DOI QR코드

DOI QR Code

A variational asymptotic approach for thermoelastic analysis of composite beams

  • Wang, Qi (Department of Mechanical and Aerospace Engineering, Utah State University) ;
  • Yu, Wenbin (School of Aeronautics and Astronautics, Purdue University)
  • Received : 2013.08.28
  • Accepted : 2013.09.28
  • Published : 2014.01.31

Abstract

A variational asymptotic composite beam model has been developed for thermoelastic analysis. Composite beams, including sandwich structure and laminates, under different boundary conditions are examined. Previously developed beam model, which is based on variational-asymptotic method, is extended to incorporate temperature-dependent materials experiencing large temperature changes. The recovery relations have been derived so that the temperatures, heat fluxes, stresses, and strains can be recovered over the cross-section. The present theory is implemented into the computer program VABS (Variational Asymptotic Beam Sectional analysis). Numerical results are compared with the 3D analysis for the purpose of demonstrating advantages of the present theory and use of VABS.

Keywords

References

  1. Bapanapalli, S.K., Martinez, O.M., Gogu, C., Sankar, B.V., Haftka, R.T. and Blosser, M.L. (2006), "Analysis and design of corrugated-core sandwich planels for thermal protection systems of space vehicles", Proceedings of 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, New Port, USA, May
  2. Berdichevsky, V.L. (1979), "Variational-asymptotic method of constructing a theory of shells", J. Appl. Math. Mech., 43, 664-687. https://doi.org/10.1016/0021-8928(79)90152-7
  3. Bickford, W.B. (1982), "A consistent higher-order beam theory", Developments in Theoretical and Applied Mechanics, 11, 137-142.
  4. Boley, B.A. and Weiner, J.H. (1997), Theory of Thermal Stresses, Dover Publications, Mineola, NY, USA.
  5. Cesnik, C.E.S. and Hodges, D.H. (1993), "Stiffness constants for initially twisted and curved composite beams", Appl. Mech. Rev., 46, 211-220. https://doi.org/10.1115/1.3120338
  6. Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2001), Concepts and Applications of Finite Element Analysis, 4th Edition, Wiley, New York, NY, USA.
  7. Copper, C.D. and Pilkey, W.D. (2002), "Thermoelasticity solutions for straight beams", J. Appl. Mech., 69, 224-229. https://doi.org/10.1115/1.1427340
  8. Frostig, Y., Baruch, M., Vilnay, O. and Sheinman, I. (1992), "High-order theory for sandwich-beam behavior with transversely flexible core", J. Eng. Mech., 118, 1026-1043. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:5(1026)
  9. Ghiringhelli, G.L. (1997a), "On the linear three-dimensional behavior of composite beams", Comp. Part B Eng., 28, 613-626.
  10. Ghiringhelli, G.L. (1997b), "On the thermal problem for composite beams using a finite element semi-discretisation", Comp. Part B Eng., 28, 483-495. https://doi.org/10.1016/S1359-8368(96)00069-8
  11. Heyliger, P.R. and Reddy, J.N. (1988), "A higher-order beam finite element for bending and vibration problems", J. Sound Vib., 126, 309-326. https://doi.org/10.1016/0022-460X(88)90244-1
  12. Hodges, D.H., Atilgan, A.R., Cesnik, C.E.S. and Fulton, M.V. (1992), "On a simplified strain energy function for geometrically nonlinear behavior of anisotropic beams", Compos. Eng., 2, 513-526. https://doi.org/10.1016/0961-9526(92)90040-D
  13. Huang, D., Ding, H. and Chen, W. (2007), "Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load", J. Zhejiang Univ. Sci. A, 8, 1351-1355. https://doi.org/10.1631/jzus.2007.A1351
  14. Kant, T. and Manjunath, B.S. (992), "Refined theories for composite and sandwich beams with C0 finite elements", Comp. Struct., 33, 755-764.
  15. 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. Solids Struct., 40, 6613-6631. https://doi.org/10.1016/j.ijsolstr.2003.08.014
  16. Khdeir, A.A. and Reddy, J.N. (1999), "Jordan canonical form solution for thermally induced deformations of cross-ply laminated composite beams", Int. J. Solids Struct., 22, 331-346.
