Evolutionary Structural Optimization
Introduction
The Evolutionary Structural Optimization (ESO) technique was originally proposed in 1992 by Professors Mike Xie and Grant Steven [1]. They aimed to develop a very simple but versatile technique for finding optimal structural designs. ESO is based on the concept of slowly removing inefficient materials from a structure so that the residual structure evolves towards the optimum.
The ESO method proves to be capable of solving size, shape and topology structural optimization for static, dynamic, stability and heat transfer problems or combinations of these [2-16]. The ESO method appeals to many practicing engineers and architects particularly because of its simplicity and effectiveness. Anyone who has a basic knowledge of finite element analysis (FEA) can readily understand and apply the ESO method. Another advantage of the ESO method is that it can be easily implemented and linked to commercial FEA packages such as ABAQUS, NASTRAN and ANSYS.
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ESO solution of an object hanging in the air under its own weight (an apple?) (click here to view the movie) |
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ESO for Tension-only or Compression- only Structures
The traditional ESO method removes material from a structure based on von Mises stress or strain energy of each element. For certain construction materials, such as concrete and steel cable, they are only suitable for sustaining compressive or tensile stress. The ESO method has been extended to the design of tension-only and compression-only structures.
To achieve an optimal tension-only structure, elements with the highest compressive stresses will be removed first. Then the less tensile elements will be deleted from the structure as well. Similarly, to achieve an optimal compression-only structure, elements with the highest tensile stresses will be removed first. Then the less compressive elements will be deleted from the structure as well.
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ESO solution of a catenary-type tension-only structure (click here to view the movie) |
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ESO solution of a compression-only structure (simulating the Passion Facade of Sagrada Familia church in Barcelona, in collaboration with Professor Mark Burry of SIAL) (click here to view the movie) |
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ESO for Non-linear Structures
To achieve a non-linear ESO design, the finite element models are analyzed by considering material nonlinearity and / or geometrical nonlinearity. Two criteria of for material removal have been experimented. One is based on deleting elements with low von Mises stress, the other is based on removing elements with low strain energy. The example shown below is based on strain energy criterion.
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(click here to view the movie for linear ESO solution) |
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(click here to view
the movie for non-linear ESO solution assuming Power-law material model σ =ε0.2)
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Comparison of load-carrying capacities of linear and non-linear ESO designs |
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Bi-directional Evolutionary Structural Optimization
The validity of the ESO method depends, to a large extent, on the assumptions that the structural modification (evolution) at each step is small and the mesh for the finite element analysis is dense. If too much material is removed in one step, the ESO method is unable to restore the elements which might have been prematurely deleted at earlier iterations. In order to make the ESO method more robust, a bi-directional ESO (BESO) method was proposed in 1999 in which material can be added to and deleted from a structure simultaneously. Recently we have developed a new BESO algorithm with much improved capabilities.
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Loading and boundary conditions of a 3D beam (a stool?)
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Initial design of the stool |
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BESO solution of the stool (click here to view the movie) |
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Loading and boundary conditions of a bridge-type structure |
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Initial design of the stool |
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BESO solution of the bridge-type structure (click here to view the movie) |
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Underground Space Supported by 16 Columns
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BESO solution for the underground space (click here to view the movie) |
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Load Transfer System for a Multi-storey Atrium of a Building
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(click here to view the movie) |
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Prototyping ESO/BESO Designs Using 3D Printers
Once the ESO/BESO shapes are obtained, the computer models can be sent to 3D printers to produce exact physical models in wax or plaster. The following photo shows a few examples of our physical models automatically made by the 3D printers from the ESO/BESO results.
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Prototyping ESO/BESO Designs Using 3D Printers |
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Examples of Real Structures Designed Using ESO/BESO Method
1. Akutagwa River Side building at Takatsuki JR station in Japan. Deigned by Professor Hiroshi Ohmori and coworkers. Construction completed in April 2004. Reference: Hiroshi Ohmori et al. ‘Application of Computational Morphogenesis to Structural Design’, in Proceedings of Frontiers of Computational Sciences Symposium, Nagoya, Japan, 11-13 October, 2005, pp 45-52.
2. Convention hall at the Qatar International Exhibition Centre. Designed by renowned Japanese structural engineer Mutsuro Sasaki and coworkers. Under construction. Reference: Changyu Cui, Hiroshi Ohmori and Mutsuro Sasaki, ‘Structural design by extended ESO method’, in Proceedings of Frontiers of Computational Sciences Symposium, Nagoya, Japan, 11-13 October, 2005, pp 149-156 (in Japanese).
References
(More publications on ESO and other topics are listed in the pages of PEOPLE)
[1] Y.M. Xie, Z.H. Zuo, X. Huang, J.W. Tang, B. Zhao and P. Felicetti, ‘Architecture and urban design through evolutionary structural optimisation algorithms’, Keynote Lecture of International Symposium on Algorithmic Design for Architecture and Urban Design, Tokyo, Japan, March 14-16, 2011, 11pp. (Downloadable, PDF format, 632KB)
[2] Y.M. Xie and G.P. Steven, 'A simple evolutionary procedure for structural optimization', Computers & Structures, Vol. 49, No. 5, pp 885-896, 1993. (Downloadable, PDF format, 1427KB)
[3] Y.M. Xie and G.P. Steven, Evolutionary Structural Optimization, Springer-Verlag, London, June, 1997, xii+188 pp., ISBN 3-540-76153-5.
[4] X. Huang and Y.M. Xie, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications, John Wiley & Sons, Chichester, England, 2010, 235 pp., ISBN: 9780470746530. [Book Flyer]
