Abstract
Shape optimization of plastic structures, or limit design in the absence of a given layout, is a problem which can be formulated as follows. The data are: the convex yield surface of a perfectly plastic material with associated flow-law (i.e. obeying “normality” [1]), some surfaces to which the structure may be fixed; an available space region (possibly with holes or cavities) where it must be contained; some other surfaces on which certain load distributions are assigned and which must form part of the boundary of the structure. The behaviour constraint is that the structure carry the given external forces and its own weight. The structure with the least material consumption (minimum volume) is sought.
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References
Kaehanov, L. M.: Foundations of Plasticity, Amsterdam: North Holland 1971.
Drucker, D. C., Shield, R. T.: Design for Minimum Weight, Proc. 9th Intern. Congr. Appl. Mech., Brussels, Vol. 5, 1957, pp. 212–222.
Prager, W.: Optimality Criteria Derived from Classical Extremum Principles, in: An Introduction to Structural Optimization, Soc. Mech. Div., Univ. of Waterloo, Ontario, 1969, pp. 165–178.
Maier, G.: Limited Design in the Absence of a Given Layout: a Finite Element, Zero-One Programming Approach. Polish Nat. Conf. Theor. Appl. Mech., Jaszowiecz, Sept. 1970, and J. Struct. Mech. 1, No. 2, 213–230 (1972).
Zienkiewicz, O. C., Campbell, J. S.: Shape Optimization and Sequential Linear Programming, in: Optimum Structural Design, Ed. R. H. Gallagher and O. C. Zienkiewicz, London: Wiley 1972, pp. 129–136.
Vitiello, E.: Shape Optimization Using Mathematical Programming and Modelling Techniques, AGARD 2nd Symposium on Struct. Optimization, Milan, 2–4 April 1973.
Zavelani, A.: A New Linear Programming Approach to Limit Analysis, Int. Conf. on Variational Methods in Engrg., Southampton Univ., September 1972.
Zavelani, A.: A Compact Linear Programming Formulation for Optimal Design in Plane Stresses. J. Structural Mech., to appear.
Maier, G., Zavelani, A., Benedetti, D.: A Finite Element Approach to Optimal Design of Plastic Structures in Plane Stress. Int. J. Num. Methods in Engrg. 4, 445–473 (1972).
Argyris, J. H.: Continua and Discountinua, in: Proc. of Int. Conf. on Matrix Methods in Struct. Mech., AFFDL-TR-66-80, Oct. 1965.
Zienkiewicz, O. C.: The Finite Element Method in Engineering Sciences, New York: McGraw-Hill 1971.
Balas, E.: Minimax and Duality for Linear and Nonlinear Mixed-Integer Programming, in: Integer and Nonlinear Programming, Ed. J. Abadie, Amsterdam: North-Holland 1970.
Greenberg, A.: Integer Programming, New York: Academic Press 1970.
Schultes, W. G.: ILONA IROS Linear Programming System-Programmers Reference, Sperry Rand UNIVAC, 1971.
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Zavelani, A., Maier, G., Binda, L. (1975). Shape Optimization of Plastic Structures by Zero-One Programming. In: Sawczuk, A., Mróz, Z. (eds) Optimization in Structural Design. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80895-1_37
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DOI: https://doi.org/10.1007/978-3-642-80895-1_37
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