Elastic state of functionally graded curved beam on the plane stress state subject to thermal load

References

• Afshin, A., M. Z. Nejad, and K. Dastani. 2017. Transient thermoelastic analysis of FGM rotating thick cylindrical pressure vessels under arbitrary boundary and initial conditions. Journal of Computational Applied Mechanics 48 (1):15–26. doi:10.22059/JCAMECH.2017.233643.144.
   Web of Science ®Google Scholar
• Arefi, M., and A. H. Soltan Arani. 2018. Higher order shear deformation bending results of a magneto electro thermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments. Mechanics Based Design of Structures and Machines 46 (6):669–92. doi:10.1080/15397734.2018.1525992.
   Web of Science ®Google Scholar
• Arslan, E., and A. N. Eraslan. 2010. Analytical solution to the bending of a nonlinearly hardening wide curved bar. Acta Mechanica 210 (1–2):71–84. doi:10.1007/s00707-009-0195-y.
   Web of Science ®Google Scholar
• Arslan, E., and A. N. Eraslan. 2013. Bending of graded curved bars at elastic limits and beyond. International Journal of Solids and Structures 50 (5):806–14. doi:10.1016/j.ijsolstr.2012.11.016.
   Web of Science ®Google Scholar
• Arslan, E., and W. Mack. 2014. Elastic-plastic states of a radially heated thick-walled cylindrically curved panel. Forschung im Ingenieurwesen 78 (1–2):1–11. doi:10.1007/s10010-014-0170-1.
   Web of Science ®Google Scholar
• Arslan, E., and W. Mack. 2015. Shrink fit with solid inclusion and functionally graded hub. Composite Structures 121:217–24. doi:10.1016/j.compstruct.2014.10.034.
   Web of Science ®Google Scholar
• Arslan, E., W. Mack, and U. Gamer. 2013. Elastic limits of a radially heated thick-walled cylindrically curved panel. Forschung im Ingenieurwesen 77 (1–2):13–23. doi:10.1007/s10010-013-0162-6.
   Web of Science ®Google Scholar
• Awaji, H., and R. Sivakumar. 2001. Temperature and stress distributions in a hollow cylinder of functionally graded material: The case of temperature‐independent material properties. Journal of the American Ceramic Society 84 (5):1059–65. doi:10.1111/j.1151-2916.2001.tb00790.x.
   Web of Science ®Google Scholar
• Birman, V., and L. W. Byrd. 2007. Modeling and analysis of functionally graded materials and structures. Applied Mechanics Reviews 60 (5):195–216. doi:10.1115/1.2777164.
   Web of Science ®Google Scholar
• Dadras, P. 2001. Plane strain elastic–plastic bending of a strain-hardening curved beam. International Journal of Mechanical Sciences 43 (1):39–56. doi:10.1016/S0020-7403(99)00102-2.
   Web of Science ®Google Scholar
• Dehrouyeh-Semnani, A. M. 2017. On boundary conditions for thermally loaded FG beams. International Journal of Engineering Science 119:109–27. doi:10.1016/j.ijengsci.2017.06.017.
   Web of Science ®Google Scholar
• Dehrouyeh-Semnani, A. M. 2018. On the thermally induced non-linear response of functionally graded beams. International Journal of Engineering Science 125:53–74. doi:10.1016/j.ijengsci.2017.12.001.
   Web of Science ®Google Scholar
• Dryden, J. 2007. Bending of inhomogeneous curved bars. International Journal of Solids and Structures 44 (11–12):4158–66. doi:10.1016/j.ijsolstr.2006.11.021.
   Web of Science ®Google Scholar
• Duc, N. D., and H. Van Tung. 2010. Nonlinear response of pressure-loaded functionally graded cylindrical panels with temperature effects. Composite Structures 92 (7):1664–72. doi:10.1016/j.compstruct.2009.11.033.
   Web of Science ®Google Scholar
• Eraslan, A. N., and T. Akis. 2006. On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica 181 (1–2):43–63. doi:10.1007/s00707-005-0276-5.
