Abstract
In this work, a reliability-based optimization technique is addressed to obtain the minimum mean value of random mass of the structures with random parameters under stationary stochastic process excitation. The challenge of the problem lies in randomness involved from both structural parameters and dynamic load, which renders the structural reliability becoming the random dynamic reliability of the first passage problem. In order to obtain minimum mean value of random gross mass, element and system dynamic reliability constraints are constructed, respectively, and the structural sizing and shape optimization models based on the dynamic reliability are then presented. Moreover, among two optimal strategies proposed for optimization models, the second one can effectively reduce the workload by avoiding the computation of the variance of the dynamic response during the iterative process. Finally, the implementation of three examples is discussed to display the feasibility and validity of optimization technique given.
Similar content being viewed by others
References
Schueller GI, Jensen HA (2008) Computational methods in optimization considering uncertainties—an overview. Comput Methods Appl Mech Eng 198(1): 2–13
Wang D (2007) Optimal shape design of a frame structure for minimization of maximum bending moment. Eng Struct 29(8): 1824–1832
Bruggi M (2009) Generating strut-and-tie patterns for reinforced concrete structures using topology optimization. Comput Struct 87(23–24): 1483–1495
Canelas A, Herskovits J, Telles JCF (2008) Shape optimization using the boundary element method and a SAND interior point algorithm for constrained optimization. Comput Struct 86(13–14): 1517–1526
Park GJ, Lee T-H, Lee KH, Hwang K-H (2006) Robust design: an overview. AIAA J 44(1): 181–191
Beyer HG, Sendhoff B (2007) Robust optimization—a comprehensive survey. Comput Methods Appl Mech Eng 196(33–34): 3190–3218
Frangopol DM, Maute K (2003) Life-cycle reliability-based optimization of civil and aerospace structures. Comput Struct 81(7): 397–410
Missoum S, Ramu P, Haftka RT (2007) A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems. Comput Methods Appl Mech Eng 196(29–30): 2895–2906
Guo X, Bai W, Zhang WS, Gao XX (2009) Confidence structural robust design and optimization under stiffness and load uncertainties. Comput Methods Appl Mech Eng 198: 3378–3399
Kaymaz I, Marti K (2007) Reliability-based design optimization for elastoplastic mechanical structures. Comput Struct 85: 15–625
Valdebenito MA, Schuëller GI (2010) Reliability-based optimization considering design variables of discrete size. Eng Struct 32: 2919–2930
Schmit LA (1960) Structural design by systematic synthesis. In: Proceedings of the second conference on electronic computation. ASCE, New York, pp 105–122
Barakat S, Bani-Hani K, Taha MQ (2004) Multi-objective reliability-based optimization of prestressed concrete beams. Struct Saf 26(3): 311–342
Kang Z, Luo YJ (2009) Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Comput Methods Appl Mech Eng 198: 3228–3238
Mogami K, Nishiwake SJ, Izui K (2006) Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques. Struct Multidiscip Optim 32: 299–311
Wu H, Yan Y, Liu YJ (2008) Reliability based optimization of composite laminates for frequency constraint. Chin J Aeronaut 21(4): 320–327
Lagaros ND, Garavelas ATh, Papadrakakis M (2008) Innovative seismic design optimization with reliability constraints. Comput Methods Appl Mech Eng 198: 28–41
Rao SS (1981) Reliability-based optimization under random vibration environment. Comput Struct 14(5–6): 345–355
Jensen HA, Valdebenito MA, Schuëller GI (2008) An efficient reliability-based optimization scheme for uncertain linear systems subject to general Gaussian excitation. Comput Methods Appl Mech Eng 198: 72–87
Chakraborty S, Roy BK (2010) Reliability based optimum design of Tuned Mass Damper in seismic vibration control of structures with bounded uncertain parameters. Probab Eng Mech (in press)
Ghanem R, Spanos PD (1991) Stochastic finite element: a spectral approach. Springer, Berlin
Kleiber M, Hien TD (1992) The stochastic finite element method, basic perturbation technique and computer implementation. Wiley, Chichester
Matthies HG, Brenner CE, Bucher CG, Guedes SC (1997) Uncertainties in probabilistic numerical analysis of structures and solids—stochastic finite elements. Struct Saf 19: 283–336
Phoon KK, Huang SP, Quek ST (2002) Simulation of second-order processes using Karhunen–Loeve expansion. Comput Struct 80: 1049–1060
Vanmarcke E (1984) Random fields, analysis and synthesis. The MIT Press, Massachusetts Institute of Technology, Cambridge, MA
Lin KY, Frangopol DM (1996) Reliability-based optimum design of reinforced concrete girders. Struct Saf 18(2/3): 239–258
Frangopol DM, Moses F (1994) Reliability-based structural optimization. In: Adeli H (ed) Chapter 13 in advances in design optimization. Chapman & Hall, London, pp 492–570
Allen M, Maute K (2002) Reliability based optimization of aeroelastic structures. In: AIAA 2002-5560, proceedings of the 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, USA, September 4–6, 2002
Murotsu Y, Shao S (1990) Optimum shape design of truss structures based on reliability. Struct Optim 2(2): 65–76
Murotsu Y, Shao S, Kogiso N, Tomioka H (1997) Optimal shape of truss structure based on reliability. In: ASCE advances in structural optimization, pp 145–156
Marti K, Stockl G (1999) Optimal topology design under stochastic uncertainty. Safety and reliability, vol 2. Balkema, Amsterdam, pp 1597–1602
Stoeckl G (2001) Topology optimization of trusses under stochastic uncertainty. J Appl Math Mech ZAMM 81: 697–800
Bae K, Wang S, Choi KK (2002) Reliability-based topology optimization. In: AIAA 2002-5542, proceedings of the 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, USA, September 4–6, 2002
Thoft-Christensen P, Murotsu Y (1986) Applications of structural systems reliability theory. Springer, Berlin
Ma J, Gao W, Wriggers P, Wu T, Sahraee S (2010) The analyses of dynamic response and reliability of fuzzy-random truss under stationary stochastic excitation. Comput Mech 45: 443–455
Gao W, Chen JJ, Ma J, Liang ZT (2004) Dynamic response analysis of stochastic frame structures under non-stationary random excitation. AIAA J 42: 1818–1822
Chen JJ, Duan BY, Zen YG (1997) Study on dynamic reliability analysis of the structures with multidegree-of-freedom system. Comput Struct 62(5): 877–881
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ma, J., Wriggers, P., Gao, W. et al. Reliability-based optimization of trusses with random parameters under dynamic loads. Comput Mech 47, 627–640 (2011). https://doi.org/10.1007/s00466-010-0561-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-010-0561-6