On dual approach to piecewise-linear elasto-plasticity. Part I: Continuum models

• Autorzy: Borkowski A.
• Języki publikacji: EN

Abstrakty

EN

This paper presents revised and extended version of theory proposed in the late 1970-ties by A. Cyras and his co-workers. This theory, based upon the notion of duality in mathematical programming, allows us to generate variational principles and to investigate existence and uniqueness of solutions for the broad class of problems of elasticity and plasticity. The paper covers analysis of solids made of linear elastic, elastic-strain hardening, elastic-perfectly plastic material. The novelty with respect to Cyras's theory lies in taking into account loads dispersed over the volume and displacements enforced on the part of surface. A new interpretation of optimum load for a rigid-perfectly plastic body is also given.

Słowa kluczowe

EN

imposed displacements; energy principles; mathematical programming

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2004
• Tom: Vol. 52, nr 4
• Strony: 329--343
• Opis fizyczny: Bibliogr. 13 poz., 4 rys., 2 tab.

Twórcy

autor

Borkowski A.

• Institute of Fundamental Technological Problems, Polish Academy of Sciences, 21 Świętokrzyska St., 00–049 Warsaw, Poland

Bibliografia

• [1] A. A. Cyras, ˇ Methods of Linear Programming in the Analysis of Elastic-plastic Systems, Leningrad: Stroiizdat, 1969 (in Russian).
• [2] A. A. Cyras, A. E. Borkauskas and R. P. Karkauskas, ˇOptimum Design of Elastic-plastic Structures – Theory and Methods, Leningrad: Stroiizdat, 1974 (in Russian).
• [3] A. Cyras, A. Borkowski and R. Karkauskas, ˇ Theory and Methods of Optimisation of Rigid-plastic Systems, Vilnius: Technika, 2004.
• [4] G. Duvaut and J.-L. Lions, Les in´equations en m´ecanique et en physique, Paris: Dunod, 1972.
• [5] B. Noble and M.J. Sewell, “On dual extremum principles in applied mathematics”, J. Inst. Math. Appl. 9, 123–193 (1972).
• [6] G. Maier, “A matrix structural theory of piecewise-linear elasto-plasticity with interacting yield planes”, Meccanica 5, 54–66 (1970).
• [7] M. Z. Cohn and G. Maier (eds.), “Engineering plasticity by mathematical programming”, Proc. NATO Advanced Study Institute, Waterloo, 1977, New York: Pergamon Press, 1979.
• [8] A. Borkowski, Analysis of Skeletal Structural Systems in the Plastic and Elastic-plastic Range, Amsterdam-Warsaw: ElsevierPWN, 1988.
• [9] P. D. Panagiotopoulos, Hemivariational Inequalities: Applications in Mechanics and Engineering, Berlin: Springer-Verlag, 1993.
• [10] J. T. Oden and J.N. Reddy, Variational Methods in Theoretic Mechanics, Berlin: Springer-Verlag, 1976.
• [11] R. W. Cottle, “Fundamentals of quadratic programming and linear complementarity”, in: Engineering Plasticity by Mathematical Programming, e dite d by M.Z. Cohn and G. Maie r, Proc. NATO Advanced Study Institute, Waterloo, 1977, New York: Pergamon Press, 1979.
• [12] E. G. Golstein, Theory of Duality in Mathematical Programming and its Applications, Moscow: Nauka, 1971 (in Russian).
• [13] I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Amsterdam-New York: North-Holland-Elsevier, 1976.