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Analysis of Cross Ply Laminated Beams Under Partial Heating

Published online by Cambridge University Press:  12 May 2016

A. A. Khdeir  and
O. J. Aldraihem
A. A. Khdeir*
Affiliation:
Mechanical Engineering DepartmentKing Saud UniversityRiyadh, Kingdom of Saudi Arabia
O. J. Aldraihem
Affiliation:
Mechanical Engineering DepartmentKing Saud UniversityRiyadh, Kingdom of Saudi Arabia
*
*Corresponding author ([email protected])
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Abstract

Thermal deformations in symmetric and antisymmetric cross-ply laminated beams subjected to partial heating are investigated. Some regions of the beam are subjected to thermal loads and the others are thermally unloaded (ΔT = 0). The thermal field is expressed in terms of Heaviside discontinuity functions. The state space approach along with Jordan canonical form is used to generate exact solutions for the thermoelastic response of beams for arbitrary boundary conditions. A first order shear deformation theory is used in the analysis. Deflections are computed for beams subjected to partial heating with various lamination schemes and boundary conditions undergoing uniform and linearly varying temperature through the thickness. Exact thermal deflection curves are presented for beams under step-wise varying temperature field. The solutions presented in this study can readily be used to investigate the thermoelastic behavior of narrow chip-substrate structure, laminated member in laser cutting, composite link in hypersonic vehicle, and etc.

Keywords

Thermoelastic responseCross ply laminatesPartial heatingAnalytical solutions
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 147 - 155
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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References

