Journal of Mechanical Science and Technology

, Volume 32, Issue 2, pp 593–603 | Cite as

Adaptive finite element analysis of steel girder deck pavement

  • Wenhuo SunEmail author
  • Lixiong Gu
  • Ronghui Wang
  • Tiedong Qi


This paper shows a more exact and practical finite element model of the steel girder deck pavement. Based on Mindlin thick plate theory, a 12-node solid thick plate element was constituted to analyze the pavement. The computation result was compared with that by traditional 4-node and 8-node thick plate finite element, and is satisfactory. A combined plate beam element method is presented to investigate the stiffened plate. A 6-node solid thin plate element was constituted to analyze the top plate based on Kirchhoff thin plate theory. The stiffeners acting as the vertical supporting function mainly are taken as Euler beam elements. A method of using the linear interpolation to realize the longitudinal displacement and the cubic Hermite interpolation to the vertical displacement is presented to analyze the stiffeners. In addition, it is essential to consider the displacement coordination between the top plate and stiffeners. A node-to-node contact scheme, which is applicable for three-dimensional contact analyses involving large deformations, was used to treat the contact problem between pavement and stiffened plate by Lagrange multiplier methods.


Steal deck pavement Stiffened plate Contact analysis Finite element 


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  1. [1]
    C. T. Metcalf, Flexural tests of paving materials for orthotropic steel plate bridges, Highway Research Record, 155 (1967) 56–78.Google Scholar
  2. [2]
    M. S. G. Cullimore, I. D. Flett and J. W. Smith, Flexure of steel bridge deck plate with asphalt surfacing, IABSE Periodical, Bristol: University of Bristol, 1 (1983) 58–83.Google Scholar
  3. [3]
    Koroneose, Oscillations measurements of an orthotropic roadway deck with bituminous cover, Bitumen Teere Asphalt Peche, 5 (1971) 223–236.Google Scholar
  4. [4]
    M. H. Kolstein and J. H. Dijkink, Behavior of modified bituminous surfacing on orthotropic steel bridge decks, Proceedings of the 4th Euro-bitumen Symposium, 1 (1989) 907–975.Google Scholar
  5. [5]
    M. H. Kolstein and J. Wardenier, Stress reduction due to surfacing on orthotropic steel decks, Proceedings of the ISAB Workshop: Evaluation of Existing Steel and Composite Bridges (1997).Google Scholar
  6. [6]
    G. H. Gunther, S. Bild and G. Sedlacek, Durability of asphaltic pavements on orthotropic decks of steel bridges, Construct Steel Research, 7 (1987) 5–106.Google Scholar
  7. [7]
    S. Bild, Durability design criteria for bituminous pavements on orthotropic steel bridge decks, Can. J. Civ. Eng., 14 (1) (1987) 41–48.CrossRefGoogle Scholar
  8. [8]
    H. Nakanishi and T. Okochi, The structural evaluation for an asphalt pavement, AAPA (2000) 113–123.Google Scholar
  9. [9]
    T. Nishizawa, K. Himeno, K. Nomura and K. Uchida, Development of a new structural model with prism and strip elements for pavement on steel bridge decks, The International J. of Geomechanics, 1 (3) (2001) 351–369.CrossRefGoogle Scholar
  10. [10]
    R. Szilard, Theories and applications of plate analysis, Hoboken, New Jersey, USA: John Wiley&Sons (2004).CrossRefGoogle Scholar
  11. [11]
    E. Reissner, The effect of transverse shear deformation on the bending of elastic plate, Transactions of ASME J. Applied Mechanics, 12 (1945) A69–A77.MathSciNetzbMATHGoogle Scholar
  12. [12]
    R. D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, J. of Applied Mechanics, 18 (1) (1951) 31–38.zbMATHGoogle Scholar
  13. [13]
    C. Y. Chia, Non-linear analysis of plates, McGraw-Hill, New York (1980).Google Scholar
  14. [14]
    I. Senjanovc, N. Vladimir and D. S. Cho, A new finite element formulation for vibration analysis of thick plates, Int. J. Nav. Archit. Ocean Eng., 7 (2015) 324–345.CrossRefGoogle Scholar
  15. [15]
    T. J. R. Hughes, R. L. Taylor and W. Kanoknukulchai, Simple and efficient element for plate bending, International J. for Numerical Methods in Engineering, 11 (10) (1977) 1529–1543.CrossRefzbMATHGoogle Scholar
  16. [16]
