As a new formulation in structural analysis, Integrated Force Method has been successfully applied to many structures for civil, mechanical, and aerospace engineering due to the accurate estimate of forces in computation. Right now, it is being further extended to the probabilistic domain. For the assessment of uncertainty effect in system optimization and identification, the probabilistic sensitivity analysis of IFM was further investigated in this study. A set of stochastic sensitivity analysis formulation of Integrated Force Method was developed using the perturbation method. Numerical examples are presented to illustrate its application. Its efficiency and accuracy were also substantiated with direct Monte Carlo simulations and the reliability-based sensitivity method. The numerical algorithm was shown to be readily adaptable to the existing program since the models of stochastic finite element and stochastic design sensitivity are almost identical. 1. Introduction As an alternative of the classical stiffness method, the force method [1–3] was also popular in structural analysis of civil, mechanical, and aerospace engineering because of its accurate estimates of forces in structural analysis. A new formulation in the force method, termed the Integrated Force Method [4–7] (IFM), was proposed by Patnaik for the analysis of discrete and continuous systems. IFM is a force method [8], which integrates both the system equilibrium equations and the global compatibility conditions together. This method has been successfully applied to many structures for their deterministic models with well-defined parameters. Realizing its potential in structural analysis, it is being further extended to consider investigations on the probabilistic analysis. Meanwhile, the probabilistic sensitivity formulation for IFM is also desirable to be investigated for assessing uncertainty effect in system optimization and identification. In general, sensitivity analysis of structural systems involves the computation of the partial derivatives of some response function with respect to the design parameters. The sensitivity analysis of structural systems to variations in their parameters is one of the ways to evaluate the performance of structures. It is very important for system optimization, parameter identification, reliability assessment, and so forth in engineering analysis. However, the conventional sensitivity analysis is based on the assumptions of complete determinacy of structural parameters. In reality, the occurrence of uncertainty associated with the system parameters is
References
[1]
A. Kaveh, “An efficient flexibility analysis of structures,” Computers & Structures, vol. 22, no. 6, pp. 973–977, 1986.
[2]
A. Kaveh, “Recent developments in the force method of structural analysis,” Applied Mechanics Reviews, vol. 45, no. 9, pp. 401–418, 1992.
[3]
A. Kaveh, Structural Mechanics: Graph and Matrix Methods, vol. 6 of Applied and Engineering Mathematics Series, Research Studies Press, Taunton, UK, 1st edition, 1992.
[4]
S. N. Patnaik and D. A. Hopkins, Strength of Materials: A Unified Theory for the 21st Century, Butterworth-Heinemann, 2004.
[5]
S. N. Patnaik and D. A. Hopkins, “Integrated force method solution to indeterminate structural mechanics problems,” NASA/TP 1999-207430, 1999.
[6]
S. N. Patnaik, D. A. Hopkins, and R. M. Coroneos, “Recent advances in the method of forces: integrated force method of structural analysis,” Advances in Engineering Software, vol. 29, no. 3–6, pp. 463–474, 1998.
[7]
S. N. Patnaik, L. Berke, and R. H. Gallagher, “Compatibility conditions of structural mechanics for finite element analysis,” AIAA Journal, vol. 29, no. 5, pp. 820–829, 1991.
[8]
S. N. Patnaik, L. Berke, and R. H. Gallagher, “Integrated force method versus displacement method for finite element analysis,” Computers & Structures, vol. 38, no. 4, pp. 377–407, 1991.
[9]
M. Kleiber, H. Antunz, T. D. Hien, and P. Kowalczyk, Parameter Sensitivity in Nonlinear Mechanics, John Wiley & Sons, New York, NY, USA, 1997.
[10]
T. D. Hien and M. Kleiber, “Stochastic structural design sensitivity of static response,” Computers & Structures, vol. 38, no. 5-6, pp. 659–667, 1991.
[11]
P. Kolakowski and J. Holnicki-Szulc, “Sensitivity analysis of truss structures (virtual distortion method approach),” International Journal for Numerical Methods in Engineering, vol. 43, no. 6, pp. 1085–1108, 1998.
[12]
T. D. Hien and M. Kleiber, “Stochastic design sensitivity in structural dynamics,” International Journal for Numerical Methods in Engineering, vol. 32, no. 6, pp. 1247–1265, 1991.
[13]
R. Ghosh, S. Chakraborty, and B. Bhattacharyya, “Stochastic sensitivity analysis of structures using first-order perturbation,” Meccanica, vol. 36, no. 3, pp. 291–296, 2001.
[14]
X. F. Wei, S. N. Patnaik, S. S. Pai, and P. P. Ling, “Extension of integrated force method into stochastic domain,” International Journal of Computational Methods in Engineering Science and Mechanics, vol. 10, no. 3, pp. 197–208, 2009.
[15]
F. Yamazaki, M. Shinozuka, and G. Dasgupta, “Neumann expansion for stochastic finite element analysis,” Journal of Engineering Mechanics, vol. 114, no. 8, pp. 1335–1354, 1988.
[16]
W. K. Liu, T. Belytschko, and A. Mani, “Computational method for the determination of the probabilistic distribution of the dynamic response of structures,” in Proceedings of the Pressure Vessels and Piping Conference. Piping, Feedwater Heater Operation, and Pumps (ASME PVP '85), vol. 98, no. 5, pp. 243–248, New Orleans, La, USA, 1985.
