DOI QR코드

DOI QR Code

C0-type Reddy's theory for composite beams using FEM under thermal loads

  • Fan, Xiaoyan (Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation, Shenyang Aerospace University) ;
  • Wu, Zhen (Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation, Shenyang Aerospace University)
  • Received : 2014.04.20
  • Accepted : 2016.01.11
  • Published : 2016.02.10

Abstract

To analyze laminated composite and sandwich beams under temperature loads, a $C^0$-type Reddy's beam theory considering transverse normal strain is proposed in this paper. Although transverse normal strain is taken into account, the number of unknowns is not increased. Moreover, the first derivatives of transverse displacement have been taken out from the in-plane displacement fields, so that the $C^0$ interpolation functions are only required for the finite element implementation. Based on the proposed model, a three-node beam element is presented for analysis of thermal responses. Numerical results show that the proposed model can accurately and efficiently analyze the thermoelastic problems of laminated composites.

Keywords

Acknowledgement

Supported by : National Natural Sciences Foundation of China

References

  1. Aydogdu, M. (2006), "Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges", J. Compos. Mater., 40(23), 2143-2155. https://doi.org/10.1177/0021998306062313
  2. Bhar, A. and Satsangi, S.K. (2011), "Accurate transverse stress evaluation in composite/ sandwich thick laminates using a C0 HSDT and a novel post-processing technique", Eur. J. Mech. A/Solid., 30(1), 46-53. https://doi.org/10.1016/j.euromechsol.2010.09.003
  3. He, G. and Yang, X. (2014), "Finite element analysis for buckling of two-layer composite beams using Reddy's higher order beam theory", Finite Elem. Anal. Des., 83, 49-57. https://doi.org/10.1016/j.finel.2014.01.004
  4. Khdeir, A.A. and Reddy, J.N. (1991), "Thermal stresses and deflections of cross-ply laminated plates using refined plate theories", J. Therm. Stress., 14(4), 419-438. https://doi.org/10.1080/01495739108927077
  5. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  6. Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56(4), 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X
  7. Kapuria, S., Dumir, P.C. and Ahmed, A. (2003), "An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading", Int. J. Solid. Struct., 40(24), 6613-6631. https://doi.org/10.1016/j.ijsolstr.2003.08.014
  8. Li, Y. and Zhu, D. (2009), "Free flexural vibration analysis of symmetric rectangular honeycomb panels using the improved Reddy's third-order plate theory", Compos. Struct., 88(1), 33-39. https://doi.org/10.1016/j.compstruct.2008.03.033
  9. 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), 16-177.
  10. Matsunaga, H. (2003), "Interlaminar stress analysis of laminated composite and sandwich circular arches subjected to thermal/mechanical loading", Compos. Struct., 60(3), 345-358. https://doi.org/10.1016/S0263-8223(02)00340-9
  11. Naganarayana, B.P., Mohan, P.R. and Prathap, G. (1997), "Accurate thermal stress predictions using $C^0$-continuous higher-order shear deformable elements", Comput. Meth. Appl. Mech. Eng., 144(1), 61-75. https://doi.org/10.1016/S0045-7825(96)01171-1
  12. Nayak, A.K., Moy, S.S.J. and Shenoi, R.A. (2002), "Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory", Compos. Part B: Eng., 33(7), 505-519. https://doi.org/10.1016/S1359-8368(02)00035-5
  13. Nayak, A.K., Shenoi, R.A. and Moy, S.S.J. (2002), "Analysis of damped composite sandwich plates using plate bending elements with substitute shear strain fields based on Reddy's higher-order theory", J. Mech. Eng. Sci., 216(5), 591-606. https://doi.org/10.1243/0954406021525377
  14. 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. Meth. Appl. Mech. Eng., 167(3), 355-368. https://doi.org/10.1016/S0045-7825(98)00150-9
  15. Reddy, J.N. and Hsu, Y.S. (1980), "Effects of shear deformation and anisotropy on the thermal bending of layered composite plates", J. Therm. Stress., 3(4), 475-493. https://doi.org/10.1080/01495738008926984
  16. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  17. 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. https://doi.org/10.1016/j.compstruct.2012.10.001
  18. Savoia, M. and Reddy, J.N. (1995), "Three-dimensional thermal analysis of laminated composite plates", Int. J. Solids Struct., 32(5), 593-608. https://doi.org/10.1016/0020-7683(94)00146-N
  19. Sheikh, A.H. and Chakrabarty, A. (2003), "A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates", Finite Elem. Anal. Des., 39(9), 883-903. https://doi.org/10.1016/S0168-874X(02)00137-3
  20. Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  21. Wu, Z., Cheung, Y.K., Lo, S.H. and Chen, W. (2010), "On the thermal expansion effects in the transverse direction of laminated composite plates by means of a global-local higher-order model", Int. J. Mech. Sci., 52(7), 970-981. https://doi.org/10.1016/j.ijmecsci.2010.03.013
  22. Wu, C.H. and Tauchert, T.R. (1980a), "Thermoelastic analysis of laminated plates. 1: Symmetric specially orthotropic laminates", J. Therm. Stress., 3(2), 247-259. https://doi.org/10.1080/01495738008926966
  23. Wu, C.H. and Tauchert, T.R. (1980b), "Thermoelastic analysis of laminated plates. 2: Antisymmetric cross-ply and angle-ply laminates", J. Therm. Stress., 3(3), 365-378. https://doi.org/10.1080/01495738008926975
  24. Wu, Z., Lo, S.H. and Sze, K.Y. (2013), "Influence of transverse normal strain and temperature profile on thermoelasticity of sandwiches in terms of the enhanced Reddy's theory", J. Therm. Stress., 36, 19-36. https://doi.org/10.1080/01495739.2012.720532
  25. Xiang, S., Jiang, S.X., Bi, Z.Y., Jin, Y.X. and Yang, M.S. (2011), "A nth-order meshless generalization of Reddy's third-order shear deformation theory for the free vibration on laminated composite plates", Compos. Struct., 93(2), 299-307. https://doi.org/10.1016/j.compstruct.2010.09.015

Cited by

  1. A 3D finite element static and free vibration analysis of magneto-electro-elastic beam vol.6, pp.4, 2017, https://doi.org/10.12989/csm.2017.6.4.465
  2. Effect of hybrid thermal cycling shocks on the mechanical properties of structural composites vol.79, pp.3, 2016, https://doi.org/10.12989/sem.2021.79.3.301
  3. Analytical solutions for laminated beams subjected to non-uniform temperature boundary conditions vol.282, pp.None, 2022, https://doi.org/10.1016/j.compstruct.2021.115044