Abstract
An approach to control the profiles of interstory drift ratios along the height of building structures via topology optimization is proposed herein. The theoretical foundation of the proposed approach involves solving a min–max optimization problem to suppress the maximum interstory drift ratio among all stories. Two formulations are suggested: one inherits the bound formulation and the other utilizes a p-norm function to aggregate all individual interstory drift ratios. The proposed methodology can shape the interstory drift ratio profiles into inverted triangular or quadratic patterns because it realizes profile control using a group of shape weight coefficients. The proposed formulations are validated via a series of numerical examples. The disparity between the two formulations is clear. The optimization results show the optimal structural features for controlling the interstory drift ratios under different requirements.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
GB50011-2010. Code for Seismic Design of Buildings. Beijing: Ministry of Construction of China, 2010 (in Chinese)
ATC. Guidelines for SEISMIC PERFORMANCE ASSessment of Buildings. Redwood City (CA): Applied Technology Council, 2007
SNZ. Concrete Structures Standard. Wellington: Standards New Zealand, 2004
ASCE/SEI 7-02. Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers, 2016
Moehle J P, Mahin S A. Observations on the behavior of reinforced concrete buildings during earthquakes. American Concrete Institute Special Publication, Earthquake-Resistant Concrete Structures—Inelastic Response and Design, 1991, 127: 67–90
Mayes R L. Interstory drift design and damage control issues. Structural Design of Tall Buildings, 1995, 4(1): 15–25
Griffis L G. Serviceability limit states under wind load. Engineering Journal AISC, 1993, 30(1): 1–16
Paulay T, Priestley M J N. Seismic Design of reinforced Concrete and Masonry Buildings. New York: John Wiley and Sons, 1992
Kirac N, Dogan M, Ozbasaran H. Failure of weak-storey during earthquakes. Engineering Failure Analysis, 2011, 18(2): 572–581
Jara J M, Hernández E J, Olmos B A, Martínez G. Building damages during the September 19, 2017 earthquake in Mexico City and seismic retrofitting of existing first soft-story buildings. Engineering Structures, 2020, 209: 109977
Agha Beigi H, Sullivan T J, Calvi G M, Christopoulos C. Controlled soft storey mechanism as a seismic protection system. In: The 10th International Conference on Urban Earthquake Engineering. Tokyo: Tokyo Institute of Technology, 2013
Lai J W, Mahin S A. Strongback system: A way to reduce damage concentration in steel-braced frames. Journal of Structural Engineering, 2015, 141(9): 04014223
Alavi B, Krawinkler H. Strengthening of moment-resisting frame structures against near-fault ground motion effects. Earthquake Engineering & Structural Dynamics, 2004, 33(6): 707–720
Moghaddam H, Hajirasouliha I, Doostan A. Optimum seismic design of concentrically braced steel frames: Concepts and design procedures. Journal of Constructional Steel Research, 2005, 61(2): 151–166
Lagaros N D, Papadrakakis M. Seismic design of RC structures: A critical assessment in the framework of multi-objective optimization. Earthquake Engineering & Structural Dynamics, 2007, 36(12): 1623–1639
Farahmand-Tabar S, Ashtari P. Simultaneous size and topology optimization of 3D outrigger-braced tall buildings with inclined belt truss using genetic algorithm. Structural Design of Tall and Special Buildings, 2020, 29(13): e1776
Kim C K, Kim H S, Hwang J S, Hong S M. Stiffness-based optimal design of tall steel frameworks subject to lateral loading. Structural Optimization, 1998, 15(3–4): 180–186
Chan C M, Zou X K. Elastic and inelastic drift performance optimization for reinforced concrete buildings under earthquake loads. Earthquake Engineering & Structural Dynamics, 2004, 33(8): 929–950
Zou X K, Chan C M. An optimal resizing technique for seismic drift design of concrete buildings subjected to response spectrum and time history loadings. Computers & Structures, 2005, 83(19–20): 1689–1704
Tomei V, Imbimbo M, Mele E. Optimization of structural patterns for tall buildings: the case of diagrid. Engineering Structures, 2018, 171: 280–197
Vu-Huu T, Phung-Van P, Nguyen-Xuan H, Abdel Wahab M. A polytree-based adaptive polygonal finite element method for topology optimization of fluid-submerged breakwater interaction. Computers & Mathematics with Applications (Oxford, England), 2018, 76(5): 1198–1218
Ghasemi H, Park H S, Rabczuk T. A multi-material level-set based topology optimization of flexoelectric composites. Computer Methods in Applied Mechanics and Engineering, 2018, 332: 47–62
Ghasemi H, Park H S, Alajlan N, Rabczuk T. A computational framework for design and optimization of flexoelectric materials. International Journal of Computational Methods, 2020, 17(1): 1850097
Hamdia K M, Ghasemi H, Zhuang X Y, Rabczuk T. Multilevel Monte Carlo method for topology optimization of flexoelectric composites with uncertain material properties. Engineering Analysis with Boundary Elements, 2022, 134: 412–418
Zhang J, Li Q. Identification of modal parameters of a 600-m-high skyscraper from field vibration tests. Earthquake Engineering & Structural Dynamics, 2019, 48(15): 1678–1698
