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

doi:10.1007/s11709-022-0888-z

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (2) : 179-190 https://doi.org/10.1007/s11709-022-0888-z

RESEARCH ARTICLE

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

Arash Tavakoli MALEKI¹, Hadi PARVIZ², Akbar A. KHATIBI³(

), Mahnaz ZAKERI¹(

)

¹. Advanced Structures Research Laboratory, K. N. Toosi University of Technology, Tehran 16569-83911, Iran
². Faculty of New Sciences and Technologies, University of Tehran, Tehran 16569-83911, Iran
³. School of Engineering, RMIT University, Melbourne VIC 3001, Australia

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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.

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

Corresponding Author(s): Akbar A. KHATIBI,Mahnaz ZAKERI

Just Accepted Date: 07 December 2022 Online First Date: 13 February 2023 Issue Date: 03 April 2023

Cite this article:

Arash Tavakoli MALEKI,Hadi PARVIZ,Akbar A. KHATIBI, et al. Probabilistic stability of uncertain composite plates and stochastic irregularity in their buckling mode shapes: A semi-analytical non-intrusive approach[J]. Front. Struct. Civ. Eng., 2023, 17(2): 179-190.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0888-z
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I2/179

Fig.1 Schematic of the composite plate with simply supported boundary conditions under: (a) uniaxial; (b) biaxial loading; and clamped boundary conditions subjected to: (c) uniaxial; (d) biaxial loading.

property	quantity
$E 11 / E 22$	40
$G 12 / E 22 = G 13 / E 22$	0.6
$G 23 / E 22$	0.5
$υ 12$	0.25

Tab.1 Material properties of composite lamina [53]

Tab.2 The normalized buckling load comparison

Fig.2 Comparison of buckling load variation coefficient obtained from our study with previous studies of plates with random properties.

Fig.3 PDF corresponding to the normalized buckling load of square plates for symmetric (a) uniaxial loading and (b) biaxial loading; for antisymmetric (c) uniaxial loading and (d) biaxial loading.

Fig.4 Uncertainty propagation in normalized buckling load: (a) uniaxial loading; (b) biaxial loading.

Fig.5 Variation coefficient of critical buckling load for plates with different boundary conditions: (a) simply supported; (b) clamped.

Tab.3 Deterministic and four stochastic samples of the three first buckling mode shapes.

Fig.6 Probability density function (PDF) for three critical buckling values in the symmetric plate with (a) simply supported and (b) clamped boundary conditions.

