Abstract
Structural optimization has become a widely used tool for various applications due to its capability of providing design freedom and promise to efficient structures. Current optimization methods are usually utilized for producing optimal structural systems subjected to design constraints under definite static or dynamic load distributions. However, engineering structures may experience randomly fluctuating loads in different physical environments. In this paper, a methodology of structural optimization with constraints on peak system responses to temporally correlated quasi-static load processes is developed. The proposed methodology provides an algorithm for generating structures of the optimal designs with constraints on their extreme responses to such environmental load sequences which have correlation features in the time domain. The computational results confirm that material distributions of optimized structures with peak response constraints highly depend on correlation levels of quasi-static load distributions under stationary processes. Furthermore, conventional optimization of structures in statics with displacement constraints is also compared with the reported optimum material distributions with peak response constraints under correlated load sequences. In consequence, the developed methodology provides a powerful tool of structural designs under stationary processes of temporally correlated loads having very low frequencies for fundamental engineering structures and further multidisciplinary mechanics researches.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arora JS, Wang Q (2005) Review of formulations for structural and mechanical system optimization. Struct Multidiscip Optim 30(4):251–272. https://doi.org/10.1007/s00158-004-0509-6
Ben-Tal A, Nemirovski A (2002) Robust optimization - methodology and applications. Math Program 92(3):453–480. https://doi.org/10.1007/s101070100286
Byrd RH, Hribar M, Nocedal J (1999) An interior point algorithm for large-scale nonlinear programming. SIAM J Appl Math 9(4):877–900. https://doi.org/10.1137/S1052623497325107
Byrd RH, Gilbert JC, Nocedal J (2000) A trust region method based on interior point techniques for nonlinear programming. Math Program Ser B 89 (1):149–185. https://doi.org/10.1007/s101070000189
Choi WS, Park GJ (1999) Transformation of dynamic loads into equivalent static loads based on modal analysis. Int J Numer Methods Eng 46(1):29–43. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<29::AID-NME661>3.0.CO;2-D
Choi WS, Park GJ (2002) Structural optimization using equivalent static loads at all time intervals. Comput Methods Appl Mech Eng 191(19-20):2105–2122. https://doi.org/10.1016/S0045-7825(01)00373-5
Díaz AR (1992) Shape optimization of structures for multiple loading conditions using a homogenization method. Struct Optim 4(1):17–22. https://doi.org/10.1007/BF01894077
Farshi B, Alinia-Ziazi A (2010) Sizing optimization of truss structures by method of centers and force formulation. Int J Solids Struct 47(18–19):2508–2524. https://doi.org/10.1016/j.ijsolstr.2010.05.009
Guest JK, Igusa T (2008) Structural optimization under uncertain loads and nodal locations. Comput Methods Appl Mech Eng 198(1):116–124. https://doi.org/10.1016/j.cma.2008.04.009
Han SP (1977) A globally convergent method for nonlinear programming. J Optim Theory Appl 22(3):297–309. https://doi.org/10.1007/BF00932858
Kang BS, Choi WS, Park GJ (2001) Structural optimization under equivalent static loads transformed from dynamic loads based on displacement. Comput Struct 79(2):145–154. https://doi.org/10.1016/S0045-7949(00)00127-9
Kanno Y, Takewaki I (2008) Semidefinite programming for uncertain linear equations in static analysis of structures. Comput Methods Appl Mech Eng 198(1):102–115. https://doi.org/10.1016/j.cma.2008.04.003
Kasperski M (1992) Extreme wind load distributions for linear and nonlinear design. Eng Struct 14(1):27–34. https://doi.org/10.1016/0141-0296(92)90005-B
Kasperski M, Niemann HJ (1992) The L.R.C. (load-response-correlation) - method a general method of estimating unfavourable wind load distributions for linear and non-linear structural behaviour. J Wind Eng Ind Aerodyn 43(1-3):1753–1763. https://doi.org/10.1016/0167-6105(92)90588-2
Katsumura A, Tamura Y, Nakamura O (2007) Universal wind load distribution simultaneously reproducing largest load effects in all subject members on large-span cantilevered roof. J Wind Eng Ind Aerodyn 95(9-11):1145–1165. https://doi.org/10.1016/j.jweia.2007.01.020
Keshavarzzadeh V, Meidani H, Tortorelli DA (2016) Gradient based design optimization under uncertainty via stochastic expansion methods. Comput Methods Appl Mech Eng 306:47–76. https://doi.org/10.1016/j.cma.2016.03.046
Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7-8):340–349. https://doi.org/10.1016/j.compstruc.2006.11.020
Mulvey JM, Vanderbei RJ, Zenios S (1995) Robust optimization of Large-Scale systems. Oper Res 43(2):264–281. https://doi.org/10.1287/opre.43.2.264
Chu Nha D, Xie Y, Hira A, Steven G (1996) Evolutionary structural optimization for problems with stiffness constraints. Finite Elem Anal Des 21(4):239–251. https://doi.org/10.1016/0168-874X(95)00043-S
Repetto MP, Solari G (2004) Equivalent static wind actions on vertical structures. J Wind Eng Ind Aerodyn 92(5):335–357. https://doi.org/10.1016/j.jweia.2004.01.002
Schuëller G I, Jensen HA (2008) Computational methods in optimization considering uncertainties - an overview. Comput Methods Appl Mech Eng 198(1):2–13. https://doi.org/10.1016/j.cma.2008.05.004
Spillers WR, MacBain KM (2009) Structural optimization. Springer US. https://doi.org/10.1007/978-0-387-95865-1
Sudret B, Kiureghian AD (2002) Comparison of finite element reliability methods. Probab Engrg Mech 17:337–348. https://doi.org/10.1016/S0266-8920(02)00031-0
Tamura Y, Fujii K, Ueda H (1992) Design wind loads for beams supporting flats roofs. J Wind Eng Ind Aerodyn 44:1841–1852. https://doi.org/10.1016/0167-6105(92)90601-6
Da Tortorelli, Michaleris P (1994) Design sensitivity analysis: Overview and review. Inverse Probl Sci Eng 1(1):71–105. https://doi.org/10.1080/174159794088027573
Waltz RA, Morales JL, Nocedal J, Orban D (2006) An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math Program 107(3):391–408. https://doi.org/10.1007/s10107-004-0560-5
Wang D, Zhang WH, Jiang JS (2002) Truss shape optimization with multiple displacement constraints. Comput Methods Appl Mech Eng 191(33):3597–3612. https://doi.org/10.1016/S0045-7825(02)00297-9
Yang R, Chuang C (1994) Optimal topology design using linear programming. Comput Struct 52(2):265–275. https://doi.org/10.1016/0045-7949(94)90279-8
Zhou Y, Kareem A (2001) Gust loading factor: New model. J Struct Eng ASCE 127(2):168–175. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:2(168)
Funding
The authors gratefully acknowledge the support provided by the Taiwan Ministry of Science and Technology (MOST 104-2218-E-032-004, 105-2221-E-032-006, 106-2221-E-032-018-MY2) and the visiting scholar program of the Academia Sinica.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: Hai Huang
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, CK., Tsai, CM., Chuang, BS. et al. Structural optimization with design constraints on peak responses to temporally correlated quasi-static load processes. Struct Multidisc Optim 59, 521–538 (2019). https://doi.org/10.1007/s00158-018-2082-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-018-2082-4