    C. Lovadina, Analysis of a mixed finite element method for the Reissner-Mindlin plate problems, Computer Methods in Applied Mechanics and Engineering, 163 (1998) 71–85.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    O. C. Zienkiewicz and R. L. Taylor, The finite element method, 5th ed., Oxford: Butterworth-Heinemann (2000).zbMATHGoogle Scholar
  18. [18]
    K. Bletzinger, M. Bischoff and E. Ramm, A unified approach for shear-locking-free triangular and rectangular shell finite elements, Computers and Structures, 75 (3) (2000) 321–334.CrossRefGoogle Scholar
  19. [19]
    H. Nguyen-Xuan, G. R. Liu, C. Thai-Hoang and T. Nguyen-Thoi, An Edge-based smoothed Finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates, Computer Methods in Applied Mechanics and Engineering, 199 (9–12) (2010) 471–489.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    P. Wriggers, Computational contact mechanics, Springer, New York (2007).CrossRefzbMATHGoogle Scholar
  21. [21]
    P. Wriggers and J. C. Simo, A note on tangent stiffness for fully nonlinear contact problems, Comp. Appl. Num. Meth., 1 (1985) 199–203.CrossRefzbMATHGoogle Scholar
  22. [22]
    J. T. Oden, Exterior penalty methods for contact problems in elasticity, Wunderlich KJBW, E. Stein (ed), Nonlinear Finite Element Analysis in Structural Mechanics, Springer, Berlin (1981).Google Scholar
  23. [23]
    S. Jin, D. Sohn and S. Im, Node-to-node scheme for threedimensional contact mechanics using polyhedral type variable-node elements, Comput. Methods Appl. Mech. Engrg., 304 (2016) 217–242.MathSciNetCrossRefGoogle Scholar
  24. [24]
    G. Pietrzak, Continuum mechanics modelling and augmented lagrange formulation of large deformation frictional contact problems, Technical Report 1656, Ecole polytechnique federale de Lausanne, EPFL (1997).Google Scholar
  25. [25]
    A. R. Mijar and J. S. Arora, An augmented Lagrangian optimization method for contact analysis problems, 2: Numerical evaluation, Struct. Multidiscip. Optim., 28 (2004) 113–126.MathSciNetzbMATHGoogle Scholar
  26. [26]
    M. Chandrashekhar and R. Ganguli, Large deformation dynamic finite element analysis of delaminated composite plates using contact-impact conditions, Computers and Structures, 144 (2016) 92–102.CrossRefGoogle Scholar
  27. [27]
    A. P. C. Dias, A. L. Serpa and M. L. Bittencourt, Highorder mortar-based element applied to nonlinear analysis of structural contact mechanics, Comput. Methods Appl. Mech. Engrg., 294 (2015) 19–55.MathSciNetCrossRefGoogle Scholar
  28. [28]
    C. J. Corbett and R. A. Sauer, Three-dimensional isogeometrically enriched finite elements for frictional contact and mixed-mode debonding, Comput. Methods Appl. Mech. Engrg., 284 (2015) 781–806.MathSciNetCrossRefGoogle Scholar
  29. [29]
    Y.-W. Kim, Finite element formulation for earthquake analysis of single-span beams involving forced deformation caused by multi-support motions, J. of Mechanical Science and Technology, 29 (2) (2015) 461–469.CrossRefGoogle Scholar
  30. [30]
    Y.-J. Kee and S.-J. Shin, Structural dynamic modeling for rotating blades using three dimensional finite elements, J. of Mechanical Science and Technology, 29 (4) (2015) 1607–1618.CrossRefGoogle Scholar
  31. [31]
    J. Yang, Y. Lei, J. Han and S. Meng, Enriched finite element method for three-dimensional viscoelastic interface crack problems, J. of Mechanical Science and Technology, 30 (2) (2016) 771–782.CrossRefGoogle Scholar
  32. [32]
    W. A. Siswanto, M. Nagentrau, A. L. Mohd Tobi and M. N. Tamin, Prediction of plastic deformation under contact condition by quasi-static and dynamic simulations using explicit finite element analysis, J. of Mechanical Science and Technology, 30 (11) (2016) 5093–5101.CrossRefGoogle Scholar
  33. [33]
    D.-K. Shin, Verification of the performance of rotatable jig for a single cantilever beam method using the finite element analysis, J. of Mechanical Science and Technology, 31 (2) (2017) 777–784.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Wenhuo Sun
    • 1
    Email author
  • Lixiong Gu
    • 1
  • Ronghui Wang
    • 1
  • Tiedong Qi
    • 2
  1. 1.School of Civil Engineering and TransportationSouth China University of TechnologyGuangzhouChina
  2. 2.Research Institute of Highway Ministry of TransportBeijingChina

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