1	S K Al-Jumaili, M J Eaton, K M Holford, M R Pearson, D Crivelli, R Pullin. Characterisation of fatigue damage in composites using an acoustic emission parameter correction technique. Composites. Part B, Engineering, 2018, 151: 237–244 https://doi.org/10.1016/j.compositesb.2018.06.020
2	S Maleki, R Rafiee, A Hasannia, M R Habibagahi. 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 https://doi.org/10.1007/s11709-019-0555-1
3	D K Rajak, D D Pagar, P L Menezes, E Linul. Fiber-reinforced polymer composites: Manufacturing, properties, and applications. Polymers, 2019, 11(10): 1667 https://doi.org/10.3390/polym11101667
4	S Sakata, K Okuda, K Ikeda. Stochastic analysis of laminated composite plate considering stochastic homogenization problem. Frontiers of Structural and Civil Engineering, 2015, 9(2): 141–153 https://doi.org/10.1007/s11709-014-0286-2
5	S Nikbakht, S Kamarian, M Shakeri. A review on optimization of composite structures Part II: Functionally graded materials. Composite Structures, 2019, 214: 83–102 https://doi.org/10.1016/j.compstruct.2019.01.105
6	C A SchenkG I Schuëller. Uncertainty assessment of large finite element systems. Lecture Notes in Applied and Computational Mechanics. Vol. 24 Series. New York: Springer Berlin Heidelberg, 2005
7	G Fishman. Monte Carlo: Concepts, Algorithms, and Applications. Springer Series in Operations Research and Financial Engineering. New York: Springer Science & Business Media, 2013
8	A H Nayfeh. Perturbation Methods. New York: John Wiley & Sons, 2008
9	P L Chow. Perturbation methods in stochastic wave propagation. SIAM Review, 1975, 17(1): 57–81 https://doi.org/10.1137/1017004
10	S HosderR WaltersR Perez. 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	A E GelfandD K DeyH Chang. Model Determination Using Predictive Distributions with Implementation via Sampling-Based Methods. Technical Report 462. Department of Statistics, Stanford University. 1992
12	A E Gelfand. Model Determination Using Sampling-Based Methods. Markov Chain Monte Carlo in Practice, Chapter 9. London: Chapman & Hall, 1996, 145–161
13	K Sepahvand, S Marburg, H J Hardtke. Uncertainty quantification in stochastic systems using polynomial chaos expansion. International Journal of Applied Mechanics, 2010, 2(2): 305–353 https://doi.org/10.1142/S1758825110000524
14	C Bisagni. Numerical analysis and experimental correlation of composite shell buckling and post-buckling. Composites. Part B, Engineering, 2000, 31(8): 655–667 https://doi.org/10.1016/S1359-8368(00)00031-7
15	R Telford, D Peeters, M Rouhi, P M Weaver. Experimental and numerical study of bending-induced buckling of stiffened composite plate assemblies. Composites. Part B, Engineering, 2022, 233: 109642 https://doi.org/10.1016/j.compositesb.2022.109642
16	P Rozylo, A Teter, H Debski, P Wysmulski, K Falkowicz. 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 https://doi.org/10.1007/s10443-017-9583-y
17	Y Zhang, W Tao, Y Chen, Z Lei, R Bai, Z Lei. 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 https://doi.org/10.3390/ma13163599
18	H B Ly, C Desceliers, L Minh Le, T T Le, B Thai Pham, L Nguyen-Ngoc, V T Doan, M Le. Quantification of uncertainties on the critical buckling load of columns under axial compression with uncertain random materials. Materials (Basel), 2019, 12(11): 1828 https://doi.org/10.3390/ma12111828
19	N Sharma, M Nishad, D K Maiti, M R Sunny, B N Singh. Uncertainty quantification in buckling strength of variable stiffness laminated composite plate under thermal loading. Composite Structures, 2021, 275: 114486 https://doi.org/10.1016/j.compstruct.2021.114486
20	N Kharghani, C Soares. 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 https://doi.org/10.1201/b21890-66
21	H X Nguyen, T Duy Hien, J Lee, H Nguyen-Xuan. Stochastic buckling behaviour of laminated composite structures with uncertain material properties. Aerospace Science and Technology, 2017, 66: 274–283 https://doi.org/10.1016/j.ast.2017.01.028
22	L Hu, P Feng, Y Meng, J Yang. Buckling behavior analysis of prestressed CFRP-reinforced steel columns via FEM and ANN. Engineering Structures, 2021, 245: 112853 https://doi.org/10.1016/j.engstruct.2021.112853
23	S Dey, T Mukhopadhyay, A Spickenheuer, U Gohs, S Adhikari. Uncertainty quantification in natural frequency of composite plates—An Artificial neural network based approach. Advanced Composites Letters, 2016, 25(2): 43–48 https://doi.org/10.1177/096369351602500203
24	P Sasikumar, A Venketeswaran, R Suresh, S Gupta. A data driven polynomial chaos based approach for stochastic analysis of CFRP laminated composite plates. Composite Structures, 2015, 125: 212–227 https://doi.org/10.1016/j.compstruct.2015.02.010
25	S Dey, T Mukhopadhyay, S Sahu, G Li, H Rabitz, S Adhikari. Thermal uncertainty quantification in frequency responses of laminated composite plates. Composites. Part B, Engineering, 2015, 80: 186–197 https://doi.org/10.1016/j.compositesb.2015.06.006
26	M Chandrashekhar, R Ganguli. Damage assessment of composite plate structures with material and measurement uncertainty. Mechanical Systems and Signal Processing, 2016, 75: 75–93 https://doi.org/10.1016/j.ymssp.2015.12.021
