Abstract
The delamination/debonding failure in laminated structures is often caused by development of concentrated stress fields near the edges. Because of their three-dimensional (3D) nature, it is important to develop accurate elasticity solutions for these fields, which should include the possibility of non-rigid layer interfaces, to have realistic predictions. This article presents an accurate 3D piezoelasticity-based analytical solution for smart composite panels featured with piezoelectric sensor/actuator layers, having interfacial bonding imperfections and showing edge effects. The displacement and electric field discontinuities at the imperfectly bonded layer interfaces are represented by adopting the generalized spring–layer model. The model is implemented into the Reissner-type mixed variational principle for the piezoelectric medium. The partial differential equations thus developed are solved using the mixed-field multiterm Kantorovich method, which exactly satisfy all the mechanical and electric boundary conditions at the panel edges, top and bottom surfaces of the panel and interlaminar continuity/jump conditions. The accuracy and convergence of the present results are established in comparison with the available exact piezoelasticity solutions for simply supported panels. The effect of compliance and imperfection location on the electromechanical response of piezolaminated composite panels with edge effects is investigated. The influence of actuator debonding on the interlaminar stress transfer and actuation authority is also shown.
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References
Blandford, G.E., Tauchert, T.R.: Thermoelastic analysis of layered structures with imperfect layer contact. Comput. Struct. 6, 1283–1291 (1985)
Chen, W.Q., Cai, J.B., Ye, G.R., Wang, Y.F.: Exact three-dimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring interlaminar bonding imperfections modeled by a general spring layer. Int. J. Solids Struct. 41, 5247–5263 (2004)
Chen, W.Q., Lee, K.Y.: Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections. Compos. Struct. 65, 329–337 (2004)
Chen, W.Q., Ying, J., Cai, J.B., Ye, G.R.: Benchmark solution of imperfect angle-ply laminated rectangular plates in cylindrical bending with surface piezoelectric layers as actuator and sensor. Comput. Struct. 82, 1773–1784 (2004)
Chrysochoidis, N.A., Saravanos, D.A.: Generalized layerwise mechanics for the static and modal response of delaminated composite beams with active piezoelectric sensors. Int. J. Solids Struct. 44, 8751–8768 (2007)
Dhanesh, N., Kapuria, S.: Edge effects in elastic and piezoelectric laminated panels under thermal loading. J. Therm. Stress. 41, 1577–1596 (2018)
Erturk, C.L., Tekinalp, O.: A layerwise approach to piezo-electric plates accounting for adhesive flexibility and delaminated regions. Comput. Struct. 83, 279–296 (2005)
Fan, H., Sze, K.Y.: A micro-mechanics model for imperfect interface in dielectric materials. Mech. Mater. 33, 363–370 (2001)
Fu, Y.M., Li, S., Jiang, Y.J.: Nonlinear free vibration analysis of piezoelastic laminated plates with interface damage. Appl. Math. Mech. 30, 129–144 (2009)
Kapuria, S., Dumir, P.C., Sengupta, S.: Three dimensional solution for shape control of a simply supported rectangular hybrid plate. J. Therm. Stress. 22, 159–176 (1999)
Kapuria, S., Kumari, P.: Multiterm extended Kantorovich method for three-dimensional elasticity solution of laminated plates. J. Appl. Mech. 79(1–9), 061018 (2012)
Kapuria, S., Kumari, P.: Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects. Proc. R. Soc. A 469(1–19), 20120565 (2013)
Kapuria, S., Nair, P.G.: Exact three-dimensional piezothermoelasticity solution for dynamics of rectangular cross-ply hybrid plates featuring interlaminar bonding imperfections. Compos. Sci. Technol. 70, 752–762 (2010)
Kerr, A.D.: An extension of the Kantorovich method. Q. Appl. Math. 26, 219–229 (1968)
Kim, G.W., Lee, K.Y.: Influence of weak interfaces on buckling of orthotropic piezoelectric rectangular laminates. Compos. Struct. 82, 290–294 (2008)
Kim, J.S., Oh, J., Cho, M.: Efficient analysis of laminated composite and sandwich plates with interfacial imperfections. Compos. B Eng. 42, 1066–1075 (2011)
Li, D., Xu, J., Qing, G.: Free vibration analysis and eigenvalues sensitivity analysis for the composite laminates with interfacial imperfection. Compos. Part B 42, 1588–1595 (2011)
Liang, W., Rui-xiang, B., Cheng, Y.: Interfacial debonding behavior of composite beam/plates with PZT patch. Compos. Struct. 92, 1410–1415 (2010)
Liu, D.Y., Chen, W.Q.: Thermal stresses in bilayer systems with weak interface. Mech. Res. Commun. 37, 520–524 (2010)
Shu, X.: Modelling of cross-ply piezoelectric composite laminates in cylindrical bending with interfacial shear slip. Int. J. Mech. Sci. 47, 1673–1692 (2005)
Shu, X.: Piezothermoelastic responses of piezoelectric composite laminates with weak interfaces. Acta Mech. 214, 327–340 (2010)
Shu, X.: A refined theory with exponential through-thickness approximation for cross-ply piezoelectric composite laminates with weak interfaces. Compos. Struct. 96, 631–642 (2013)
Sun, D., Tong, L., Atluri, S.N.: Effects of piezoelectric sensor/actuator debonding on vibration control of smart beams. Int. J. Solids Struct. 38, 9033–9051 (2001)
Wang, H., Zou, L.: Interfacial effect on the electromechanical behaviors of piezoelectric/elastic composite smart beams. J. Intell. Mater. Syst. Struct. 24, 421–430 (2012)
Wang, H.M., Zou, L.: The performance of a piezoelectric cantilevered energy harvester with an imperfectly bonded interface. Smart Mater. Struct. 22, 1–8 (2013)
Zhou, Y.Y., Chen, W.Q., Lü, C.F.: Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections. Compos. Struct. 92, 1009–1018 (2010)
Acknowledgements
S. Kapuria acknowledges the financial support for this work provided by the Science and Engineering Research Board, Department of Science and Technology, Government of India, through J. C. Bose National Fellowship (Grant No. JCB/2018/000025).
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Dhanesh, N., Kapuria, S. Piezoelasticity solution for edge stress field in weakly bonded piezoelectric composite laminates. Arch Appl Mech 91, 2411–2434 (2021). https://doi.org/10.1007/s00419-021-01892-7
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DOI: https://doi.org/10.1007/s00419-021-01892-7