Reliability analysis based on polynomial chaos expansion method in composite structures

Noorian, Mohammad; Ravandi, Mohammad

doi:10.22068/jstc.2019.107476.1546

Document Type : Research Paper

Authors

Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran.

10.22068/jstc.2019.107476.1546

Abstract

Reliability analysis of composite structures has gained increased attention due to the growing use of composite materials in many industries such as aerospace, automotive and construction in recent decades. Uncertainty analysis approaches are effective tools in order to probabilistically assess the behavior and evaluate the reliability of composite structures with variabilities in material properties. In this study, a computationally efficient surrogate model based on the polynomial chaos expansion for reliability analysis of composite structures with a large number of uncertain parameters is presented. The uncertain input parameters including composite material properties, geometry and loads, are assumed as random variables with a normal distribution and are taken into account for reliability evaluation. A sparse grid collocation strategy is used to determine the sample points for constructing the surrogate model relating the uncertain variables to the structural response. In the end, a numerical example is performed to demonstrate the accuracy and efficiency of this methodology for a higher number of uncertain variables by comparing the results with the direct Monte Carlo simulation method.

Keywords

Main Subjects

Stochastic modeling

References

[1] Saeedifar, M. Najafabadi, MA. Toudeshky, HH. Mohammadi, R., "Investigation of Initiation and Evolution of Delamination in Glass/ Epoxy Laminated Composites Using Acoustic Emission Method," In Persian, AmirKabir Jounrnal of Science & Research Mechanical Engineering, Vol. 48, No. 4, pp. 153-156, 2017.

[2]Dey, S. Mukhopadhyay, T. Adhikari, S., "Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment," Composite Structures, Vol. 171, pp. 227–250, 2017.

[3]Baran, I. Cinar, K. Ersoy, N. Akkerman, R. Hattel, JH., "A Review on the Mechanical Modeling of Composite Manufacturing Processes," Archives of Computational Methods in Engineering, Vol. 24, pp. 365–395,2017.

[4] Fisher, J. Bhattacharya, R., "Linear quadratic regulation of systems with stochastic parameter uncertainties," Automatica Vol. 45, pp. 2831–2841, 2017.

[5]Chen, X. Qiu, Z., "A novel uncertainty analysis method for composite structures with mixed uncertainties including random and interval variables," Composite Structures Vol. 184, pp. 400–410, 2018.

[6]Thapa, M. Mulani, SB. Walters, RW., "Stochastic multi-scale modeling of carbon fiber reinforced composites with polynomial chaos," Composite Structures,

[7]Peng, X. Li, D. Wu, H. Liu, Z. Li, J. Jiang, S. et al., "Uncertainty analysis of composite laminated plate with data-driven polynomial chaos expansion method under insufficient input data of uncertain parameters," Composite Structures, Vol. 209, pp. 625–633, 2019.

[8]Sasikumar, P. Venketeswaran, A. Suresh, R. Gupta, S., "A data driven polynomial chaos based approach for stochastic analysis of CFRP laminated composite plates," Composite Structures, Vol. 125, pp. 212–227, 2015.

[9]Balokas, G. Czichon, S. Rolfes, R., "Neural network assisted multiscale analysis for the elastic properties prediction of 3D braided composites under uncertainty," Composite Structures, Vol. 183, pp. 550–562, 2018.

[10]Naskar, S. Mukhopadhyay, T. Sriramula, S., "Probabilistic micromechanical spatial variability quantification in laminated composites," Composites Part B: Engineering, Vol. 151, pp. 291–325, 2018.

[11]Ghasemi, H. Rafiee, R. Zhuang, X. Muthu, J. Rabczuk, T., "Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling," Computational Materials Science, Vol. 85, pp. 295–305, 2014.

[12]Whiteside MB., "Stochastic Analysis of Composite Materials. Doctoral dissertation," Imperial College of Science,Technology and Medicine, 2012.

[13]Marburg, S. Hardtke, H-J., "Uncertainty quantification in stochastic systems using polynomial chaos expansion," International Journal of Applied Mechanics, Vol. 02, pp. 305–353, 2010.

[14]Choi, S-K. Grandhi, RV. Canfield, RA., "Structural reliability under non-Gaussian stochastic behavior," Computers & Structures, Vol. 82, pp. 1113–1121, 2004.

[15]Choi, S-K. Grandhi, RV. Canfield, RA. Pettit, CL., "Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability," AIAA Journal, Vol. 42, pp. 1191–1198, 2004.

[16] Xiu, D. Hesthaven, JS., "High-Order Collocation Methods for Differential Equations with Random Inputs," SIAM Journal on Scientific Computing, Vol. 27, pp. 1118–1139, 2005.

[17]Xiu, D. Karniadakis, GE., "Modeling uncertainty in flow simulations via generalized polynomial chaos," Journal of Computational Physics, Vol. 187, pp. 137–167, 2003.

[18]Nobile, F. Tempone, R. Webster, CG., "A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data," SIAM Journal on Numerical Analysis, Vol. 46, pp. 2309–2345, 2008.

[19]Burkardt, J., "Slow Exponential Growth for Clenshaw Curtis Sparse Grids," 2014.

[20]Bhaduri, A. Graham-Brady, L., "An efficient adaptive sparse grid collocation method through derivative estimation. Probabilistic Engineering Mechanics," Vol. 51, pp. 11–22, 2018.

[21]Dey, S. Mukhopadhyay, T. Spickenheuer, A. Gohs, U. Adhikari, S., "Uncertainty Quantification in Natural Frequency of Composite Plates - An Artificial Neural Network Based Approach," Advanced Composites Letters, Vol. 25, pp. 43-48, 2016.

[22]Reddy, JN., "Mechanics of laminated composite plates and shells: theory and analysis," 2nd ed. USA, CRC Press, 2004.

[23]Ghannadpour, AM. Kurkaani Barvaj, A., "Ultimate strength analysis of imperfect composite plates under both in-plane compressive load and lateral pressure using Ritz method," In Persian, Journal of Science and Technology of Composites, Vol. 5, pp. 1-10, 2018.

[24]Ghannadpour, A. Barekati, M., "Post-buckling analysis of anti-symmetric cross-ply composite plates under end-shortening," In Persian, Journal of Science and Technology of Composites, Vol. 2, pp. 35-42, 2018.

[25]Jeong, HK. Shenoi, RA., "Reliability analysis of mid-plane symmetric laminated plates using direct simulation method," Composite Structures, Vol. 43, pp. 1-13, 1998.;43:1–13.

Reliability analysis based on polynomial chaos expansion method in composite structures

References

Volume 6, Issue 4March 2020Pages 627-636

Volume 6, Issue 4
March 2020
Pages 627-636