Abstract
In this chapter the homogenization method for plane stress problems is extended to deal with the creation of optimal layout and reinforcement topologies of plate structures. In this formulation the problem is to determine the stiffest plate strueture with a volume constraint for the reinforcement material. Introducing plate microcell models, a formulation for homogenization of plates based on the first order thick plate theory is presented. To solve the optimization problem the optimality criteria method is used. Using different material models some examples are provided.
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References
Olhoff N., On singularities, local optima and formulation of stiffeners in optimal design of plates, in Optimization in structural design, edited by Sawczuk A. and Mroz Z., pp. 82–103. Springer-Verlag, New York (1975)
Lurie K.A. and Cheirkaev A.V., Prager theorem application to optimal design of thin plates, MTT (Mecnanics of solids), 11, 157–159 (1976)
Cheng K.T. and Olhoff N., An investigation concerning optimal design of solid elastic plates, Int J. Solids Struct., 16 , 305–323 (1982)
Rozvany G.I.N., Olhoff N., Bends0e M.P., Cheng K.T. and Taylor J.E., On the solid plate paradox in structural optimization, J. Struct. Mech., 10(1), 1–32 (1982)
Bends0e M.P., Some smear-out models for integrally stiffened plates with applications to optimal design, in In proceedings of Int Symp. Optimum Structural Design, pp. 13–34, Univ. Ariz., Tucson Arizona (1982)
Bourgeat A. and Tapiero R., Homogenization of a transversely perforated plate in the frame of Hencky Mindlin’s theory, in the thermoelastic case with non-uniform oscillating coefficients, C. R. Acad. Sei. Paris, Serie /, 297, 213–216 (1983)
Suzuki K. and Kikuchi N., Generalized layout optimization of threedimensional shell structures, in Geometrie aspects of industrial design, edited by Komkov V. SIAM (1991)
Tenek L.H. and Hagiwara I., Optimization of material distribution within isotropic and anisotropic plates using homogenization, Comp. Meth. Appl. Mech. Engrg109, 155–167 (1993)
Tenek L.H. and Hagiwara I., Optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization, Comp. Meth. Appl. Mech. Engrg., 115, 111–124 (1994)
Soto C.A. and Diaz A.R., Optimum layout and shape of plate structures using homogenization, in Topology design of structures, edited by Bends0e M.P. and Mota Soares C.A.. pp. 407–420. Kluwer Academic Publishers (1993)
Diaz A.R., Lipton R. and Soto C.A., A new formulation of the problem of Optimum reinforcement of Reissner-Mindlin plates, Private communications
Kikuchi N. and Suzuki K., Structural optimization of a linearly elastic strueture using the homogenization method, in Shape and Layout Optimization in Structural Design, edited by Rozvany G. (1990)
Bends0e M.P., Diaz A.R. and Kikuchi N., Topology and generalized layout optimization of elastic structures, in Topology design of structures, edited by Bendsöe M.P. and Mota Soares C.A., pp. 159–205. Kluwer Academic Publishers (1993)
Hinton E. and Abdel Rahman H.H., Mindlin plate finite elements, in Finite element Software for plates and shells, edited by Hinton E. and Owen D.R.J., pp. 157–233. Pineridge Press, Swansea (1984)
Hughes T.J.R., Cohen M. and Haroun M., Reduced and selective Integration techniques in the finite element analysis of plates, Nuclear Engineering and Design, 46, 203–222 (1978)
Hughes T.J.R. and Cohen M., The ’heterosis’ family of plate finite elements, in Proceedings of the ASCE Electronic Computations Conference, St. Louis, Missouri (1979)
Bends0e M.P., Optimization of structural topology, shape} and material Springer, Berlin (1995)
Hughes T.J.R., The finite element method. Prentice-Hall International, Inc., Englewood Cliffs, New Jersey (1987)
Hinton E. and Owen D.R.J., Finite Element Programming. Academic Press, London (1977)
Zienkiewicz O.G. and Taylor R.L., The finite element method, vol. 2. McGraw-Hill, London, 4th edn. (1989)
Zienkiewicz O.G. and Taylor R.L., The finite element method, vol. 1. McGraw-Hill, London, 4th edn. (1989)
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Hassani, B., Hinton, E. (1999). Topological Layout and Reinforcement Optimization of Plate Structures. In: Homogenization and Structural Topology Optimization. Springer, London. https://doi.org/10.1007/978-1-4471-0891-7_6
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DOI: https://doi.org/10.1007/978-1-4471-0891-7_6
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1229-7
Online ISBN: 978-1-4471-0891-7
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