Efficient Finite Element Formulation for Thermal Stress Analysis of Laminated Composite and Sandwich Plates
Publication: Journal of Aerospace Engineering
Volume 28, Issue 4
Abstract
By introducing thermal expansion coefficients in the transverse displacement field, this paper proposes an approach to improve the performance of the global-local higher-order theory for thermal stress analysis of laminated composite plates. Transverse normal deformation has been considered in the proposed model, whereas the additional displacement variables have not increased because thermal loads could be included in the generalized force vector. The proposed model a priori satisfies the continuity conditions of transverse shear stresses at interfaces, and the number of displacement variables involved in the present model is independent of the number of layers. The derivatives of transverse displacement have been eliminated from the displacement field so that the interpolation functions are only required for the finite-element implementation. Based on the proposed model, a six-node triangular element is proposed for thermal expansion problems of laminated composite and sandwich plates. Numerical results show that the proposed model can produce a more accurate response of laminated composite plates under temperature loads than other models.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work described in this paper was supported by the National Natural Sciences Foundation of China (No. 11272217) and the Program for Liaoning Excellent Talents in University (LR201033).
References
Carrera, E. (2000). “An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates.” J. Therm. Stresses, 23(9), 797–831.
Carrera, E., and Ciuffreda, A. (2004). “Closed-form solutions to assess multilayered-plate theories for various thermal stress problems.” J. Therm. Stresses, 27(11), 1001–1031.
Carrera, E., and Cosatto, C. (2010). “Flight mechanics analysis of a motorized trike with composite wing.” J. Aerosp. Eng., 251–264.
Chakrabarti, A., and Sheikh, A. H. (2004). “Vibration of laminated-faced sandwich plate by a new refined element.” J. Aerosp. Eng., 123–134.
Chakrabarti, A., and Sheikh, A. H. (2005). “Analysis of laminated sandwich plates based on interlaminar shear stress continuous plate theory.” J. Eng. Mech., 377–384.
Cho, M., and Oh, J. (2003). “Higher order zig-zag plate theory under thermo- electric-mechanical loads combined.” Composites Part B, 34(1), 67–82.
Cho, M., and Parmerter, R. R. (1993). “Efficient higher-order plate theory for general lamination configurations.” AIAA J., 31(7), 1299–1306.
Di Sciuva, M. (1987). “An improved shear deformation theory for moderately thick multilayered anisotropic shells and plates.” J. Appl. Mech., 54(3), 589–596.
Jeychandrabose, C., Kirkhope, J., and Meekisho, L. (1987). “An improved discrete Kirchhoff quadrilateral thin-plate bending element.” Int. J. Numer. Methods Eng., 24(3), 635–654.
Kapuria, S., and Achary, G. G. S. (2004). “An efficient higher order zigzag theory for laminated plates subjected to thermal loading.” Int. J. Solids Struct., 41(16–17), 4661–4684.
Khandelwal, R. P., Chakrabarti, A., and Bhargava, P. (2012). “An efficient FE model and least square error method for accurate calculation of transverse shear stresses in composites and sandwich laminates.” Composites Part B, 43(4), 1695–1704.
Khare, R. K., Kant, T., and Garg, A. K. (2003). “Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells.” Compos. Struct., 59(3), 313–340.
Kulkarni, S. D., and Kapuria, S. (2008). “Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory.” Comput. Mech., 42(6), 803–824.
Kumar, S. K., and Singh, B. N. (2009). “Thermal buckling analysis of SMA fiber-reinforced composite plates using layerwise model.” J. Aerosp. Eng., 342–353.
Li, X. Y., and Liu, D. S. (1997). “Generalized laminate theories based on double superposition hypothesis.” Int. J. Numer. Methods Eng., 40(7), 1197–1212.
Lo, S. H., Wu, Z., Sze, K. Y., and Chen, W. J. (2011). “-type global-local theory with non-zero normal strain for the analysis of thick multilayer composite plates.” Comput. Mech., 47(5), 479–491.
