Abstract
A generalized layout problem involving sizing, shape, and topology optimization is solved by using the homogenization method for three-dimensional linearly elastic shell structures in order to seek a possibility of establishment of an integrated design system of automotive car bodies, as an extension of the previous work by Bendsøe and Kikuchi. A formulation of a three-dimensional homogenized shell, a solution algorithm, and several examples of computing the optimum layout are presented in this first part of the two articles.
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
Schmit, L.A., Structural design by systematic synthesis,Proceedings 2nd ASCE Conference on Electronic Computation (1960) pp.105–132, New York
Fox, R. L., Constraint surface normals for structural synthesis techniques, AIAA J. 3–8 (1965) pp. 1517–1518
Prager, W and Taylor,J.E., Problems of optimal structural design, J. Appl. Mech. 35 (1968) pp. 102–106
Prager,W., A note on discretized Michell structures, Comput. Mechs. Appl. Mech. Engrg., 3–3 (1974) pp. 349–355
Michell, A.G.M., The limits of economy of material in framed structures, Phil. Mag. 6 (1904) pp. 589–597
Rozvany, G.I.N., Structural Design via Optimality Criteria, Kluwer, (1989), Dordrecht
Rozvany, G.I.N., Zhou, M., Rotthaus, M., and Gollub, W., Continuum optimality methods for large finite element systems with a displacement constraint, Part I, Structural Optimization Vol.1-No. 1, (1989) pp. 47–71
Rozvany, G.I.N., Zhou, M., and Gollub, W., Continuum optimality methods for large finite element systems with a displacement constraint, Part II, Structural Optimization Vol.2-No. 2, (1990) pp. 77–104
Bendsøe, M.P., and Ben-Tal, A., and Haftka, R.T., New displacement-based methods for optimal truss topology design, in Proceedings of AIAA /ASME/ ASCE/ AHS/ ASC 32nd Structures, Structural Dynamics and Materials Conference, Baltimore, Maryland, April 8–10, 1991
Bend*, M.P., and Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Comput. Meth. Appl. Mech. Engrg., 71 (1988) pp. 197–224
Suzuki K, Kikuchi N, Homogenization Method for Shape and Topology Optimization, Comp. Meth. Appl. Mech. Enginrg. to Appear in 1991
Noor A.K., Belytschko, T., and Simo, J.C., Analytical and Computational Models of Shells, CED-Vol. 3, American Society of Mechanical Engineers, (1989), New York
Bendse, M.P., Generalized Plate Models and Optimum Design, in Homogenization and Effective Moduli of Materials and Media,ed. J.L. Ericksen et al., Springer-Verlag, (1986), New York, pp.1–26
Diaz, A.R., and Soto, C.A., Optimum Shape and Layout of Plate Structures, Technical Report in Department of Mechanical Engineering, Michigan State University, (1991), East Lansing, Michiga, U.S.A.
Schmit, L.A., Kicher, T.P., and Morrow, W.M., Structural Synthesis capability for integrally stiffened waffle plates, AIAA Journal, 1, (1963) pp. 2820–2836
Morrow, W.M., and Schmit, L.A., Structural Synthesis of a Stiffened Cylinder,NASA (1968) CR-1217
Simitses, G.J., Optimal versus the stiffened circular plate, AIAA Journal, 1110, (1973) pp. 1409–1412
Banichuk, N.V., Problems and Methods of Optimal Structural Design, Plenum Press, (1983), New York
Haftka, R.T., and Prasad, B., Optimum structural design with plate bending elements–A Survey, AIAA Journal, 19–4, (1981) pp. 517–522
Cheng, K.T., On non-smoothness in optimal design of solid, elastic plates, International Journal of Solids and Structures, 17, (1981) pp. 795–810
Cheng, K.T., and Olhoff N., An investigation concerning optimal design of solid elastic plates,International Journal of Solids and Structures, 17, (1981) pp.305323
Cheng, K.T., and Olhoff, N., Regularized formulation for optimal design of axisymmetric plates, International Journal of Solids and Structures, 18, (1982) pp. 153–169
Rozvany, G.I.N., Structural Layout Theory - The Present State of Knowledge, in New Directions in Optimum Structural Design, ed. E. Atrek et al, John Wiley & Sons, 1984, Chichester, pp.167–195
Yang W.H., Minimization Approach to Limit Solutions of Plate, Comp Meth Appl Mech Enginrg 28 (1981) pp. 265–274
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Suzuki, K., Kikuchi, N. (1993). Layout Optimization using the Homogenization Method. In: Rozvany, G.I.N. (eds) Optimization of Large Structural Systems. NATO ASI Series, vol 231. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9577-8_7
Download citation
DOI: https://doi.org/10.1007/978-94-010-9577-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9579-2
Online ISBN: 978-94-010-9577-8
eBook Packages: Springer Book Archive