Abstract
In this paper, by using a combination of finite element analysis and a hybrid random convex model, a new numerical algorithm named hybrid perturbation Lagrange method (HPLM) is presented to address an uncertain static response problem of structures with a mixture of random and convex variables. The random variables are used to treat the uncertain parameters with sufficient statistical information, whereas the convex variables are used to describe the uncertain parameters with limited information. The expectation and variance of the random convex responses can be calculated effectively based on the matrix perturbation theory. Then, the interval bounds of these probabilistic characters of the structural responses can be obtained by means of the first-order Taylor series and the Lagrange multiplier method. Numerical results illustrate the feasibility and effectiveness of the proposed method to solve the static response problem of structures with hybrid or pure uncertain parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Moens, D., Vandepitte, D.: A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput. Methods Appl. Mech. Eng. 194, 1527–1555 (2005)
Feng, Y.T., Li, C.F., Owen, D.R.J.: A direct Monte Carlo solution of linear stochastic algebraic system of equations. Finite Elem. Anal. Des. 46, 462–473 (2010)
Kamiński, M., Lauke, B.: Uncertainty in effective elastic properties of particle filled polymers by the Monte Carlo simulation. Compos. Struct. 123, 374–382 (2015)
Kamiński, M.M.: A generalized stochastic perturbation technique for plasticity problems. Comput. Mech. 45, 349–361 (2010)
Wang, X.Y., Cen, S., Li, C.F., Owen, D.R.J.: A priori estimation for the stochastic perturbation method. Comput. Methods Appl. Mech. Eng. 286, 1–21 (2015)
Ngah, M.F., Young, A.: Application of the spectral stochastic finite element method for performance prediction of composite structures. Compos. Struct. 78, 447–456 (2007)
Chen, N.Z., Soares, C.G.: Spectral stochastic finite element analysis for laminated composite plates. Comput. Methods Appl. Mech. Eng. 197, 4830–4839 (2008)
Verhoosel, C.V., Gutierrez, M.A., Hulshoff, S.J.: Iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems. Int. J. Numer. Methods Eng. 68, 401–424 (2006)
Gao, W., Zhang, N., Ji, J.C.: A new method for random vibration analysis of stochastic truss structures. Finite Elem. Anal. Des. 45, 190–199 (2009)
Deng, Z.M., Guo, Z.P., Zhang, X.J.: Interval model updating using perturbation method and radial basis function neural networks. Mech. Syst. Signal Process. 84, 699–716 (2017)
Sofi, A., Muscolino, G., Elishakoff, I.: Static response bounds of Timoshenko beams with spatially varying interval uncertainties. Acta Mech. 226, 3737–3748 (2015)
Ben-Haim, Y., Elishakoff, I.: Convex Models of Uncertainties in Applied Mechanics. Elsevier, Amsterdam (1990)
Ben-Haim, Y.: Convex models of uncertainty in radial pulse buckling of shells. J. Appl. Mech. 60, 683–688 (1993)
Elishakoff, I., Elisseeff, P.: Non-probabilistic convex-theoretic modeling of scatter in material properties. AIAA J. 32, 843–849 (1994)
Jiang, C., Han, X., Lu, G.Y., et al.: Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Comput. Methods Appl. Mech. Eng. 200, 2528–2546 (2011)
Wang, X.J., Elishakoff, I.I., Qiu, Z.P.: Experimental data have to decide which of the non-probabilistic uncertainty description-convex modeling or interval analysis-to utilize. J. Appl. Mech. 75, 041018–041025 (2008)
Xia, B., Dejie, Y.: Response analysis of acoustic field with convex parameters. J. Vib. Acoust. 136, 041017 (2014)
Deng, Z.M., Guo, Z.P., Zhang, X.D.: Non-probabilistic set-theoretic models for transient heat conduction of thermal protection systems with uncertain parameters. Appl. Thermal Eng. 95, 10–17 (2016)
Wang, L., Wang, X.J., Xia, Y.: Hybrid reliability analysis of structures with multi-source uncertainty. Acta Mech. 225, 413–430 (2014)
Gao, W., Song, C.M., Tin-Loi, F.: Probabilistic interval analysis for structures with uncertainty. Struct. Saf. 32, 191–199 (2010)
Gao, W., Wu, D., Song, C.M., Tin-Loi, F., Li, X.J.: Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method. Finite Elem. Anal. Des. 47, 643–652 (2011)
Xia, B.Z., Yu, D.J., Liu, J.: Hybrid uncertain analysis for structural-acoustic problem with random and interval parameters. J. Sound Vib. 332, 2701–2720 (2013)
Wang, C., Qiu, Z.P.: Hybrid uncertain analysis for steady-state heat conduction with random and interval parameters. Int. J. Heat Mass Transf. 80, 319–328 (2015)
Penmetsa, R.C., Grandhi, R.V.: Efficient estimation of structural reliability for problems with uncertain intervals. Comput. Struct. 80, 1103–1112 (2002)
Adduri, P.R., Penmetsa, R.C.: Systems reliability analysis for mixed uncertain variables. Struct. Saf. 227, 1441–1453 (2009)
Karanki, D.R., Kushwaha, H.S., Verma, K.A., Ajit, S.: Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment. Risk Anal. 29, 662–675 (2009)
Xiaoping, D., Sudjianto, A., Huang, B.: Reliability-based design with the mixture of random and interval variables. J. Mech. Des. 127, 1068–1076 (2005)
Luo, Y., Kang, Z., Li, A.: Structural reliability assessment based on probability and convex set mixed model. Comput. Struct. 87, 1408–1415 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guo, Z., Deng, Z., Li, X. et al. Hybrid uncertainty analysis for a static response problem of structures with random and convex parameters. Acta Mech 228, 2987–3001 (2017). https://doi.org/10.1007/s00707-017-1869-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-017-1869-5