Abstract
The paper concerns distribution of the force fields within Michell cantilevers supported on a segment of a straight line. The allowable yield stresses for tension and compression are not necessarily equal. The paper puts emphasis on checking the final results for the optimal weight by computing the weight in two manners: as a virtual work or, alternatively, by finding the force fields, the density of fibres and then by summing up the weights of all the parts of the optimal cantilever, i.e. the weights of the reinforcing bars and the weights of all the fibrous domains. If this duality gap vanishes, the solution is correct.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chan, H.S.Y. (1967) Half-plane slip-line fields and Michell structures, Q. J. Mech. Appl. Math., 20, 453–469.
Chan, H.S.Y. (1975) Symmetric plane frameworks of least weight, in Optimization in Structural Design, A. Sawczuk and Z. Mróz, (eds), Springer-Verlag, Berlin, pp. 313–326.
Gilbert, M., Darwich, W., Tyas, A. and Shepherd, P. (2005) Application of large-scale layout optimization techniques in structural engineering practice, in 6th World Congress of Structural and Multidisciplinary Optimization, Rio de Janeiro, 30 May–3 June 2005, Brasil, CD ROM, in press.
Golay, F. and Seppecher, P. (2001) Locking materials and the topology of optimal shapes, Eur. J. Mech. A/Solids, 20, 631–644.
Graczykowski, C. and Lewiński, T. (2005a) The lightest plane structures of a bounded stress level, transmitting a point load to a circular support, Control and Cybernetics, 34, 227–253.
Graczykowski, C. and Lewiński, T. (2005b) New designs of Michell-like cantilevers corresponding to different allowable tensile and compressive stresses, in 6th World Congress of Structural and Multidisciplinary Optimization, Rio de Janeiro, 30 May–3 June 2005, Brazil, CD ROM, in press.
Graczykowski, C. and Lewiński, T. (2006) Michell cantilevers constructed within trapezoidal domains — Part I: Geometry of Hencky nets, Part II: Virtual displacement fields, Part III: Force fields, Part IV: Complete exact solutions of selected optimal designs and their approximations by trusses of finite number of joints, Struct. Multidisc. Optimiz., in press.
Hemp, W.S. (1973) Optimum Structures, Clarendon Press, Oxford.
Lewiński, T. and Telega, J.J. (2001) Michell-like grillages and structures with locking, Arch. Mech., 53, 303–331.
Lewiński, T., Zhou, M. and Rozvany, G.I.N. (1994) Extended exact solutions for least-weight truss layouts — Part I: Cantilever with a horizontal axis of symmetry, Part II: Unsymmetric cantilevers, Int. J. Mech. Sci., 36, 375–398, 399–419.
Michell, A.G.M. (1904) The limits of economy of material in frame-structures, Phil. Mag., 8, 589–597.
Prager, W. (1959) On a problem of optimal design, in Proc. IUTAMSymp. on Non-Homogeneity in Elasticity and Plasticity, W. Olszak (ed.), Pergamon Press, London, pp. 125–132.
Rozvany, G.I.N. (1997) Some shortcomings in Michell’s truss theory, Struct. Optimiz., 12, 244–250.
Strang, G. and Kohn, R.V. (1983) Hencky-Prandtl nets and constrained Michell trusses, Comp. Meth. Appl. Mech. Eng., 36, 207–222.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Graczykowski, C., Lewiński, T. (2006). Force Fields within Michell-Like Cantilevers Transmitting a Point Load to a Straight Support. In: Bendsøe, M.P., Olhoff, N., Sigmund, O. (eds) IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials. Solid Mechanics and Its Applications, vol 137. Springer, Dordrecht . https://doi.org/10.1007/1-4020-4752-5_6
Download citation
DOI: https://doi.org/10.1007/1-4020-4752-5_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4729-9
Online ISBN: 978-1-4020-4752-7
eBook Packages: EngineeringEngineering (R0)