Stress-Based Topology Optimization of Steel-Frame Structures Using Members with Standard Cross Sections: Gradient-Based Approach
Publication: Journal of Structural Engineering
Volume 143, Issue 8
Abstract
This article presents a computationally efficient methodology for stress-based topology optimization of steel frame structures with cross-sectional properties that are mapped from I-beam sections of a design manual. To account for the natural variability of the data, this mapping is achieved via quantile regression to derive continuous relationships between cross-sectional area (the design variable) and other section properties. These relationships are used for deriving the gradient of structural performance, which allows using computationally efficient gradient-based optimization schemes. Three frame structures are designed using the proposed algorithm, the resulting designs are compared with traditional compliance-based topology optimization algorithms, and changes in the designs are discussed. A comparison of stress distribution within the designed structures verified the effectiveness of the proposed methodology.
Get full access to this article
View all available purchase options and get full access to this article.
References
Achtziger, W. (1999). “Local stability of trusses in the context of topology optimization. Part I: Exact modelling.” Struct. Optim., 17(4), 235–246.
Achtziger, W., and Stolpe, M. (2007). “Truss topology optimization with discrete design variables guaranteed global optimality and benchmark examples.” Struct. Multidiscip. Optim., 34(1), 1–20.
AISC (American Institute of Steel Construction). (2015). “Steel construction manual shapes database.” ⟨https://www.aisc.org/globalassets/product-files-not-searched/manuals/aiscshapesdatabasev14_1-current.zip⟩ (Feb. 12, 2017).
Amini, K., Jalalpour, M., and Delatte, N. (2016). “Advancing concrete strength prediction using non-destructive testing: Development and verification of a generalizable model.” Constr. Build. Mater., 102(1), 762–768.
Beghini, L. L., Beghini, A., Baker, W. F., and Paulino, G. H. (2014). “Integrated discrete/continuum topology optimization framework for stiffness or global stability of high-rise buildings.” J. Struct. Eng., 141(8), 04014207.
Bendsoe, M. P., and Sigmund, O. (2004). Topology optimization: Theory, methods and applications, Springer, Stone Harbor, NJ.
Bruggi, M. (2008). “On an alternative approach to stress constraints relaxation in topology optimization.” Struct. Multidiscip. Optim., 36(2), 125–141.
Changizi, N., and Jalalpour, M. (2017). “Robust topology optimization of frames under geometric or material uncertainty.” Struct. Multidiscip. Optim., 398–407.
Changizi, N., Kaboodanian, H., and Jalalpour, M. (2017). “Stress-based topology optimization of frame structures under geometric uncertainty.” Comput. Methods Appl. Mech. Eng., 315, 121–140.
Cheng, G., and Guo, X. (1997). “-relaxed approach in structural topology optimization.” Struct. Optim., 13(4), 258–266.
Cheng, G., and Jiang, Z. (1992). “Study on topology optimization with stress constraints.” Eng. Optim., 20(2), 129–148.
Duysinx, P., and Bendsøe, M. P. (1998). “Topology optimization of continuum structures with local stress constraints.” Int. J. Numer. Methods Eng., 43(8), 1453–1478.
Duysinx, P., and Sigmund, O. (1998). “New developments in handling stress constraints in optimal material distribution.” Proc.,7th AIAA/USAF/NASAISSMO Symp. on Multidisciplinary Analysis and Optimization, AIAA, Reston, VA, Vol. 1, 1501–1509.
Fredricson, H. (2005). “Topology optimization of frame structuresjoint penalty and material selection.” Struct. Multidiscip. Optim., 30(3), 193–200.
Fredricson, H., Johansen, T., Klarbring, A., and Petersson, J. (2003). “Topology optimization of frame structures with flexible joints.” Struct. Multidiscip. Optim., 25(3), 199–214.
Gaynor, A. T., Guest, J. K., and Moen, C. D. (2012). “Reinforced concrete force visualization and design using bilinear truss-continuum topology optimization.” J. Struct. Eng., 607–618.
Grinsted, A. (2015). “Quantile regression.” ⟨http://www.mathworks.com/matlabcentral/fileexchange/32115-quantreg-x-y-tau-order-nboot-⟩ (Jul. 7, 2016).
Kanno, Y., and Guo, X. (2010). “A mixed integer programming for robust truss topology optimization with stress constraints.” Int. J. Numer. Methods Eng., 83(13), 1675–1699.
