Optimum design of lead-rubber bearing system with uncertainty parameters

- Journal title : Structural Engineering and Mechanics
- Volume 56, Issue 6, 2015, pp.959-982
- Publisher : Techno-Press
- DOI : 10.12989/sem.2015.56.6.959

Title & Authors

Optimum design of lead-rubber bearing system with uncertainty parameters

Fan, Jian; Long, Xiaohong; Zhang, Yanping;

Fan, Jian; Long, Xiaohong; Zhang, Yanping;

Abstract

In this study, a non-stationary random earthquake Clough-Penzien model is used to describe earthquake ground motion. Using stochastic direct integration in combination with an equivalent linear method, a solution is established to describe the non-stationary response of lead-rubber bearing (LRB) system to a stochastic earthquake. Two parameters are used to develop an optimization method for bearing design: the post-yielding stiffness and the normalized yield strength of the isolation bearing. Using the minimization of the maximum energy response level of the upper structure subjected to an earthquake as an objective function, and with the constraints that the bearing failure probability is no more than 5% and the second shape factor of the bearing is less than 5, a calculation method for the two optimal design parameters is presented. In this optimization process, the radial basis function (RBF) response surface was applied, instead of the implicit objective function and constraints, and a sequential quadratic programming (SQP) algorithm was used to solve the optimization problems. By considering the uncertainties of the structural parameters and seismic ground motion input parameters for the optimization of the bearing design, convex set models (such as the interval model and ellipsoidal model) are used to describe the uncertainty parameters. Subsequently, the optimal bearing design parameters were expanded at their median values into first-order Taylor series expansions, and then, the Lagrange multipliers method was used to determine the upper and lower boundaries of the parameters. Moreover, using a calculation example, the impacts of site soil parameters, such as input peak ground acceleration, bearing diameter and rubber shore hardness on the optimization parameters, are investigated.

Keywords

seismic isolated structure;optimal design;lead-core rubber bearing (LRB);stochastic analysis;convex sets;

Language

English

Cited by

References

1.

Chaudhuri, A. and Chakraborty, S. (2004), "Sensitivity evaluation in seismic reliability analysis of structures", Comput. Meth. Appl. Mech. Eng., 93, 59-68.

2.

Baratta, A. and Corbi, L. (2004), "Optimal design of base-isolators in multi-storey buildings", Comput. Struct., 82, 2199-209.

3.

4.

Bucher, C. (2009), "Probability-based optimal design of friction-based seismic isolation devices", Struct. Saf., 31, 500-507.

5.

Clough, R.W. and Penzien, J. (1977), Dynamics of structures, McGraw-Hill Inc, New York, NY, USA.

6.

Constantinou, M.C. and Tadjbakhsh, I.G. (1984), "Optimum design of a base isolation system with frictional elements", Earthq. Eng. Struct. Dyn., 12, 203-14.

7.

Dicleli, M. and Karalar, M. (2011), "Optimum characteristic properties of isolators with bilinear force-displacement hysteresis for seismic protection of bridges built on various site soils", Soil Dyn. Earthq., 31, 982-995.

8.

Ellishakoff, I. (1995), "Essay on uncertainties in elastic and viscoelastic structures: from AM Freudenthal's criticisms to modern convex modeling", Comput. Struct., 56(6), 871 - 895.

9.

Fang, H. and Horstemeyer, M.F. (2006), "Global response approximation with radial basis functions", Eng. Optim., 38, 407-424.

10.

Gur, S. and Mishra, S.K. (2013), "Multi-objective stochastic-structural-optimization of shape-memory-alloy assisted pure-friction bearing for isolating building against random earthquakes", Soil Dyn. Earthq., 54, 1-16.

11.

Iemura, H., Taghikhany, T. and Jain, S.K. (2007), "Optimum design of resilient sliding isolation system for seismic protection of equipments", B. Earthq. Eng., 5, 85-103.

12.

Islam, A.B.M.S., Hussain, R.R., Jameel, M. and Jumaat, M.Z. (2012), "Non-linear time domain analysis of base isolated multi-storey building under site specific bi-directional seismic loading", Automat. Constr., 22, 554-566.

13.

Jangid, R.S. (2005), "Optimum friction pendulum system for near-fault motions", Eng. Struct., 27, 349-59.

14.

Jangid, R.S. (2007), "Optimum lead-rubber isolation bearings for near-fault motions", Eng. Struct., 29, 2503-13.

15.

Jangid, R.S. (2008), "Equivalent linear stochastic seismic response of isolated bridges", J. Sound Vib., 309, 805-22.

16.

Jennings, P.C. and Housener, G.W. (1968), "Simulated earthquake motions for design purpose", Proceedings of the 4th World Conference on Earthquake Engineering , Santiago, Chile.

17.

Jensen, H.A. (2005), "Design and sensitivity analysis of dynamical systems subjected to stochastic loading", Comput. Struct., 83, 1062-75.

18.

Marano, G.C., Greco, R. and Morrone, E. (2011), "Analytical evaluation of essential facilities fragility curves by using a stochastic approach", Eng. Struct., 33,191-201.

19.

McDonald, D.B., Grantham, W.J. and Tabor, W.L. (2007), "Global and local optimization using radial basis function response surface models", Appl. Math. Model., 31, 2095-2110

20.

Mishra, S.K. and Chakraborty, S. (2013), "Performance of a base-isolated building with system parameter uncertainty subjected to a stochastic earthquake", Int. J. Acoust. Vib., 18(1), 7-19.

21.

Mishra, S.K., Roy, B.K. and Chakraborty, S. (2013), "Reliability-based-design-optimization of base isolated buildings considering stochastic system parameters subjected to random earthquakes", Int. J. Mech. Sci., 75, 123-33.

22.

Ozbulut, O.E. and Hurlebaus, S. (2011), "Optimal design of superelastic-friction base isolators for seismic protection of highway bridges against near-field earthquakes", Earthq. Eng. Struct. Dyn., 40, 273-91.

23.

Park, J.G. and Otsuka, H. (1999), "Optimal yield level of bilinear seismic isolation devices", Earthq. Eng. Struct. Dyn., 28, 941-55.

24.

Pourzeynali, S. and Zarif, M. (2008), "Multi-objective optimization of seismically isolated high-rise building structures using genetic algorithms", J. Sound Vib., 311, 1141-60.

25.

Qiu, Z. and Wang, J. (2010), "The interval estimation of reliability for probabilistic and non-probabilistic hybrid structural system", Eng. Fail. Anal., 17(5), 1142-1154.

26.

Schueller, G.I. and Jensen, H.A. (2008), "Computational methods in optimization considering uncertainties-an overview", Comput. Meth. Appl. Mech. Eng., 198(1), 2-13.