods having multiply connected sections. Prior to this the problem is formulated as the two obstacle minimization problem. If $\Omega\sb k$ $(k=1,...,n)$ stand for the holes in the cross section of the rod then the stress function assumes constant (unknown) values over $\Omega\sb k$. To find these values a second minimization problem has to be solved. Thus in fact the elastic-plastic torsion problem studied belongs to the so-called implicit variational problems [see {\it U. Mosco}, Nonlin. Oper. Calc. Var., Summer Sch. Bruxelles 1975, Lect. Notes Math. 543, 83-156 (1976; Zbl 0346.49003)]. By using piecewise linear approximation over the triangulated domain, error estimates are derived. Two simple numerical examples are also given. The paper constitutes a valuable contribution to mathematical problems of plasticity. J.J.Telega