Kirsch, U. (1990). “On singular topologies in optimum structural design.” Struct. Optim., 2(3), 133–142.
Koenker, R., and Bassett, G., Jr. (1978). “Regression quantiles.” Econometrica: J. Econometric Soc., 46(1), 33–50.
Kureta, R., and Kanno, Y. (2014). “A mixed integer programming approach to designing periodic frame structures with negative poissons ratio.” Optim. Eng., 15(3), 773–800.
Le, C., Norato, J., Bruns, T., Ha, C., and Tortorelli, D. (2010). “Stress-based topology optimization for continua.” Struct. Multidiscip. Optim., 41(4), 605–620.
Liang, Q. Q., Xie, Y. M., and Steven, G. P. (2000). “Optimal topology design of bracing systems for multistory steel frames.” J. Struct. Eng., 823–829.
MATLAB vR2016a [Computer software]. MathWorks, Natick, MA.
Mogami, K., Nishiwaki, S., Izui, K., Yoshimura, M., and Kogiso, N. (2006). “Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques.” Struct. Multi. Optim., 32(4), 299–311.
Ohsaki, M., and Katoh, N. (2005). “Topology optimization of trusses with stress and local constraints on nodal stability and member intersection.” Struct. Multidiscip. Optim., 29(3), 190–197.
Pedersen, C. B. (2003). “Topology optimization design of crushed 2D-frames for desired energy absorption history.” Struct. Multidiscip. Optim., 25(5-6), 368–382.
Pedersen, C. B. (2004). “Crashworthiness design of transient frame structures using topology optimization.” Comput. Methods Appl. Mech. Eng., 193(6), 653–678.
Rasmussen, M., and Stolpe, M. (2008). “Global optimization of discrete truss topology design problems using a parallel cut-and-branch method.” Comput. Struct., 86(13), 1527–1538.
Richardson, J. N., Adriaenssens, S., Bouillard, P., and Coelho, R. F. (2012). “Multiobjective topology optimization of truss structures with kinematic stability repair.” Struct. Multidiscip. Optim., 46(4), 513–532.
Rojas-Labanda, S., and Stolpe, M. (2015). “Benchmarking optimization solvers for structural topology optimization.” Struct. Multidiscip. Optim., 52(3), 527–547.
Rozvany, G. (2001). “On design-dependent constraints and singular topologies.” Struct. Multidiscip. Optim., 21(2), 164–172.
Rozvany, G., and Sobieszczanski-Sobieski, J. (1992). “New optimality criteria methods: Forcing uniqueness of the adjoint strains by corner-rounding at constraint intersections.” Struct. Optim., 4(3-4), 244–246.
Sarma, K. C., and Adeli, H. (2000). “Fuzzy genetic algorithm for optimization of steel structures.” J. Struct. Eng., 596–604.
Shea, K., and Smith, I. F. (2006). “Improving full-scale transmission tower design through topology and shape optimization.” J. Struct. Eng., 781–790.
Sigmund, O. (2011). “On the usefulness of non-gradient approaches in topology optimization.” Struct. Multidiscip. Optim., 43(5), 589–596.
Stolpe, M. (2015). “Truss topology optimization with discrete design variables by outer approximation.” J. Global Optim., 61(1), 139–163.
Svanberg, K. (1987). “The method of moving asymptotesa new method for structural optimization.” Int. J. Numer. Methods Eng., 24(2), 359–373.
Swan, C. C., and Rahmatalla, S. (2001). “Does continuum topology optimization have a place in design of large-scale structures?” Structures 2001: A Structural Engineering Odyssey, AIAA, Reston, VA, 1–9.
Takezawa, A., Nishiwaki, S., Izui, K., and Yoshimura, M. (2007). “Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties.” Struct. Multidiscip. Optim., 34(1), 41–60.
Torii, A. J., Lopez, R. H., and Miguel, L. F. (2015). “Modeling of global and local stability in optimization of truss-like structures using frame elements.” Struct. Multidiscip. Optim., 51(6), 1187–1198.
Yang, R., and Chen, C. (1996). “Stress-based topology optimization.” Struct. Optim., 12(2-3), 98–105.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 143 • Issue 8 • August 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Dec 23, 2015
Accepted: Jan 27, 2017
Published online: Apr 13, 2017
Published in print: Aug 1, 2017
Discussion open until: Sep 13, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.