Integrated Discrete/Continuum Topology Optimization Framework for Stiffness or Global Stability of High-Rise Buildings
Publication: Journal of Structural Engineering
Volume 141, Issue 8
Abstract
This paper describes an integrated topology optimization framework using discrete and continuum elements for buckling and stiffness optimization of high-rise buildings. The discrete (beam/truss) elements are optimized based on their cross-sectional areas, whereas the continuum (polygonal) elements are concurrently optimized using the commonly known density method. Emphasis is placed on linearized buckling and stability as objectives. Several practical examples are given to establish benchmarks and illustrate the proposed methodology for high-rise building design.
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Acknowledgments
The first author gratefully acknowledges the support form the National Science Foundation (NSF) Graduate Research Fellowship Program (GRFP). The authors also acknowledge support from the NSF under grants CMMI #1234243 and CMMI #1335160, and from the Donald B. and Elizabeth M. Willett endowment at the University of Illinois at Urbana-Champaign. Any opinion, finding, conclusions, or recommendations expressed here are those of the authors and do not necessarily reflect the views of the sponsors.
References
Adams, N., Frampton, K., and van Leeuwen, T. (2012). SOM journal 7, Hatje Cantz & Company KG.
Baker, W. F. (1992). “Energy-based design of lateral systems.” Struct. Eng. Int., 2(2), 99–102.
Bendsoe, M. P. (1989). “Optimal shape design as a material distribution problem.” Struct. Optim., 1(4), 193–202.
Bendsoe, M. P., and Sigmund, O. (1999). “Material interpolation schemes in topology optimization.” Arch. Appl. Mech., 69(9–10), 635–654.
Bendsoe, M. P., and Sigmund, O. (2002). Topology optimization: Theory, methods and applications, Springer, Berlin, Heidelberg.
Christensen, P. W., and Klarbring, A. (2008). An introduction to structural optimization, Springer, New York.
Cook, R. D., Malkus, D. S., Plesha, M. E., and Witt, R. J. (2001). Concepts and applications of finite element analysis, 4th Ed., Wiley, New York.
Diaz, A. R., and Kikuchi, N. (1992). “Solutions to shape and topology eigenvalue optimization problems using a homogenization method.” Int. J. Numer. Meth. Eng., 35(7), 1487–1502.
Folgado, J., and Rodrigues, H. C. (1998). “Structural optimization with a non-smooth buckling load criterion.” Control Cyber., 27(2), 235–253.
Huang, X., and Xie, M. (2010). Evolutionary topology optimization of continuum structures: Methods and applications, Wiley, New York.
Kemmler, R., Lipka, A., and Ramm, E. (2005). “Large deformations and stability in topology optimization.” Struct. Multidisc. Optim., 30(6), 459–476.
Kosaka, I., and Swan, C. C. (1999). “A symmetry reduction method for continuum structural topology optimization.” Comput. Struct., 70(1), 47–61.
LeMessurier, W. J. (1976). “A practical method of second order analysis: Part I—Pin-jointed systems.” Eng. J. AISC, 13(4), 89–96.
LeMessurier, W. J. (1977). “A practical method of second order analysis: Part II—Rigid frames.” Eng. J. AISC, 14(2), 49–67.
Martini, K. (2011). “Harmony search method for multimodal size, shape, and topology optimization of structural frameworks.” J. Struct. Eng., 1332–1339.
Min, S., and Kikuchi, N. (1997). “Optimal reinforcement design of structures under the buckling load using the homogenization design method.” Struct. Eng. Mech., 5(5), 565–576.
Neves, M. M., Rodrigues, H. C., and Guedes, J. M. (1995). “Generalized topology design of structures with a buckling load criterion.” Struct. Multidisc. Optim., 10(2), 71–78.
Neves, M. M., Sigmund, O., and Bendsoe, M. P. (2002). “Topology optimization of periodic microstructures with a penalization of highly localized buckling modes.” Int. J. Numer. Meth. Eng., 54(6), 809–834.
Niu, B., Yan, J., and Cheng, G. D. (2008). “Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency.” Struct. Multidisc. Optim., 39(2), 115–132.
Olhoff, N., and Du, J. (2012). “On topological design optimization of vibrating structures.” Lecture notes from CISM, Udine, Italy.
Olhoff, N., and Rasmussen, S. H. (1977). “On bimodal optimum loads of clamped columns.” Int. J. Solids Struct., 13(7), 605–614.
Pedersen, N. L. (2000). “Maximization of eigenvalues using topology optimization.” Struct. Multidisc. Optim., 20(1), 2–11.
Rahmatalla, S. F. (2004). “Continuum topology design of sparse structures and compliant mechanisms.” Ph.D. thesis, Univ. of Iowa, Iowa City, IA.
Rahmatalla, S. F., and Swan, C. C. (2003). “Form finding of sparse structures with continuum topology optimization.” J. Struct. Eng., 1707–1716.
Rozvany, G. I. N., Zhou, M., and Birker, T. (1992). “Generalized shape optimization without homogenization.” Struct. Multidisc. Optim., 4(3), 250–252.
Sekimoto, T., and Noguchi, H. (2001). “Homologous topology optimization in large displacement and buckling problems.” JSME Int. J. Series A, 44(4), 616–622.
Seyranian, A. P., Lund, E., and Olhoff, N. (1994). “Multiple eigenvalues in structural optimization problems.” Struct. Optim., 8(4), 207–227.
Sigmund, O. (2001). “A 99 line topology optimization code written in Matlab.” Struct. Multidisc. Optim., 21(2), 120–127.
Stromberg, L. L., Beghini, A., Baker, W. F., and Paulino, G. H. (2012). “Topology optimization for braced frames: Combining continuum and beam/column elements.” Eng. Struct., 37, 106–124.
Svanberg, K. (1987). “The method of moving asymptotes—A new method for structural optimization.” Int. J. Numer. Meth. Eng., 24(2), 359–373.
Swan, C. C. (2012). “Developing benchmark problems for civil structural applications of continuum topology optimization.” Proc., 20th Anal Comput Specialty Conf., ASCE, Reston, VA, 310–322.
Talischi, C., Paulino, G. H., Pereira, A., and Menezes, I. F. M. (2010). “Polygonal finite elements for topology optimization: A unifying paradigm.” Int. J. Numer. Meth. Eng., 82(6), 671–698.
Talischi, C., Paulino, G. H., Pereira, A., and Menezes, I. F. M. (2012a). “PolyMesher: A general-purpose mesh generator for polygonal elements written in Matlab.” Struct. Multidisc. Optim., 45(3), 309–328.
Talischi, C., Paulino, G. H., Pereira, A., and Menezes, I. F. M. (2012b). “PolyTop: A Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes.” Struct. Multidisc. Optim., 45(3), 329–357.
Zyczkowski, M., and Gajewski, A. (1988). Optimal structural design under stability constraints, Kluwer Academic Press, Dordrecht, Netherlands.
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Published In
Journal of Structural Engineering
Volume 141 • Issue 8 • August 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Mar 3, 2013
Accepted: Aug 6, 2014
Published online: Sep 25, 2014
Discussion open until: Feb 25, 2015
Published in print: Aug 1, 2015
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