27	P R Swain, P Dash, B N Singh. 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 https://doi.org/10.1080/15397734.2019.1674663
28	B N Singh, N Iyengar, D Yadav. Effects of random material properties on buckling of composite plates. Journal of Engineering Mechanics, 2001, 127(9): 873–879 https://doi.org/10.1061/(ASCE)0733-9399(2001)127:9(873
29	C D Kalfountzos, G S Bikakis, E E Theotokoglou. Deterministic and probabilistic buckling response of fiber–metal laminate panels under uniaxial compression. Aircraft Engineering and Aerospace Technology, 2022, 94(5): 745–759 https://doi.org/10.1108/AEAT-02-2021-0044
30	X Zhuang, H Guo, N Alajlan, H Zhu, T Rabczuk. 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 https://doi.org/10.1016/j.euromechsol.2021.104225
31	H Guo, X Zhuang, T Rabczuk. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–456 https://doi.org/10.32604/cmc.2019.06660
32	H Guo, H Zheng, X Zhuang. Numerical manifold method for vibration analysis of Kirchhoff’s plates of arbitrary geometry. Applied Mathematical Modelling, 2019, 66: 695–727 https://doi.org/10.1016/j.apm.2018.10.006
33	H Guo, H Zheng. The linear analysis of thin shell problems using the numerical manifold method. Thin-walled Structures, 2018, 124: 366–383 https://doi.org/10.1016/j.tws.2017.12.027
34	N Vu-Bac, T X Duong, T Lahmer, X Zhuang, R A Sauer, H S Park, T Rabczuk. 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 https://doi.org/10.1016/j.cma.2017.09.034
35	N Vu-Bac, T Duong, T Lahmer, P Areias, R A Sauer, H S Park, T Rabczuk. A NURBS-based inverse analysis of thermal expansion induced morphing of thin shells. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 480–510 https://doi.org/10.1016/j.cma.2019.03.011
36	N Vu-Bac, T Rabczuk, H Park, X Fu, X Zhuang. 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 https://doi.org/10.1016/j.cma.2022.115049
37	N Vu-Bac, T Lahmer, H Keitel, J Zhao, X Zhuang, T Rabczuk. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014, 68: 70–84 https://doi.org/10.1016/j.mechmat.2013.07.021
38	N Vu-Bac, T Lahmer, Y Zhang, X Zhuang, T Rabczuk. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014, 59: 80–95 https://doi.org/10.1016/j.compositesb.2013.11.014
39	N Vu-Bac, M Silani, T Lahmer, X Zhuang, T Rabczuk. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535 https://doi.org/10.1016/j.commatsci.2014.04.066
40	S Adhikari. 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	N Vu-Bac, R Rafiee, X Zhuang, T Lahmer, T Rabczuk. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464 https://doi.org/10.1016/j.compositesb.2014.09.008
42	N Vu-Bac, T Lahmer, X Zhuang, T Nguyen-Thoi, T Rabczuk. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31 https://doi.org/10.1016/j.advengsoft.2016.06.005
43	N Vu-Bac, X Zhuang, T Rabczuk. Uncertainty quantification for mechanical properties of polyethylene based on fully atomistic model. Materials (Basel), 2019, 12(21): 3613 https://doi.org/10.3390/ma12213613
44	B Liu, N Vu-Bac, X Zhuang, T Rabczuk. Stochastic multiscale modeling of heat conductivity of Polymeric clay nanocomposites. Mechanics of Materials, 2020, 142: 103280 https://doi.org/10.1016/j.mechmat.2019.103280
45	B Liu, N Vu-Bac, X Zhuang, X Fu, T Rabczuk. Stochastic full-range multiscale modeling of thermal conductivity of Polymeric carbon nanotubes composites: A machine learning approach. Composite Structures, 2022, 289: 115393 https://doi.org/10.1016/j.compstruct.2022.115393
46	B Liu, N Vu-Bac, T Rabczuk. A stochastic multiscale method for the prediction of the thermal conductivity of Polymer nanocomposites through hybrid machine learning algorithms. Composite Structures, 2021, 273: 114269 https://doi.org/10.1016/j.compstruct.2021.114269
47	M Fakoor, H Parviz. 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 https://doi.org/10.1007/s11709-020-0658-8
48	M Fakoor, H Parviz, A Abbasi. 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	S Sriramula, M K Chryssanthopoulos. An experimental characterisation of spatial variability in GFRP composite panels. Structural Safety, 2013, 42: 1–11 https://doi.org/10.1016/j.strusafe.2013.01.002
50	R G Ghanem, P D Spanos. Stochastic finite element method: Response statistics. In: Stochastic Finite Elements: A Spectral Approach. New York: Springer, 1991, 101–119
51	J Fish, W Wu. A nonintrusive stochastic multiscale solver. International Journal for Numerical Methods in Engineering, 2011, 88(9): 862–879 https://doi.org/10.1002/nme.3201
52	J N Reddy. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. 2nd ed. New York: CRC Press, 2003
53	S E Kim, H T Thai, J Lee. A two variable refined plate theory for laminated composite plates. Composite Structures, 2009, 89(2): 197–205 https://doi.org/10.1016/j.compstruct.2008.07.017
54	L V Tran, C H Thai, H T Le, B S Gan, J Lee, H Nguyen-Xuan. Isogeometric analysis of laminated composite plates based on a four-variable refined plate theory. Engineering Analysis with Boundary Elements, 2014, 47: 68–81 https://doi.org/10.1016/j.enganabound.2014.05.013

[1]	Mahdi FAKOOR, Hadi PARVIZ. Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach[J]. Front. Struct. Civ. Eng., 2020, 14(6): 1359-1371.

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