Probabilistic stability of uncertain composite plates and stochastic irregularity in their buckling mode shapes: A semi-analytical non-intrusive approach

Abstract

In this study, the mechanical properties of the composite plate were considered Gaussian random fields and their effects on the buckling load and corresponding mode shapes were studied by developing a semi-analytical non-intrusive approach. The random fields were decomposed by the Karhunen−Loève method. The strains were defined based on the assumptions of the first-order and higher-order shear-deformation theories. Stochastic equations of motion were extracted using Euler–Lagrange equations. The probabilistic response space was obtained by employing the non-intrusive polynomial chaos method. Finally, the effect of spatially varying stochastic properties on the critical load of the plate and the irregularity of buckling mode shapes and their sequences were studied for the first time. Our findings showed that different shear deformation plate theories could significantly influence the reliability of thicker plates under compressive loading. It is suggested that a linear relationship exists between the mechanical properties’ variation coefficient and critical loads’ variation coefficient. Also, in modeling the plate properties as random fields, a significant stochastic irregularity is obtained in buckling mode shapes, which is crucial in practical applications.

Graphical abstract

Keywords

uncertain composite plate / stochastic assume mode method / Karhunen−Loève theorem / polynomial chaos approach / plate buckling / irregularity in buckling mode shapes

References

[1] Al-Jumaili S K, Eaton M J, Holford K M, Pearson M R, Crivelli D, Pullin R. Characterisation of fatigue damage in composites using an acoustic emission parameter correction technique. Composites. Part B, Engineering, 2018, 151: 237–244

[2] Maleki S, Rafiee R, Hasannia A, Habibagahi M R. Investigating the influence of delamination on the stiffness of composite pipes under compressive transverse loading using cohesive zone method. Frontiers of Structural and Civil Engineering, 2019, 13(6): 1316–1323

[3] Rajak D K, Pagar D D, Menezes P L, Linul E. Fiber-reinforced polymer composites: Manufacturing, properties, and applications. Polymers, 2019, 11(10): 1667

[4] Sakata S, Okuda K, Ikeda K. Stochastic analysis of laminated composite plate considering stochastic homogenization problem. Frontiers of Structural and Civil Engineering, 2015, 9(2): 141–153

[5] Nikbakht S, Kamarian S, Shakeri M. A review on optimization of composite structures Part II: Functionally graded materials. Composite Structures, 2019, 214: 83–102

[6] SchenkC ASchuëllerG I. Uncertainty assessment of large finite element systems. Lecture Notes in Applied and Computational Mechanics. Vol. 24 Series. New York: Springer Berlin Heidelberg, 2005

[7] FishmanG. Monte Carlo: Concepts, Algorithms, and Applications. Springer Series in Operations Research and Financial Engineering. New York: Springer Science & Business Media, 2013

[8] NayfehA H. Perturbation Methods. New York: John Wiley & Sons, 2008

[9] Chow P L. Perturbation methods in stochastic wave propagation. SIAM Review, 1975, 17(1): 57–81

[10] HosderSWaltersRPerezR. A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations. In: 44th AIAA aerospace sciences meeting and exhibit. Nevada: American Institute of Aeronautics and Astronautics, 2006

[11] GelfandA EDeyD KChangH. Model Determination Using Predictive Distributions with Implementation via Sampling-Based Methods. Technical Report 462. Department of Statistics, Stanford University. 1992

[12] Gelfand A E. Model Determination Using Sampling-Based Methods. Markov Chain Monte Carlo in Practice, Chapter 9. London: Chapman & Hall, 1996, 145–161

[13] Sepahvand K, Marburg S, Hardtke H J. Uncertainty quantification in stochastic systems using polynomial chaos expansion. International Journal of Applied Mechanics, 2010, 2(2): 305–353

[14] Bisagni C. Numerical analysis and experimental correlation of composite shell buckling and post-buckling. Composites. Part B, Engineering, 2000, 31(8): 655–667

[15] Telford R, Peeters D, Rouhi M, Weaver P M. Experimental and numerical study of bending-induced buckling of stiffened composite plate assemblies. Composites. Part B, Engineering, 2022, 233: 109642

[16] Rozylo P, Teter A, Debski H, Wysmulski P, Falkowicz K. Experimental and numerical study of the buckling of composite profiles with open cross section under axial compression. Applied Composite Materials, 2017, 24(5): 1251–1264

[17] Zhang Y, Tao W, Chen Y, Lei Z, Bai R, Lei Z. Experiment and numerical simulation for the compressive buckling behavior of double-sided laser-welded Al–Li alloy aircraft fuselage panel. Materials (Basel), 2020, 13(16): 3599

[18] Ly H B, Desceliers C, Minh Le L, Le T T, Thai Pham B, Nguyen-Ngoc L, Doan V T, Le M. Quantification of uncertainties on the critical buckling load of columns under axial compression with uncertain random materials. Materials (Basel), 2019, 12(11): 1828

[19] Sharma N, Nishad M, Maiti D K, Sunny M R, Singh B N. Uncertainty quantification in buckling strength of variable stiffness laminated composite plate under thermal loading. Composite Structures, 2021, 275: 114486

[20] Kharghani N, Soares C. Effect of uncertainty in the geometry and material properties on the post-buckling behavior of a composite laminate. Maritime Technology and Engineering, 2016, 3: 497–503

[21] Nguyen H X, Duy Hien T, Lee J, Nguyen-Xuan H. Stochastic buckling behaviour of laminated composite structures with uncertain material properties. Aerospace Science and Technology, 2017, 66: 274–283