Beghini L L, Beghini A, Katz N, Baker W F, Paulino G H. Connecting architecture and engineering through structural topology optimization. Engineering Structures, 2014, 59: 716–726
Xu J, Spencer B F Jr, Lu X. Performance-based optimization of nonlinear structures subject to stochastic dynamic loading. Engineering Structures, 2017, 134: 334–345
Wu S, He H, Cheng S, Chen Y. Story stiffness optimization of frame subjected to earthquake under uniform displacement criterion. Structural and Multidisciplinary Optimization, 2021, 63(3): 1533–1546
Gomez F, Spencer B F Jr, Carrion J. Topology optimization of buildings subjected to stochastic base excitation. Engineering Structures, 2020, 223: 111111
Kreisselmeier G, Steinhauser R. Systematic control design by optimizing a vector performance index. In: International Federation of Active Controls Symposium on Computer-Aided Design of Control Systems. Zurich: Pergamon Press Ltd., 1979
Lu X, Cui Y, Liu J, Gao W. Shaking table test and numerical simulation of a 1/2-scale self-centering reinforced concrete frame. Earthquake Engineering & Structural Dynamics, 2015, 44(12): 1899–1917
Gao W, Lu X. Modelling unbonded prestressing tendons in self-centering connections through improved sliding cable elements. Engineering Structures, 2019, 180: 809–828
Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197–224
Bendsoe M P, Sigmund O. Topology Optimization—Theory, Methods and Applications. Berlin: Springer, 2003
Wang F, Lazarov B S, Sigmund O. On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization, 2011, 43(6): 767–784
Gao W, Wang F, Sigmund O. Systematic design of high-Q prestressed micro membrane resonators. Computer Methods in Applied Mechanics and Engineering, 2020, 361: 112692
Chopra A K. Dynamics of Structures: Theory and Applications to Earthquake Engineering. New Jersey: Prentice-Hall, 1995
Bendsøe M P, Olhoff N, Taylor J E. A variational formulation for multicriteria structural optimization. Journal of Structural Mechanics, 1983, 11(4): 523–544
James K A, Hansen J S, Martins J R R A. Structural topology optimization for multiple load cases using a dynamic aggregation technique. Engineering Optimization, 2009, 41(12): 1103–1118
Le C, Norato J, Bruns T, Ha C, Tortorelli D. Stress-based topology optimization for continua. Structural and Multidisciplinary Optimization, 2010, 41(4): 605–620
Gao W, Lu X, Wang S. Seismic topology optimization based on spectral approaches. Journal of Building Engineering, 2022, 47: 103781
Poon N M K, Martins J R R A. An adaptive approach to constraint aggregation using adjoint sensitivity analysis. Structural and Multidisciplinary Optimization, 2007, 34(1): 61–73
Sigmund O A. 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, 2001, 21(2): 120–127
Andreassen E, Clausen A, Schevenels M, Lazarov B S, Sigmund O. Efficient topology optimization in Matlab using 88 lines of code. Structural and Multidisciplinary Optimization, 2011, 43(1): 1–16
Stolpe M, Svanberg K. An alternative interpolation scheme for minimum compliance topology optimization. Structural and Multidisciplinary Optimization, 2001, 22(2): 116–124
Feng T T, Arora J S, Haug E J. Optimal structural design under dynamic loads. International Journal for Numerical Methods in Engineering, 1977, 11(1): 39–52
Arora J S, Haug E J. Methods of design sensitivity analysis in structural optimization. AIAA Journal, 1979, 17(9): 970–974
Mijar A R, Swan C C, Arora J S, Kosaka I. Continuum topology optimization for concept design of frame bracing systems. Journal of Structural Engineering, 1998, 124(5): 541–550
Stromberg L L, Beghini A, Baker W F, Paulino G H. Topology optimization for braced frames: combining continuum and beam/column elements. Engineering Structures, 2012, 37: 106–124
Zhou Y, Zhang C, Lu X. An inter-story drift-based parameter analysis of the optimal location of outriggers in tall buildings. Structural Design of Tall and Special Buildings, 2016, 25(5): 215–231
Svanberg K. The method of moving asymptotes—A new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359–373
Svanberg K. A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM Journal on Optimization, 2002, 12(2): 555–573
Allahdadian S, Boroomand B, Barekatein A R. Towards optimal design of bracing system of multi-story structures under harmonic base excitation through a topology optimization scheme. Finite Elements in Analysis and Design, 2012, 61: 60–74
Allahdadian S, Boroomand B. Topology optimization of planar frames under seismic loads induced by actual and artificial earthquake records. Engineering Structures, 2016, 115: 140–154
Acknowledgements
We thank Professor Krister Svanberg (Department of Mathematics, KTH Royal Institute of Technology) for providing the MMA code. This study was supported by the National Natural Science Foundation of China (Grant No. 51638012). The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported herein.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Gao, W., Lu, X. Controlling interstory drift ratio profiles via topology optimization strategies. Front. Struct. Civ. Eng. 17, 165–178 (2023). https://doi.org/10.1007/s11709-022-0892-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11709-022-0892-3