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Shakedown theory in perfect elastoplasticity with associated and nonassociated flow-laws: A finite element linear programming approach. (English) Zbl 0219.73039

74S05 Finite element methods applied to problems in solid mechanics
74R20 Anelastic fracture and damage
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[1] F. G. Hodge,Plastic analysis of structures, McGraw-Hill Book Comp., Inc., New York, 1959. · Zbl 0113.17903
[2] B. G. Neal,The plastic methods of structural analysis, Chapman & Hall Ltd., London, 1963.
[3] W. T. Koiter,General theorems for elastic-plastic solids, ”Progr. in Solid Mech.”, North-Holland Pub., Amsterdam, 1960. · Zbl 0109.43002
[4] V. Franciosi, Scienza delle Costruzioni, Vol. IV,Calcolo a rottura, Liguori, Napoli, 1964.
[5] D. C. Drucker,Coulomb friction, plasticity, and limit loads, ”J. Appl. Mech.”, Vol. 21, no. 1, 1954.
[6] D. C. Drucker,Concepts of path indepenence and material stability for soils, ”Proc. I.U.T.A.M. Symp. on Rheology and Soil Mechanics, Grenoble, 1964”, Springer, Berlin, 1966.
[7] D. Radenkovic,Theorèmes limites pour un matériau de Coulomb à dilatation non standardisée, Note Ac. Sciences Paris, Meeting of June 12th, 1961.
[8] D. Radenkovic,Theorèmes des charges limites, extension à la mécanique des sols, ”Seminaires de Plasticité Ec. Polytech.”, Pub. Sc. et Tech. Minist. Air. n. N. T. 116, 1961.
[9] G. de Josselin de Jone,Lower bound collapse theorem and lack of normality of strain rate to yield surface for soils, ”Proc. I.U.T.A.M. Symp. on Rheology and Soil Mechanics, Grenoble, 1964”, Springer, Berlin, 1966.
[10] A. C. Palmer,A limit theorem for materials with non-associated flow laws, ”J. de Mecanique”, Vol. V, no. 2, 1966.
[11] G. Sacchi andM. Save,A note on the limit loads of non-standard materials, ”Meccanica”, Vol. 3, no. 1, 1968.
[12] W. S. Dorn andH. J. Greenberg,Linear programming and plastic limit analysis of structures, ”Techn. Rep. no. 7”, Dept. of Math., Carnegie Inst. of Technology, 1955. · Zbl 0079.17305
[13] A. Charnes andC. E. Lemke andO. C. Zienkiewicz,Virtual work, linear programming and plastic limit analysis, ”Proc. Roy. Soc.”, A, v. 251, 1959. · Zbl 0095.19701
[14] W. Prager,Lineare Ungleichungen in der Baustatik, ”Schweizerische Bauzeitung”, no. 19, May, 1962.
[15] G. Ceradini andC. Gavarini,Calcolo a rottura e programmazione lineare, ”Giornale del Genio Civile”, no. 1, 1965.
[16] C. Gavarini,Plastic analysis of structures and duality in linear programming, ”Mcccanica”, Vol. I, no. 3–4, 1966.
[17] D. C. A. Koopman andR. H. Lance,On linear programming and plastic limit analysis, ”J. Mechs. Phys. Solids”, v. 13, 1965.
[18] R. H. Lance,Duality in the finite-difference method of plastic limit analysis, Dpt. Theor. Appl. Mechs., Cornell Un., Tech. Report NSF GK 687/2, Apr. 1967.
[19] J. L. Tocher andE. P. Popov,Incremental collapse analysis of rigid frames, ”Proc. of the Fourth U.S. Nat. Congr. of Appl. Mech.”, 1964.
[20] O. C. Zienkiewicz,The finite element method in structural and continuum mechanics, McGraw-Hill, New York, 1967. · Zbl 0189.24902
[21] J. S. Przemieniecki,Theory of matrix structural analysis, McGraw-Hill Comp., New York, 1968. · Zbl 0177.53201
[22] J. F. Besseling,Matrix analysis of creep and plasticity problems, in ”Matrix Methods in Structural Mechanics”, Proc. Conference Wright-Patterson AFB, Ohio, 1965.
[23] H. Argyris,Elastoplastic matrix displacement analysis of three dimensional continua, ”Jl. R. aeronaut. Soc.”, 69, 1965. · Zbl 0127.40004
[24] P. V. Marcal andI. P. King,Elastic-plastic analysis of two dimensional stress systems by the finite element method, ”Int. J. mech. Sci.”, no. 9, 1967.
[25] O. C. Zienkiewicz andS. Valliappan andI. P. King,Elasto-plastic solutions of engineering problems ”initial stress”, finite element approach, ”Int. J. Numer. Meth. in Engin.”, Vol. I, no. 1, 1969. · Zbl 0247.73087
[26] J. F. Besseling,The complete analogy between the matrix equations and the continuous field equations of structural analysis, ”Internal Symp. Analogue and Digital Techn. Appl. to Aeron.”, Liege, 1963.
[27] B. Fraeis de Veubeke,Displacement and equilibrium models in the finite element method, in ”Stress Analysis”, O. C. Zienkiewicz and G. S. Holister Eds., John Wiley & Sons, Ltd., 1965.
[28] W. T. Koiter,A new general theorem on shake-down of elastic-plastic structures, ”Proc. Kon. Nederl. Akad. Wet.”, B 59, 24, 1956. · Zbl 0074.40801
[29] W. Prager,Shakedown in elastic, plastic media subjected to cycles of load and temperature, ”Symp. sulla Plast. nella Scienza delle Costr.”, Varenna, N. Zanichelli Ed., 1956. · Zbl 0082.17902
[30] G. Hadley,Linear programming, Addison-Wesley, 1962. · Zbl 0102.36304
[31] H.P. Künzi andW. Krelle,Nonlinear programming, Blaisdell Publ. Comp., Waltham, Mass., 1966.
[32] H. P. Künzi andH. G. Tzschach andC. A. Zehnder,Numerische Methoden der mathematischen Optimierung, B. G. Teubner, Stuttgart, 1967. · Zbl 0161.38902
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