Analytical and numerical investigation of the critical thermal buckling load in the fixed – fixed and fixed – pinned uniform and compound columns

References

• Akbas, S. D., and T. Kocatürk. 2011. “Post-buckling Analysis of a Simply Supported Beam under Uniform Thermal Loading.” Scientific Research and Essays 6 (4): 1135–1142.
   Google Scholar
• Al-Ansari, L. S. 2012. “Calculating of Natural Frequency of Stepping Cantilever Beam.” International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS 12 (5): 59–68.
   Google Scholar
• AL-ANSARI, L. U. A. Y. S. 2013. “Calculating Static Deflection and Natural Frequency of Stepped Cantilever Beam Using Modified Rayleigh Method.” International Journal of Mechanical and Production Engineering Research and Development (IJMPERD). 3 (4): 113–124.
   Google Scholar
• Al-Ansari, L. S., M. Ali, H. Al-Hajjar, and J. A. Husam. 2018. “Calculating the Natural Frequency of Cantilever Tapered Beam Using Classical Rayleigh, Modified Rayleigh and Finite Element Methods.” International Journal of Engineering & Technology 7 (4): 4866–4872.
   Google Scholar
• Alansari, L. S., H. Z. Zainy, A. A. Yaseen, and M. Aljanabi. 2019. “Calculating the Natural Frequency of Hollow Stepped Cantilever Beam.” International Journal of Mechanical Engineering and Technology (IJMET). Article ID: IJMET_10_01_093.10 (1): 898–914.
   Google Scholar
• Aristizabal-Ochoa, J. D. 2007. “Large Deflection and Post-buckling Behavior of Timoshenko Beam-columns with Semi-rigid Connections Including Shear and Axial Effects.” Journal Engineering Structures 29 (6): 991–1003. doi:10.1016/j.engstruct.2006.07.012.
   Web of Science ®Google Scholar
• Boley, B. A., and J. H. Winner. 1997. Theory of Thermal Stresses, 415–418. New York: Dover.
   Google Scholar
• Chen, B., Y. Gu, G. Zhao, W. Lin, T. Y. P. Chang, and J. S. Kuang. 2003. “Design Optimization for Structural Thermal Buckling.” Journal of Thermal Stresses 26 (5): 479–494. doi:10.1080/713855939.
   Web of Science ®Google Scholar
• Cisternas, J., and P. Holmes. 2002. “Buckling of Extensible Thermoelastic Rods, Math.” Mathematical and Computer Modelling 36 (3): 233–243. doi:10.1016/S0895-7177(02)00122-X.
   Google Scholar
• Coffin, D. W., and F. Bloom. 1999. “Elastica Solution for the Hygrothermal Buckling of a Beam, Int.” International Journal of Non-Linear Mechanics 34 (5): 935–947. doi:10.1016/S0020-7462(98)00067-5.
   Web of Science ®Google Scholar
• Euler, L. 1744. “De Curvis Elasticis, in Methodus Inveniendi Leneas Curva Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Is Operimetrici Lattisimo Sensu Accepti.” Lausannae. 65A (24): 231–297. O. O. Ser. I.
   Google Scholar
• Gauss, R. C., and S. S. Antman. 1984. “Large Thermal Buckling of Non-uniform Beam and Plates.” International Journal of Solids and Structures 20 (11–12): 979–1000. doi:10.1016/0020-7683(84)90085-4.
   Web of Science ®Google Scholar
• Gupta, R. K., J. B. Gunda, G. R. Janardhan, and G. V. Rao. 2009. “Comparative Study of Thermal Post- Buckling Analysis of Uniform Slender & Shear Flexible Columns Using Rigorous Finite Element and Intuitive Formulations, Int.” International Journal of Mechanical Sciences 51 (3): 204–212. doi:10.1016/j.ijmecsci.2009.01.002.
   Web of Science ®Google Scholar
• Gupta, R. K., J. B. Gunda, G. R. Janardhan, and G. V. Rao. 2010a. “Post-buckling Analysis of Composite Beams: Simple and Accurate Closed-form Expressions.” Composite Structures 92 (8): 1947–1956. doi:10.1016/j.compstruct.2009.12.010.
   Web of Science ®Google Scholar
• Gupta, R. K., J. B. Gunda, G. R. Janardhan, and G. V. Rao. 2010b. “Thermal Post Buckling Analysis of Slender Columns Using the Concept of Coupled Displacement Field.” International Journal of Mechanical Sciences 52 (4): 590–594. doi:10.1016/j.ijmecsci.2009.12.005.
