Adhesive joint modeling using compatible element formulation

Authors

1 School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

2 Department of Mechanical Engineering, Arak University of Technology, Arak, Iran

Abstract

The use of structural adhesives in automotive structures has been increased recently for their role in noise, vibration and harshness (NVH). Therefore, the dynamic behavior of structures containing bonded joints has become an area with numerous investigations over the past decades. Development of accurate formulations capable of representing adhesively bonded joint dynamics is a step forward in constructing the numerical models for one of the most useful kinds of joints in industry. Analysis of the adhesive layer between the two parts requires special assumptions which leads to using nonlinear and three dimensional models. Obtaining shape functions for an adhesive element by using finite element (F.E.) theory is a complicated and difficult task to do. The complexity is increased when it is assumed that the adhesive element is compatible with the plate element. In this paper, a new finite element formulation is developed for the adhesive layer which does not rely on shape functions and is compatible with the plate element. The accuracy of the proposed element is evaluated by using numerical and experimental results.

Highlights

  • A new F.E. formulation of an element is developed for modeling adhesive joints.
  • The developed brick-like element is found compatible with plate elements.
  • The formulation is derived employing the displacement field of a plate element.
  • Experimental results are used to show the accuracy of the new element formulation.

Keywords

Main Subjects


[1] L.F.M. da Silva, P.J.C. das Neves, R.D. Adams, J.K. Spelt, Analytical models of adhesively bonded joints—Part I: Literature survey, International Journal of Adhesion and Adhesives, 29 (2009) 319-330.
[2] L.F.M. da Silva, P.J.C. das Neves, R.D. Adams, A. Wang, J.K. Spelt, Analytical models of adhesively bonded joints—Part II: Comparative study, International Journal of Adhesion and Adhesives, 29 (2009) 331-341.
[3] S. El-Sayed, S. Sridharan, Predicting and tracking interlaminar crack growth in composites using a cohesive layer model, Composites Part B: Engineering, 32 (2001) 545-553.
[4] M.A. McCarthy, C.G. Harte, J.F.M. Wiggenraad, A.L.P.J. Michielsen, D. Kohlgrueber, A. Kamoulakos, Finite element modelling of crash response of composite aerospace sub-floor structures, Computational Mechanics, 26 (2000) 250-258.
[5] A. Kaya, M.S. Tekelioğlu, F. Findik, Effects of various parameters on dynamic characteristics in adhesively bonded joints, Materials Letters, 58 (2004) 3451-3456.
[6] X. He, Finite element analysis of torsional free vibration of adhesively bonded single-lap joints, International Journal of Adhesion and Adhesives, 48 (2014) 59-66.
[7] A.S. Nobari, K. Jahani, Identification of damping characteristic of a structural adhesive by extended modal based direct model updating method, Experimental mechanics, 49 (2009) 785-798.
[8] K. Jahani, A.S. Nobari, Identification of dynamic (Young’s and shear) moduli of a structural adhesive using modal based direct model updating method, Experimental Mechanics, 48 (2008) 599-611.
[9] T. Naraghi, A.S. Nobari, Identification of the dynamic characteristics of a viscoelastic, nonlinear adhesive joint, Journal of Sound and Vibration, 352 (2015) 92-102.
[10] X. He, S.O. Oyadiji, Influence of adhesive characteristics on the transverse free vibration of single lap-jointed cantilevered beams, Journal of Materials Processing Technology, 119 (2001) 366-373.
[11] Y. Du, L. Shi, Effect of vibration fatigue on modal properties of single lap adhesive joints, International Journal of Adhesion and Adhesives, 53 (2014) 72-79.
[12] E. Nwankwo, A.S. Fallah, L.A. Louca, An investigation of interfacial stresses in adhesively-bonded single lap joints subject to transverse pulse loading, Journal of Sound and Vibration, 332 (2013) 1843-1858.
[13] D.J. Allman, A compatible triangular element including vertex rotations for plane elasticity analysis, Computers & Structures, 19 (1984) 1-8.
[14] E. Abdullah, J.F. Ferrero, J.J. Barrau, J.B. Mouillet, Development of a new finite element for composite delamination analysis, Composites Science and Technology, 67 (2007) 2208-2218.
[15] K.Y. Sze, A. Ghali, A hybrid brick element with rotational degrees of freedom, Computational Mechanics, 12 (1993) 147-163.
[16] R.H. Macneal, R.L. Harder, A refined four-noded membrane element with rotational degrees of freedom, Computers & Structures, 28 (1988) 75-84.
[17] S.M. Yunus, T.P. Pawlak, R.D. Cook, Solid elements with rotational degrees of freedom: Part 1—hexahedron elements, International Journal for Numerical Methods in Engineering, 31 (1991) 573-592.
[18] R.D. Cook, On the Allman triangle and a related quadrilateral element, Computers & Structures, 22 (1986) 1065-1067.
[19] G.R. Liu, S.S. Quek, The finite element method: a practical course, Butterworth-Heinemann, 2013.