Quantifying Uncertainty in Structural Responses of Polymer Sandwich Composites: A Comparative Analysis of Neural Networks

Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 81)


The manufacturing and fabrication of complex polymer sandwich composite plates involve various processes and parameters, and the lack of control over them causes uncertain system parameters. It is essential to consider randomness in varying parameters to analyse polymer sandwich composite plates. The present study portrays uncertainty quantification in structural responses (such as natural frequencies) of polymer sandwich composite plates using the surrogate model. The comparative study of artificial neural network (ANN) and polynomial neural network (PNN) for uncertain structural responses of the sandwich plate is presented. The proposed ANN as well as PNN algorithm is found to be convergent with intensive Monte Carlo simulation (MCS) for uncertain vibration responses. The predictability of PNN is observed to be more efficient than that of ANN. Typical material properties, skew angle, fibre orientation angle, number of laminate and core thickness are randomly varied to quantify the uncertainties. The use of both the surrogate models (PNN and ANN) results in a significant saving of computational time and cost compared to that of full-scale intensive finite element-based MCS approach.


Polymer sandwich plate Artificial neural network Polynomial neural network Monte carlo simulation Randomness 



The first author would like to acknowledge the financial support received from MHRD, Government of India during this research work.


  1. 1.
    Pflug J, Verpoest I (2006) Sandwich materials selection charts. J Sandwich Struct Mater 8(5):407–421CrossRefGoogle Scholar
  2. 2.
    Mukhopadhyay T, Chowdhury R, Chakrabarti A (2016) Structural damage identification: a random sampling-high dimensional model representation approach. Adv Struct Eng 19(6):908–927CrossRefGoogle Scholar
  3. 3.
    Dey TK, Mukhopadhyay T, Chakrabarti A, Sharma UK (2015) Efficient lightweight design of FRP bridge deck . Proc Inst Civil Eng—Struct Build 168(10):697–707CrossRefGoogle Scholar
  4. 4.
    Mahata A, Mukhopadhyay T, Adhikari S (2016) A polynomial chaos expansion based molecular dynamics study for probabilistic strength analysis of nano-twinned copper. Mater Res Express 3:036501CrossRefGoogle Scholar
  5. 5.
    Mukhopadhyay T, Mahata A, Dey S, Adhikari S (2016) Probabilistic analysis and design of HCP nanowires: an efficient surrogate based molecular dynamics simulation approach. J Mater Sci Technol 32(12):1345–1351CrossRefGoogle Scholar
  6. 6.
    Metya S, Mukhopadhyay T, Adhikari S, Bhattacharya G (2017) System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines. Comput Geotech 87:212–228CrossRefGoogle Scholar
  7. 7.
    Dey S, Mukhopadhyay T, Sahu SK, Adhikari S (2018) Stochastic dynamic stability analysis of composite curved panels subjected to non-uniform partial edge loading. Eur J Mech/A Solids 67:108–122MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dey S, Mukhopadhyay T, Khodaparast HH, Adhikari S (2016) A response surface modelling approach for resonance driven reliability based optimization of composite shells. Periodica Polytechnica—Civ Eng 60(1):103–111CrossRefGoogle Scholar
  9. 9.
    Karsh PK, Mukhopadhyay T, Dey S (2018a) Spatial vulnerability analysis for the first ply failure strength of composite laminates including effect of delamination. Compos Struct 184:554–567CrossRefGoogle Scholar
  10. 10.
    Naskar S, Mukhopadhyay T, Sriramula S (2018) Probabilistic micromechanical spatial variability quantification in laminated composites. Compos B Eng 151:291–325CrossRefGoogle Scholar
  11. 11.
    Maharshi K, Mukhopadhyay T, Roy B, Roy L, Dey S (2018) Stochastic dynamic behaviour of hydrodynamic journal bearings including the effect of surface roughness. Int J Mech Sci 142–143:370–383CrossRefGoogle Scholar