[22] Hu L, Feng P, Meng Y, Yang J. Buckling behavior analysis of prestressed CFRP-reinforced steel columns via FEM and ANN. Engineering Structures, 2021, 245: 112853

[23] 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, 2016, 25(2): 43–48

[24] 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, 2015, 125: 212–227

[25] Dey S, Mukhopadhyay T, Sahu S, Li G, Rabitz H, Adhikari S. Thermal uncertainty quantification in frequency responses of laminated composite plates. Composites. Part B, Engineering, 2015, 80: 186–197

[26] Chandrashekhar M, Ganguli R. Damage assessment of composite plate structures with material and measurement uncertainty. Mechanical Systems and Signal Processing, 2016, 75: 75–93

[27] Swain P R, Dash P, Singh B N. Stochastic nonlinear bending analysis of piezoelectric laminated composite plates with uncertainty in material properties. Mechanics Based Design of Structures and Machines, 2021, 49(2): 194–216

[28] Singh B N, Iyengar N, Yadav D. Effects of random material properties on buckling of composite plates. Journal of Engineering Mechanics, 2001, 127(9): 873–879

[29] Kalfountzos C D, Bikakis G S, Theotokoglou E E. Deterministic and probabilistic buckling response of fiber–metal laminate panels under uniaxial compression. Aircraft Engineering and Aerospace Technology, 2022, 94(5): 745–759

[30] Zhuang X, Guo H, Alajlan N, Zhu H, Rabczuk T. Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning. European Journal of Mechanics. A, Solids, 2021, 87: 104225

[31] Guo H, Zhuang X, Rabczuk T. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–456

[32] Guo H, Zheng H, Zhuang X. Numerical manifold method for vibration analysis of Kirchhoff’s plates of arbitrary geometry. Applied Mathematical Modelling, 2019, 66: 695–727

[33] Guo H, Zheng H. The linear analysis of thin shell problems using the numerical manifold method. Thin-walled Structures, 2018, 124: 366–383

[34] Vu-Bac N, Duong T X, Lahmer T, Zhuang X, Sauer R A, Park H S, Rabczuk T. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics and Engineering, 2018, 331: 427–455

[35] Vu-Bac N, Duong T, Lahmer T, Areias P, Sauer R A, Park H S, Rabczuk T. A NURBS-based inverse analysis of thermal expansion induced morphing of thin shells. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 480–510

[36] Vu-Bac N, Rabczuk T, Park H, Fu X, Zhuang X. A NURBS-based inverse analysis of swelling induced morphing of thin stimuli-responsive polymer gels. Computer Methods in Applied Mechanics and Engineering, 2022, 397: 115049

[37] Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014, 68: 70–84

[38] Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014, 59: 80–95

[39] Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535

[40] AdhikariS. Free vibration analysis of angle-ply composite plates with uncertain properties. In: 17th AIAA Non-Deterministic Approaches Conference. Florida: American Institute of Aeronautics and Astronautics, 2015

[41] Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464

[42] Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

[43] Vu-Bac N, Zhuang X, Rabczuk T. Uncertainty quantification for mechanical properties of polyethylene based on fully atomistic model. Materials (Basel), 2019, 12(21): 3613

[44] Liu B, Vu-Bac N, Zhuang X, Rabczuk T. Stochastic multiscale modeling of heat conductivity of Polymeric clay nanocomposites. Mechanics of Materials, 2020, 142: 103280

[45] Liu B, Vu-Bac N, Zhuang X, Fu X, Rabczuk T. Stochastic full-range multiscale modeling of thermal conductivity of Polymeric carbon nanotubes composites: A machine learning approach. Composite Structures, 2022, 289: 115393

[46] Liu B, Vu-Bac N, Rabczuk T. A stochastic multiscale method for the prediction of the thermal conductivity of Polymer nanocomposites through hybrid machine learning algorithms. Composite Structures, 2021, 273: 114269

[47] Fakoor M, Parviz H. Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach. Frontiers of Structural and Civil Engineering, 2020, 14(6): 1359–1371

[48] Fakoor M, Parviz H, Abbasi A. Uncertainty propagation analysis in free vibration of uncertain composite plate using stochastic finite element method. Amirkabir Journal of Mechanical Engineering, 2019, 52(12): 3503–3520

[49] Sriramula S, Chryssanthopoulos M K. An experimental characterisation of spatial variability in GFRP composite panels. Structural Safety, 2013, 42: 1–11

[50] Ghanem R G, Spanos P D. Stochastic finite element method: Response statistics. In: Stochastic Finite Elements: A Spectral Approach. New York: Springer, 1991, 101–119

[51] Fish J, Wu W. A nonintrusive stochastic multiscale solver. International Journal for Numerical Methods in Engineering, 2011, 88(9): 862–879

[52] ReddyJ N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. 2nd ed. New York: CRC Press, 2003

[53] Kim S E, Thai H T, Lee J. A two variable refined plate theory for laminated composite plates. Composite Structures, 2009, 89(2): 197–205

[54] Tran L V, Thai C H, Le H T, Gan B S, Lee J, Nguyen-Xuan H. Isogeometric analysis of laminated composite plates based on a four-variable refined plate theory. Engineering Analysis with Boundary Elements, 2014, 47: 68–81

RIGHTS & PERMISSIONS

The Author(s). This article is published with open access at link.springer.com and journal.hep.com.cn