zbMATH — the first resource for mathematics

On the collapse solution in limit analysis. (English) Zbl 0584.73036
A rigid-ideal-plastic body is subject to prescribed displacements of one part of the boundary and to prescribed tractions at the other part of the boundary. Furthermore the distribution of body forces is given. Surface tractions and body forces depend on the same parameter \(\lambda\). The problem is to find the limit load carrying factor \(\lambda_ 0\). Based on dual (static and kinematic) formulation of the problem the existence and regularity of collapse solutions is examined by defining a generalized Green formula.
Reviewer: Th.Lehmann

74R20 Anelastic fracture and damage
Full Text: DOI
[1] Christiansen, E., Limit analysis in plasticity as a mathematical programming problem, Calcolo, 17, 41–65 (1980). · Zbl 0445.73021
[2] Christiansen, E., Limit analysis for plastic plates, SIAM J. Math. Anal., 11, 514–522 (1980). · Zbl 0453.73036
[3] Christiansen, E., Computation of limit loads, Int. J. Num. Meth. Engng., 17, 1547–1570 (1981). · Zbl 0483.73030
[4] Christiansen, E., Examples of collapse solutions in limit analysis, Utilitas Math., 22, 77–102 (1982). · Zbl 0508.73028
[5] Dunford, N. & Schwartz, J. T., Linear operators I, John Wiley, N.Y., 1957.
[6] Ekeland, I. &. Temam, R., Convex analysis and variational problems, North-Holland, Amsterdam, 1976. · Zbl 0322.90046
[7] Foias, C. &. Temam, R., Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcations, Ann. Sc. Norm. Sup., Pisa, Serie IV, Vol. V, No. 1, 29–63 (1978). · Zbl 0384.35047
[8] Kohn, R. & Temam, R., Dual spaces of stresses and strains, with applications to Hencky plasticity, to appear in Applied Math. and Optimization. · Zbl 0532.73039
[9] Matthies, H., Strang, G. & Christiansen, E., The saddle point of a differential program, in ”Energy methods in finite element analysis”, Glowinsky, R., Rodin, E. & Zienkiewicz, O. C., eds., John Wiley, New York, 1979.
[10] Nečas, J., Sur les normes équivalentes dans Wpk({\(\Omega\)}) et sur la coercivité des formes formellement positives, in Equations aux dérivées partielles, 102–128, Presses de l’Université de Montréal, 1966.
[11] Nečas, J., Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967.
[12] Strang, G., A family of model problems in plasticity, Proc. Symp. Comp. Meth. in Appl. Sc., Versailles, 191–205 (1977).
[13] Strang, G., A minimax problem in plasticity theory, Springer Lecture Notes 701, 319–333 (1979). · Zbl 0433.73034
[14] Suquet, P.-M., Existence and regularity of solutions for plasticity problems, in Variational methods in the mechanics of solids, ed. S. Nemat-Nasser, pp. 304–309, Bergman Press, New York, 1980.
[15] Temam, R., Navier-Stokes equations, North-Holland, Amsterdam, 1977. · Zbl 0383.35057
[16] Temam, R., On the continuity of the trace of vector functions with bounded deformation, Appl. Anal., 11, 291–302 (1981). · Zbl 0504.46027
[17] Temam, R. & Strang, G., Functions of bounded deformation, Arch. Rational Mech. Anal., 75, 7–21 (1980). · Zbl 0472.73031
[18] Temam, R. & Strang, G., Duality and relaxation in the variational problems of plasticity, J. de Mécanique, 19, 493–527 (1980). · Zbl 0465.73033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.