Abstract
This paper presents a simple evolutionary method for optimization of plates subject to constant weight, where design variable thicknesses are discrete. Sensitivity numbers for sizing elements are derived using optimality criteria methods. An optimal design with minimum displacement or minimum strain energy is obtained by gradually shifting material from elements to the others according to their sensitivity numbers. A simple smoothing technique is additionally employed to suppress formation of checkerboard patterns. It is shown that the proposed method can directly deal with discrete design variables. Examples are provided to show the capacity of the proposed evolutionary method for structural optimization with discrete design variables.
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Bendsøe, M.P.; Díaz, A.; Kikuchi, N. 1993: Topology and generalized layout optimization of elastic structures. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.)Topology design of structures, pp. 159–205. Dordrecht: Kluwer
Chu, D.N. 1997:Evolutionary structural optimization method for systems with stiffness and displacement constraints. Ph. D. Thesis, Victoria University of Technology, Melbourne
Chu, D.N.; Xie, Y.M. 1997: Evolutionary method for truss topology optimization subject to displacement constraints.Proc. 6-th National Conf. on Mechanics (held in Hanoi, Vietnam), pp. 185–191
Chu, D.N.; Xie, Y.M.; Steven, G.P. 1998: An evolutionary structural optimization method for sizing problems with discrete design variables.Comp. & Struct. (in press).
Chu, D.N.; Xie, Y.M.; Hira, A.; Steven, G.P. 1995: An evolutionary procedure for structural optimization with displacement constraints.Building for the 21 st Century-Proc. 5-th East Asia-Racific Conf. on Structural Engineering and Construction, Vol. 2, pp. 1091–1096
Chu, D.N.; Xie, Y.M.; Hira, A.; Steven, G.P. 1996: Evolutionary structural optimization for problems with stiffness constraints.Finite Elements in Analysis & Design 21, 239–251
Chu, D.N.; Xie, Y.M.; Hira, A.; Steven, G.P. 1997: On various aspects of evolutionary structural optimization for problems with stiffness constraints.Finite Elements in Analysis & Design 24, 197–212
Chu, D.N.; Xie, Y.M.; Hira, A.; Steven, G.P. 1998: Evolutionary topology optimization of structures subject to displacement constraints.Proc. Australasian Conf. on Structural Optimization (held in Sydney), pp. 419–426
Diaz, A.; Sigmund, O. 1995: Checkerboard patterns in layout optimization.Struct. Optim. 10, 40–45
Huang, M.W.; Arora, J.S. 1995: Engineering optimization with discrete variables.A collection of technical papers, 36-th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. and AIAA/ASME Adaptive Structures Forum, Part 1 (held in New Orleans), pp. 1475–1483
Manickarajah, D.; Xie, Y.M.; Steven, G.P. 1995. A simple method for the optimization of columns, frames and plates against buckling. in: Kitipornchai, S.; Hancock, G.J.; Bradford, M.A. (eds.)Structural stability and design, pp. 175–180. Rotterdam: A.A. Balkema Publishers
Olsen, G.R.; Vanderplaats, G.N. 1989: Methods for nonlinear optimization with discrete design variables.AIAA J. 27, 1584–1589
Ringertz, U.T. 1988: On methods for discrete structural optimization.Eng. Opt. 13, 47–64
Rodrigues, H.C.; Fernandes, P.A. 1993: Topology optimization of linear elastic structures subjected to thermal loads. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.)Topology design of structures, pp. 437–450. Dordrecht: Kluwer
Sandgren, E. 1990: Nonlinear integer and discrete programming in mechanical design optimization.J. Mech. Des., ASME 112, 223–229
Schmit, L.; Fleury, C. 1980: Discrete-continuous variables structural synthesis using dual methods.AIAA J. 18, 1515–1524.
Suzuki, K.; Kikuchi, N.; Ohtsubo, H. 1992: Optimal shape and layout design of plate using microstructure.J. Japan Soc. Mech. Eng. 2, 345–351.
Tenek, L.H.; Hagiwara, I. 1994: Optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization.Comput. Meth. Appl. Mech. Engrg. 115, 111–124
Xie, Y.M.; Steven, G.P. 1993: A simple evolutionary procedure for structural optimization.Comp. & Struct. 49, 885–896.
Xie, Y.M.; Steven, G.P. 1994: Optimal design of multiple load case structures using an evolutionary procedure.Eng. Computations 11, 295–302
Xie, Y.M.; Steven, G.P. 1996. Evolutionary structural optimization for dynamic problems.Comp. & Struct. 58, 1067–1073
Youn, S.K.; Park, S.H. 1995: A study on the shape and topology optimization of structures.Computational. Mechanics '95-Theory and Applications, Proc. Int. Conf. on Computational Engineering Science (held in Hawaii), pp. 183–188. Berlin, Heidelberg, New York: Springer
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Chu, D.N., Xie, Y.M. & Steven, G.P. An evolutionary method for optimal design of plates with discrete variable thicknesses subject to constant weight. Structural Optimization 17, 55–64 (1999). https://doi.org/10.1007/BF01197713
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DOI: https://doi.org/10.1007/BF01197713