Abstract
A novel topology/shape optimisation method for axisymmetric elastic solids, based on solid modeling and FE analysis, is presented. Optimal profiles of minimum-mass axisymmetric structures are sought by growing and degenerating simple initial structures subject to response constraints. The rates of the growth and degeneration are controlled based on the current objective and constraint functions of the optimisation problem under consideration. The optimal structures are developed metamorphically in specified infinite design domains using both quadrilateral and triangular axisymmetric finite elements that are ideally suited for modeling continua involving curved boundaries.
The robustness of this fully automatic method is studied and validated with the first example of seeking the optimal shape of a centrally suspended axisymmetric object with minimum strain energy caused by self-weight. Then the method is applied to a practical industrial design problem: the design of a turbine disk. The variations of load and boundary conditions caused by shape change in these problems, including the gravitational and centrifugal loads, and temperature distribution are accommodated in the optimisation procedures. Thus, the design model closely resembles the real design problem. The results demonstrate the success of the method in generating optimal but realistic solutions to practical design problems.
Similar content being viewed by others
References
Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng71, 197–224
Bendsøe, M.P. 1995: Methods for optimization of structural topology, shape and material. Berlin Heidelberg New York: Springer
Bhavikatti, S.S.; Ramakrishnan, C.V. 1980: Optimum shape design of rotating disks. Comput Struct11, 397–401
Botkin, M.E. 1992: Three-dimensional shape optimization using fully automatic mesh generation. AIAA J30, 1932–1934
Braibant, V.; Fleury, C. 1984: Shape optimal design using B-spline . Comput Struct44, 247–267
Cheu, T.-C. 1990: Procedures for shape optimization of gas turbine disks. Comput Struct34, 1–4
Ding, Y.L. 1986: Shape optimization of structures: a literature survey. Comput Struct24, 985–1004
Donath, M. 1912: Die Berechnung rotierender Scheiben und Ringe. Berlin
Haftka, R.T.; Grandhi, R.V. 1986: Structural shape optimization – a survey. Comput Methods Appl Mech Eng57, 91–106
Hassani, B.; Hinton, E. 1998: Homogenization and structural topology optimization. Berlin Heidelberg New York: Springer
Hibbitt, Karlsson & Sorenson, Inc. 1998: ABAQUS manual,Version 5.7-5. Pawtucket RI: Hibbitt, Karlsson & Sorenson
Iman, M.H. 1982: Three dimensional shape optimization. Int J Numer Mech Eng18, 661–673
Kodiyalan, S.; Vanderplaats, G.N. 1989: Shape optimization of three-dimensional continuum structures via force approximation techniques. AIAA J27, 1256–1263
Lee, B.Y. 1996: Consideration of body forces in axisymmetric design sensitivity analysis using the BEM. Comput Struct61, 587–596
Lee, S.H.; Liu, J.-S.; Parks, G.T. 2000: Optimal shapes of axisymmetric suspended objects loaded under self-weight (fruit optimisation). In: Sienz, J. (ed.), Engineering design optimization – product and process improvement, Proceedings of 2nd ASMO UK/ISSMO Conference on Engineering Design Optimization, (held in Swansea, UK), pp. 117–123
Liu, J.-S.; Parks, G.T.; Clarkson, P.J. 1999a: Metamorphic Development: a new topology optimisation method for truss structures. 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, St. Louis, MO, USA, Paper AIAA-99-1387, Vol. 3, 1578–1588
Liu, J.-S.; Parks, G.T.; Clarkson, P.J. 1999b: Can a structure grow towards an optimum topology layout? – Metamorphic Development: a new topology optimisation method. Proceedings of the 3rd World Congress of Structural and Multidisciplinary Optimisation (WCSMO-3) (held in Buffalo, USA), on CD-ROM
Liu, J.-S.; Parks, G.T.; Clarkson, P.J. 2000: Metamorphic Development: a new topology optimisation method for continuum structures. Struct Multidisc Optim20, 288–300
Liu, J.-S.; Parks, G.T.; Clarkson, P.J. 2001: Shape optimisation of axisymmetric cylindrical nozzles in spherical pressure vessels subject to stress constraints. Int J Pres Ves Pip78, 1–9
Luchi, M.L.; Poggialini, A.; Persiani, F. 1980: An interactive optimization procedure applied to the design of gas turbine discs. Comput Struct11, 629–637
Mattheck, C. 1998: Design in Nature: Learning from Trees. Berlin: Springer
Mota Soares, C.A.; Rodrigues, H.C.; Choi, K.K. 1984: Shape optimal structure design using boundary elements and minimum compliance techniques. J Mech Transm Automat Des ASME106, 518–523
Olhoff, N.; Ronholt, E.; Schell, J. 1998: Topology optimization of three-dimensional structures using optimum microstructures. Struct Optim16, 1–18
Rozvany, G.I.N.; Bendsøe, M.P.; Kirsch, U. 1995: Layout optimization of structures, Appl Mech Rev (ASME)48, 41–119
Rozvany, G.I.N.; Zhou, M.; Birker, T. 1992: Generalized shape optimization without homogenization. Struct Optim4, 250–252
Stodola, A. (translated by Loewenstein, L.C.) 1927: Steam and Gas Turbines, 6th edn. New York: McGraw-Hill
Vincent, J. 1989: Relationship between density and stiffness of apple flesh. J Sci Food Agri47, 443–462
Wegst, U.G.K.; Ashby, M.F. 1997: Material Selection Charts for Natural Materials. CUED/C-EDC/TR55, internal report, Engineering Department, University of Cambridge, UK
Xie, Y.M.; Steven, G.P. 1997: Evolutionary structural optimization. Berlin Heidelberg New York: Springer
Yang, R.J.; Choi, K.K. 1985: Accuracy of finite element based shape sensitivity analysis. J Struct Mech13, 223–289
Yang, R.J. 1989: A three dimensional shape optimization system – SHOP3D. Comput Struct31, 885–890
Zhou, M.; Rozvany, G.I.N. 1991: The COC algorithm, part II: topology, geometry and generalized shape optimization. Comput Methods Appl Mech Eng89, 197–224
Zienkiewich, O.C.; Campbell, J.S. 1973: Shape optimization and sequential linear programming. In: Gallagher, R.H.; Zienkiewich, O.C. (eds.), Optimal Structural Design. New York: Wiley
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, JS., Parks, G. & Clarkson, P. Topology/shape optimisation of axisymmetric continuum structures – a metamorphic development approach. Struct Multidisc Optim 29, 73–83 (2005). https://doi.org/10.1007/s00158-004-0445-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-004-0445-5