1. Akarapu, R., Li, B. Q. and Segall, A., “A Thermal Stress and Failure Model for Laser Cutting and Forming Operations,” Journal of Failure Analysis and Prevention, 4, pp. 51–62 (2004).Google Scholar
2. Wu, L. and Wang, H., “Thermoelastic Solutions for Multilayered Electronic Assemblies,” Thin Solid Films, 510, pp. 203–212 (2006).Google Scholar
3. Ko, W. L., Thermal Buckling Analysis of Rectangular Panels Subjected to Humped Temperature Profile Heating, NASA/TP-2004-212041 (2004).Google Scholar
4. Rao, D. M. and Sinha, P. K., “Finite Element Coupled Thermostructural Analysis of Composite Beams,” Computers & Structures, 63, pp. 539–549 (1997).Google Scholar
5. Khdeir, A. A. and Reddy, J. N., “Jordan Canonical Form Solution for Thermally Induced Deformations of Cross-Ply Laminated Composite Beams,” Journal of Thermal Stresses, 22, pp. 331–346 (1999).Google Scholar
6. Rivera, J. E. M. and Oquendo, H. P., “The Transmission Problem for Thermoelastic Beams,” Journal of Thermal Stresses, 24, pp. 1137–1158 (2001).CrossRefGoogle Scholar
7. Sayman, O., “Elastic-Plastic Thermal Stress Analysis in Aluminum Metal-Matrix Composite Beam: Analytic Solution,” Journal of Thermal Stresses, 25, pp. 69–82 (2002).Google Scholar
8. Callioglu, H., Tarakcilar, A. R. and Bektas, N. B., “Elastic-Plastic Stress Analysis of Laminated Composite Beams Under Linear Temperature Distribution,” Journal of Thermal Stresses, 27, pp. 1075–1088 (2004).Google Scholar
9. Sakata, S., Ashida, F. and Zako, M., “A Layout Optimization of Beam Reinforcements to Decrease Thermal Deformation of Beam Structures,” Journal of Thermal Stresses, 25, pp. 1081–1101 (2002).Google Scholar
10. Li, S. and Zhou, Y., “Geometrically Nonlinear Analysis of Timoshenko Beams Under Thermomechanical Loadings,” Journal of Thermal Stresses, 26, pp. 861–872 (2003).Google Scholar
11. Li, S. and Song, X., “Large Thermal Deflections of Timoshenko Beams Under Transversely Nonuniform Temperature Rise,” Mechanics Research Communications, 33, pp. 84–92 (2006).Google Scholar
12. Kapuria, S., Dumir, P. C. and Ahmed, A., “An Efficient Higher Order Zigzag Theory for Composite and Sandwich Beams Subjected to Thermal Loading,” International Journal of Solids and Structures, 40, pp. 6613–6631 (2003).Google Scholar
13. Kapuria, S., Ahmed, A. and Dumir, P. C., “Coupled Consistent Third-Order Theory for Hybrid Piezoelectric Beams Under Thermal Loads,” Journal of Thermal Stresses, 27, pp. 405–424 (2004).Google Scholar
14. Kapuria, S. and Alam, N., “Exact 2D Solution and Assessment of a 1D Zigzag Theory for Vibration of Thermally Stressed Hybrid Beams,” Journal of Thermal Stresses, 28, pp. 943–963 (2005).Google Scholar
15. Kapuria, S. and Alam, N., “Coupled Efficient Zigzag Finite Element Analysis of Piezoelectric Hybrid Beams Under Thermal Loads,” Journal of Thermal Stresses, 29, pp. 553–583 (2006).CrossRefGoogle Scholar
16. Aydogdu, M., “Thermal Buckling Analysis of Cross-Ply Laminated Composite Beams with General Boundary Conditions,” Composite Science and Technology, 67, pp. 1096–1104 (2007).Google Scholar
17. Fu, Y., Chen, Y. and Zhang, P., “Thermal Buckling Analysis of Functionally Graded Beam with Longitudinal Crack,” Meccanica, 48, pp. 1227–1237 (2013).Google Scholar
18. Zhang, D. G., “Thermal Post-Buckling and Nonlinear Vibration Analysis of FGM Beams Based on Physical Neutral Surface and High Order Shear Deformation Theory,” Meccanica, 49, pp. 283–293 (2014).Google Scholar
19. Arantes, S. and Rivera, J., “Exponential Decay for a Thermoelastic Beam Between Two Stops,” Journal of Thermal Stresses, 31, pp. 537–556 (2008).CrossRefGoogle Scholar
20. Syed, K. A., Su, C. W. and Chan, W. S., “Analysis of Fiber-Reinforced Composite Beams Under Temperature Environment,” Journal of Thermal Stresses, 32, pp. 311–321 (2009).Google Scholar
21. Wang, Q. and Yu, W., “Variational-Asymptotic Modeling of the Thermoelastic Behavior of Composite Beams,” Composite Structures, 93, pp. 2330–2339 (2011).Google Scholar
22. Pourrostami, H., Zohoor, H. and Kargarnovin, M., “Development, Modeling and Deflection Analysis of Hybrid Micro Actuator with Integrated Thermal and Piezoelectric Actuation,” Meccanica, 48, pp. 1081–1091 (2013).Google Scholar
23. Elsibai, K. A. and Youssef, H. M., “State-Space Approach to Vibration of Gold Nano-Beam Induced by Ramp Type Heating Without Energy Dissipation in Femtoseconds Scale,” Journal of Thermal Stresses, 34, pp. 244–263 (2011).Google Scholar
24. Sharma, J. N., “Thermoelastic Damping and Frequency Shift in Micro/Nanoscale Anisotropic Beams,” Journal of Thermal Stresses, 34, pp. 650–666 (2011).Google Scholar
25. Boley, B. A. and Weiner, J. H., Theory of Thermal Stresses, Robert E. Krieger Publishing Company, Inc. Malabar (1985).Google Scholar
26. Brogan, W. L., Modern Control Theory, Prentice-Hall International, Inc. Englewood Cliffs, New Jersey (1991).Google Scholar
27. Basaran, C. and Wen, Y., “Analysis of Multilayered Microelectronic Packaging Under Thermal Gradient Loading,” IEEE Transactions on Components and Packaging Technologies, 29, pp. 850–855 (2006).Google Scholar
28. Wen, Y. and Basaran, C., “An Analytical Model for Thermal Stress Analysis of Multi-Layered Microelectronic Packaging,” Mechanics of Materials, 36, pp. 369–385 (2004).Google Scholar
29. Herakovich, C. T., Mechanics of Fibrous Composites, John Wiley & Sons, New Jersey (1998).Google Scholar