  12. 12.
    Naskar S, Mukhopadhyay T, Sriramula S, Adhikari S (2017) Stochastic natural frequency analysis of damaged thin-walled laminated composite beams with uncertainty in micromechanical properties. Compos Struct 160:312–334CrossRefGoogle Scholar
  13. 13.
    Mukhopadhyay T, A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise. J Sandwich Struct Mater.
  14. 14.
    Kumar RR, Mukhopadhyay T, Pandey KM, Dey S (2019) Stochastic buckling analysis of sandwich plates: the importance of higher order modes. Int J Mech Sci 152:630–643CrossRefGoogle Scholar
  15. 15.
    Kumar RR, Karsh PK, Vaishali Pandey KM, Dey S (2019) Stochastic natural frequency analysis of skewed sandwich plates. Eng Computations.
  16. 16.
    Mukhopadhyay T, Adhikari S (2017a) Stochastic mechanics of metamaterials. Compos Struct 162:85–97CrossRefGoogle Scholar
  17. 17.
    Mukhopadhyay T, Adhikari S (2016) Free vibration analysis of sandwich panels with randomly irregular honeycomb core. J Eng Mech 142(11):06016008CrossRefGoogle Scholar
  18. 18.
    Mukhopadhyay T, Adhikari S (2017b) Effective in-plane elastic moduli of quasi-random spatially irregular hexagonal lattices. Int J Eng Sci 119:142–179CrossRefGoogle Scholar
  19. 19.
    Mukhopadhyay T, Mahata A, Adhikari S, Asle ZM (2018) Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures. Nanoscale 10:5280–5294CrossRefGoogle Scholar
  20. 20.
    Mukhopadhyay T, Mahata A, Adhikari S, Asle ZM (2017) Effective mechanical properties of multilayer nano-heterostructures. Nat Sci Rep 7:15818CrossRefGoogle Scholar
  21. 21.
    Mukhopadhyay T, Mahata A, Adhikari S, Asle Zaeem M (2017) Effective elastic properties of two dimensional multiplanar hexagonal nano-structures, 2D Materials, 4:025006Google Scholar
  22. 22.
    Mahata A, Mukhopadhyay T, Probing the chirality-dependent elastic properties and crack propagation behavior of single and bilayer stanine. Phys Chem Chem Phys.
  23. 23.
    Mukhopadhyay T, Adhikari S, Batou A, Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices. Int J Mech Sci.
  24. 24.
    Kumar RR, Mukhopadhyay T, Naskar S, Pandey KM, Dey S (2019) Stochastic low-velocity impact analysis of sandwich plates including the effects of obliqueness and twist. Thin-Walled Struct 145:106411Google Scholar
  25. 25.
    Karsh PK, Mukhopadhyay T, Dey S (2018b) Stochastic dynamic analysis of twisted functionally graded plates. Compos B Eng 147:259–278CrossRefGoogle Scholar
  26. 26.
    Dey S, Mukhopadhyay T, Spickenheuer A, Gohs U, Adhikari S (2016) Uncertainty quantification in natural frequency of composite plates—an artificial neural network based approach. Adv Compos Lett 25(2):43–48CrossRefGoogle Scholar
  27. 27.
    Dey S, Mukhopadhyay T, Adhikari S (2018) Uncertainty quantification in laminated composites: a meta-model based approach. CRC Press, ISBN, p 9781498784450CrossRefGoogle Scholar
  28. 28.
    Dey S, Naskar S, Mukhopadhyay T, Gohs U, Sriramula S, Adhikari S, Heinrich G (2016) Uncertain natural frequency analysis of composite plates including effect of noise—a polynomial neural network approach. Compos Struct 143:130–142CrossRefGoogle Scholar
  29. 29.
    Dey S, Mukhopadhyay T, Naskar S, Dey TK, Chalak HD, Adhikari S, Probabilistic characterisation for dynamics and stability of laminated soft core sandwich plates. J Sandwich Struct Mater.
  30. 30.
    Dey S, Mukhopadhyay T, Adhikari S (2017) Metamodel based high-fidelity stochastic analysis of composite laminates: a concise review with critical comparative assessment. Compos Struct 171:227–250CrossRefGoogle Scholar
  31. 31.
    Chalak HD, Chakrabarti A, Iqbal MA, Sheikh AH (2013) Free vibration analysis of laminated soft core sandwich plates. J Vib Acoust 135(1):011013CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNIT SilcharSilcharIndia
  2. 2.Department of Aerospace EngineeringIIT KanpurKanpurIndia

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