  17. Marur, S.R. and Kant, T. (1997), "On the performance of higher order theories for transient dynamic analysis of sandwich and composite beams", Comp. Struct., 65, 741-759. https://doi.org/10.1016/S0045-7949(96)00427-0
  18. Noda, N. (1991), "Thermal stresses in materials with temperature-dependent properties", Appl. Mech. Rev., 44, 383-397. https://doi.org/10.1115/1.3119511
  19. Okamoto, N., Kusakari, M., Tanaka, K., Inui, H., Yamaguchi, M. and Otani, S. (2003), "Temperature dependence of thermal expansion and elastic constants of single crystals of $ZrB_2$ and the suitability of $ZrB_2$ as a substrate for GaN film", J. Appl. Phys., 93, 88-93. https://doi.org/10.1063/1.1525404
  20. Popescu, B. and Hodges, D.H. (2000), "On asymptotically correct Timoshenko-like anisotropic beam theory", Int. J. Solids Struct., 37, 535-558. https://doi.org/10.1016/S0020-7683(99)00020-7
  21. Rao, D.M. and Sinha, P.K. (1997), "Finite element coupled thermostructural analysis of composite beams", Comp. Struct., 63, 539-549. https://doi.org/10.1016/S0045-7949(96)00358-6
  22. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, (2nd Edition), CRC Press, Boca Raton, FL, USA.
  23. Reddy, J.N. (2008), An Introduction to Continuum Mechanics, Cambridge University Press, New York, NY, USA.
  24. Soldatos, K.P. and Elishakoff, I. (1992), "A transverse shear and normal deformable orthotropic beam theory", J. Sound Vib., 154, 528-533.
  25. Tanigawa, Y., Murakami, H. and Ootao, Y. (1989), "Transient thermal stress analysis of a laminated composite beam", J. Therm. Stresses, 12, 25-39. https://doi.org/10.1080/01495738908961952
  26. Teng, C., Yu, W. and Chen, M. (2012) "Variational asymptotic homogenization of temperature-dependent heterogeneous materials under finite temperature changes", Int. J. Solids Struct., 49, 2439-2449. https://doi.org/10.1016/j.ijsolstr.2012.05.006
  27. Vidal, P. and Polit, O. (2006), "A thermomechanical finite element for the analysis of rectangular laminated beams", Finite Elem. Anal. Des., 42, 868-883. https://doi.org/10.1016/j.finel.2006.01.005
  28. Wang, Q. and Yu, W. (2011), "Variational asymptotic modeling of the thermal problem of composite beams", Comp. Struct., 93, 2330-2339. https://doi.org/10.1016/j.compstruct.2011.03.021
  29. Wang, Q. and Yu, W. (2013), "A refined model for thermoelastic analysis of initially curved and twisted composite beams", Eng. Struct., 48, 233-244. https://doi.org/10.1016/j.engstruct.2012.09.007
  30. Wikipedia (2011), "Sandwich-structured composite", Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Sandwich-structured_composite&oldid=565387616
  31. Yu, W., Hodges, D.H. and Ho, J.C. (2012), "Variational asymptotic beam sectional analysis - an updated version", Int. J. Eng. Sci., 59, 40-64. https://doi.org/10.1016/j.ijengsci.2012.03.006
  32. Yu, W., Hodges, D.H., Volovoi, V. and Cesnik, C.E.S. (2002), "On Timoshenko-like modeling of initially curved and twisted composite beams", Int. J. Solids Struct., 39, 5101-5121. https://doi.org/10.1016/S0020-7683(02)00399-2

Cited by

  1. Free Vibrations of Damaged Aircraft Structures by Component-Wise Analysis vol.54, pp.10, 2016, https://doi.org/10.2514/1.J054640
  2. Influence of Non-Structural Localized Inertia on Free Vibration Response of Thin-Walled Structures by Variable Kinematic Beam Formulations vol.2014, 2014, https://doi.org/10.1155/2014/141982
  3. Thin-walled beams subjected to load factors and non-structural masses vol.81, 2014, https://doi.org/10.1016/j.ijmecsci.2014.02.015
  4. Recent developments on refined theories for beams with applications vol.2, pp.2, 2015, https://doi.org/10.1299/mer.14-00298
  5. Structural Dynamic Analysis of a Tidal Current Turbine Using Geometrically Exact Beam Theory vol.140, pp.2, 2018, https://doi.org/10.1115/1.4038172
  6. Three-dimensional effective properties of layered composites with imperfect interfaces vol.4, pp.6, 2017, https://doi.org/10.12989/aas.2017.4.6.639