   Web of Science ®Google Scholar
• Isaac, M., and D. Ori Lshai. 2006. Engineering Mechanics of Composite Materials. Second Edition ed. OXFORD UNIVERSITY PRESS. UK.
   Google Scholar
• Jankang, C., and W. Rupeng. 1994. “Analysis of the Characteristic of Thermally Expansive Buckling of Elastic Rods.” Mechanics and Practice 16 (3): 23–26.
   Google Scholar
• Jekot, T. 1996. “Nonlinear Problems of Thermal Post Buckling of a Beam.” Journal of Thermal Stresses 19 (4): 359–367. doi:10.1080/01495739608946180.
   Web of Science ®Google Scholar
• Khurmi, R. S. 2008. Strength of Materials – Mechanics of Solids, Multicolor Edition. S. Chand & Company.India .
   Google Scholar
• Li, S.-R., and C.-J. Cheng. 2000. “Analysis of Thermal Post Buckling of Heated Elastic Rods, Appl.” Applied Mathematics and Mechanics 21 (2): 133–140. doi:10.1007/BF02458513.
   Web of Science ®Google Scholar
• Li, S.-R., Y.-H. Zhou, and X. Zheng. 2002. “Thermal Post Buckling of a Heated Elastic Rod with Pinned- Fixed Ends, J.” Journal of Thermal Stresses 25 (1): 45–56. doi:10.1080/014957302753305862.
   Web of Science ®Google Scholar
• Luay, S. A., A. Muhannad, and M. H. Y. Ali. 2012. “Vibration Analysis of Hyper Composite Material Beam Utilizing Shear Deformation and Rotary Inertia Effects.” International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS 12 (4).1122-1137.
   Google Scholar
• Nash, W., and M. C. Potter. 2011. Strength of Materials. Fifth ed. Schaum’s Outline Series, Mc Graw Hill.USA.
   Google Scholar
• Nowinski, J. L. 1978. Theory of Thermal Elasticity with Applications. Groningen, The Netherlands: Sijihoff and Noordhoff Int. Publishers. 547–564
   Google Scholar
• Raju, K. K., and G. V. Rao. 1984. “Thermal Post Buckling Behavior of Tapered Columns.” AIAA Journal 22 (10): 1499–1501. doi:10.2514/3.48590.
   Web of Science ®Google Scholar
• Robert, L. M., and J. A. Untener. 2017. Applied Strength of Materials. Sixth ed. Taylor & Francis Group, LLC.UK.
   Google Scholar
• Song, X., and S.-R. Li. 2007. “Thermal Buckling and Post-buckling of Pinned–fixed Euler–Bernoulli Beams on an Elastic Foundation.” . Mechanics Research Communications 34 (2): 164–171. doi:10.1016/j.mechrescom.2006.06.006.
   Web of Science ®Google Scholar
• Vaz, M. A., J. C. R. Cyrino, and A. C. Neves. 2010. “Initial Thermo- Mechanical Post Buckling of Beams with Temperature-dependent Physical Properties, Int.” International Journal of Non-Linear Mechanics 45 (3): 256–262. doi:10.1016/j.ijnonlinmec.2009.11.006.
   Web of Science ®Google Scholar
• Vaz, M. A., M. S. Nascimento, and R. F. Solano. 2007. “Initial Post-buckling of Elastic Rods Subjected to Thermal Loads and Resting on an Elastic Foundation.” Journal of Thermal Stresses 30 (4): 381–393. doi:10.1080/01495730601146352.
   Web of Science ®Google Scholar
• Vaz, M. A., and R. F. Solano. 2003. “Postbuckling Analysis of Slender Elastic Rod Subjected to Uniform Thermal Loads.” Journal of Thermal Stresses 26 (9): 847–860. doi:10.1080/01495730306293.
   Web of Science ®Google Scholar
• Vaz, M. A., and R. F. Solano. 2004. “Thermal Postbuckling of Slender Elastic Rods with Hinged Ends Constrained by a Linear Spring.” Journal of Thermal Stresses 27 (4): 367–380. doi:10.1080/01495730490427591.
   Web of Science ®Google Scholar
• Zainy, H. Z., L. S. Al-Ansari, M. Ali, H. Al-Hajjar, M. Mahdi, and S. Shareef. 2018. “Analytical and Numerical Approaches for Calculating the Static Deflection of Functionally Graded Beam under Mechanical Load.” International Journal of Engineering & Technology 7 (4): 3889–3896.
   Google Scholar