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2019 | OriginalPaper | Buchkapitel

3. Theory of Michell Structures. Single Load Case

verfasst von : Tomasz Lewiński, Tomasz Sokół, Cezary Graczykowski

Erschienen in: Michell Structures

Verlag: Springer International Publishing

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Abstract

The Michell structures are solutions to the problems of optimum design put forward and discussed in Sects. 2.1 and 2.2 provided that the nodes of the trusses may be placed at arbitrary point of the design domain being a subdomain of the plane or of the Euclidean space. The present chapter introduces the reader to the main topic of the book.

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Vorheriges Kapitel Optimum Design of Structures of Finite Number of Bars. Single Load Variant

Nächstes Kapitel Constructing Michell Structures in Plane. Single Load Case

Allaire, G. (2002). Shape optimization by the homogenization method. New York: Springer.CrossRef

Bouchitté, G., & Buttazzo, G. (2001). Characterization of optimal shapes and masses through Monge-Kantorovich equation. Journal of the European Mathematical Society, 3, 139–168.MathSciNetCrossRef

Bouchitté, G., Gangbo, W., & Seppecher, P. (2008). Michell trusses and lines of principal action. Mathematical Models and Methods in Applied Sciences, 18, 1571–1603.MathSciNetCrossRef

Chan, A. S. L. (1960). The design of Michell optimum structures. Cranfield: The College of Aeronautics (Report 142).

Cherkaev, A. V. (2000). Variational methods for structural optimization. New York: Springer.CrossRef

Cherry, T. M. (1962). Anthony George Maldon Michell: 1870–1959. Biographical Memoirs of Fellows of the Royal Society (pp. 90–103). www.jstor.org.

Cox, H. L. (1965). The design of structures of least weight. Oxford: Pergamon Press.

Čyras, A. (1972). Optimization theory of perfectly locking bodies. Archives of Mechanics, 24, 203–210.MathSciNetMATH

Demengel, F., & Suquet, P. (1986). On locking materials. Acta Applicandae Mathematicae, 6, 185–211.MathSciNetCrossRef

Desmorat, B., & Duvaut, G. (2003). Compliance optimization with nonlinear elastic materials. Application to constitutive laws dissymmetric in tension-compression. European Journal of Mechanics A/Solids, 22, 179–192.MathSciNetCrossRef

Hemp, W. S. (1958). Theory of structural design. The College of Aeronautics, Cranfield. Report no 115.

Hemp, W. S. (1973). Optimum structures. Oxford: Clarendon Press.

Hu, T.-C., & Shield, T. T. (1961). Minimum weight design of discs. Zeitschrift für Angewandte Mathematik und Physik, 12, 414–433.CrossRef

Lagache, J.-M. (1981). Developments in Michell theory, pp. 4–9 to 4–16. In A. Atrek & R. H. Gallagher (Eds.), Proceedings of the International Symposium on Optimal Structural design. The 11th ONR Naval Structural Mechanics Symposium, 19–22 October 1981.

Lewiński, T., & Sokół, T. (2014). On basic properties of Michell’s structures. In G. I. N. Rozvany & T. Lewiński (Eds.), Topology optimization in structural and continuum mechanics (Vol. 549). CISM international centre for mechanical sciences. Courses and lectures. Wien: Springer.CrossRef

Lewiński, T., & Telega, J. J. (2000). Plates, laminates and shells. Asymptotic analysis and homogenization. Singapore, New Jersey, London, Hong Kong: World Scientific.

Maxwell, C. (1870). On reciprocal figures, frames and diagrams of forces. Scientific Papers II, 26, 161–207.

Michell, A. G. M. (1899). Elastic stability of long beams under transverse forces. Philosophical Magazine. Series 5, 48(292), 298–309.CrossRef

Michell, A. G. M. (1904). The limits of economy of material in frame structures. Philosophical Magazine. Series 6, 8(47), 589–597.CrossRef

Naghdi, P. M. (1963). Foundation of elastic shell theory. In I. N. Sneddon & R. Hill (Eds.), Progress in solid mechanics (pp. 2–90). Amsterdam: North Holland.

Ostoja-Starzewski, M. (2001). Michell trusses in the presence of microscale material randomness: limitation of optimality. Proceedings of the Royal Society of London, 457, 1787–1797.CrossRef

Prager, W., & Shield, R. T. (1967). A general theory of optimal plastic design. Journal of Applied Mechanics, Transactions ASME, 34, 184–186.CrossRef

Rockafellar, R. T. (1970). Convex analysis. New Jersey: Princeton University Press.CrossRef

Rozvany, G. I. N. (1976). Optimal design of flexural systems. London: Pergamon Press.

Rozvany, G. I. N. (1989). Structural design via optimality criteria. Dordrecht: Kluwer Academic Publishers.CrossRef

Sigmund, O., Aage, N., & Andreassen, E. (2016). On the (non-) optimality of Michell’s structures. Structural and Multidisciplinary Optimization, 54, 361–373.MathSciNetCrossRef

Stavroulakis, G. E., & Tzaferopoulos, M. Ap. (1994). A variational inequality approach to optimal plastic design of structures via the Prager-Rozvany theory. Structural Optimization, 7, 160–169.CrossRef

Strang, G., & Kohn, R. V. (1983). Hencky-Prandtl nets and constrained Michell trusses. Computer Methods in Applied Mechanics and Engineering, 36, 207–222.MathSciNetCrossRef

Telega, J. J., & Jemioło, S. (1998). Macroscopic behaviour of locking materials with microstructure. Part I. Primal and dual locking potential. Relaxation. Bulletin of the Polish Academy of Sciences, 46, 265–276.MATH

Titel: Theory of Michell Structures. Single Load Case
verfasst von: Tomasz Lewiński
Tomasz Sokół
Cezary Graczykowski
Verlag: Springer International Publishing
Buch: Michell Structures
Print ISBN: 978-3-319-95179-9

Electronic ISBN: 978-3-319-95180-5

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-319-95180-5_3

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