Matsunaga, H. (2003). “Interlaminar stress analysis of laminated composite and sandwich circular arches subjected to thermal/mechanical loading.” Compos. Struct., 60(3), 345–358.
Matsunaga, H. (2004). “A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loading.” Compos. Struct., 64(2), 161–177.
Naganarayana, B. P., Mohan, P. R., and Prathap, G. (1997). “Accurate thermal stress predictions using -continuous higher-order shear deformable elements.” Comput. Methods Appl. Mech. Eng., 144(1–2), 61–75.
Noor, A. K., and Malik, M. (2000). “An assessment of five modeling approaches for thermo-mechanical stress analysis of laminated composite panels.” Comput. Mech., 25(1), 43–58.
Oh, J., and Cho, M. (2004). “A finite element based on cubic zig-zag plate theory for the prediction of thermo-electric-mechanical behaviors.” Int. J. Solids Struct., 41(5–6), 1357–1375.
Ojalvo, I. V. (1974). “Improved thermal stress determination by finite element methods.” AIAA J., 12(8), 1131–1132.
Pittr, J., and Hartl, H. (1980). “Improved stress evaluation under thermal loads for simple finite element.” Int. J. Numer. Methods Eng., 15(10), 1507–1515.
Qiao, P., and Binienda, W. K. (2008). “Impact mechanics of composite materials for aerospace application.” J. Aerosp. Eng., 117–118.
Reddy, J. N. (1984). “A simple higher-order theory for laminated composite plates.” J. Appl. Mech., 51(4), 745–752.
Rolfs, R., Noor, A. K., and Sparr, H. (1998). “Evaluation of transverse thermal stresses in composite plates based on first-order shear deformation theory.” Comput. Methods Appl. Mech. Eng., 167(3–4), 355–368.
Shokrieh, M. M., Akbari, S., and Daneshvar, A. (2013). “A comparison between the slitting method and the classical lamination theory in determination of macro-residual stresses in laminated composites.” Compos. Struct., 96, 708–715.
Thai, C. H., Tran, L. V., Tran, D. T., Thoi, T. N., and Xuan, H. N. (2012a). “Analysis of laminated composite plates using higher-order shear deformation theory and node-based smoothed discrete shear gap method.” Appl. Math. Modell., 36(11), 5657–5677.
Thai, C. H., Xuan, H. N., Thanh, N. N., Le, T. H., Thoi, T. N., and Rabczuk, T. (2012b). “Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach.” Int. J. Num. Methods Eng., 91(6), 571–603.
Wu, Z., and Chen, W. J. (2007). “A quadrilateral element based on refined global-local higher-order theory for coupling bending and extension thermo-elastic multilayered plates.” Int. J. Solids Struct., 44(10), 3187–3217.
Wu, Z., and Chen, W. J. (2010). “A global-local higher order theory including interlaminar stress continuity and plate bending element.” Comput. Mech., 45(5), 387–400.
Xuan, H. N., Rabczuk, T., Bordas, S., and Debongnie, J. F. (2008). “A smoothed finite element method for plate analysis.” Comput. Methods Appl. Mech. Eng., 197(13–16), 1184–1203.
Yang, L., Yan, Y., Ma, J., and Liu, B. (2013). “Effects of inter-fiber spacing and thermal residual stress on transverse failure of fiber-reinforced polymer-matrix composites.” Comput. Mater. Sci., 68, 255–262.
Zenkour, A. M. (2004). “Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading.” Compos. Struct., 65(3–4), 367–379.
Zenkour, A. M., and Alghamdi, N. A. (2008). “Thermoelastic bending analysis of functionally graded sandwich plates.” J. Mater. Sci., 43(8), 2574–2589.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 27, 2012
Accepted: Jun 30, 2014
Published online: Aug 14, 2014
Discussion open until: Jan 14, 2015
Published in print: Jul 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.