   Web of Science ®Google Scholar
• Eraslan, A. N., and E. Arslan. 2008. A concise analytical treatment of elastic‐plastic bending of a strain hardening curved beam. ZAMM 88 (8):600–16. doi:10.1002/zamm.200600037.
   Web of Science ®Google Scholar
• Evci, C., and M. Gülgec. 2018. Functionally graded hollow cylinder under pressure and thermal loading: Effect of material parameters on stress and temperature distributions. International Journal of Engineering Science 123:92–108. doi:10.1016/j.ijengsci.2017.11.019.
   Web of Science ®Google Scholar
• Gharibi, M., M. Z. Nejad, and A. Hadi. 2017. Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius. Journal of Computational Applied Mechanics 48 (1):89–98. doi:10.22059/jcamech.2017.233633.143.
   Web of Science ®Google Scholar
• Hadi, A., M. Z. Nejad, and M. Hosseini. 2018. Vibrations of three-dimensionally graded nanobeams. International Journal of Engineering Science 128:12–23. doi:10.1016/j.ijengsci.2018.03.004.
   Web of Science ®Google Scholar
• Hadi, A., M. Z. Nejad, A. Rastgoo, and M. Hosseini. 2018. Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory. Steel and Composite Structures 26 (6):663–72. doi:10.12989/scs.2018.26.6.663.
   Web of Science ®Google Scholar
• Horgan, C. O., and A. M. Chan. 1999. The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. Journal of Elasticity 55 (1):43–59. doi:10.1023/A:1007625401963.
   Web of Science ®Google Scholar
• Hosseini, M., M. Shishesaz, and A. Hadi. 2019. Thermoelastic analysis of rotating functionally graded micro/nanodisks of variable thickness. Thin-Walled Structures 134:508–23. doi:10.1016/j.tws.2018.10.030.
   Web of Science ®Google Scholar
• Hosseini, M., M. Shishesaz, K. N. Tahan, and A. Hadi. 2016. Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials. International Journal of Engineering Science 109:29–53. doi:10.1016/j.ijengsci.2016.09.002.
   Web of Science ®Google Scholar
• Kiani, Y., M. Shakeri, and M. R. Eslami. 2012. Thermoelastic free vibration and dynamic behavior of an FGM doubly curved panel via the analytical hybrid Laplace–Fourier transformation. Acta Mechanica 223 (6):1199–218. doi:10.1007/s00707-012-0629-9.
   Web of Science ®Google Scholar
• Librescu, L., M. P. Nemeth, J. H. Starnes, and W. Lin. 2000. Nonlinear response of flat and curved panels subjected to thermomechanical loads. Journal of Thermal Stresses 23 (6):549–82. doi:10.1080/01495730050143134.
   Web of Science ®Google Scholar
• Mazarei, Z., M. Z. Nejad, and A. Hadi. 2016. Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials. International Journal of Applied Mechanics 8 (4):1650054. doi:10.1142/S175882511650054X.
   Web of Science ®Google Scholar
• Miyamoto, Y., W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford. 2013. Functionally graded materials: Design, processing and applications. Vol. 5. New York: Springer Science & Business Media.
   Google Scholar
• Moradi, A., A. Yaghootian, M. Jalalvand, and A. Ghanbarzadeh. 2018. Magneto-Thermo mechanical vibration analysis of FG nanoplate embedded on Visco Pasternak foundation. Journal of Computational Applied Mechanics 49 (2):395–407. doi:10.22059/JCAMECH.2018.261764.300.
   Web of Science ®Google Scholar
• Naebe, M., and K. Shirvanimoghaddam. 2016. Functionally graded materials: A review of fabrication and properties. Applied Materials Today 5:223–45. doi:10.1016/j.apmt.2016.10.001.
   Web of Science ®Google Scholar
• Nejad, M. Z., N. Alamzadeh, and A. Hadi. 2018. Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition. Composites Part B: Engineering 154:410–22. doi:10.1016/j.compositesb.2018.09.022.
   Web of Science ®Google Scholar
• Nejad, M. Z., and A. Hadi. 2016. Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams. International Journal of Engineering Science 105:1–11. doi:10.1016/j.ijengsci.2016.04.011.
   Web of Science ®Google Scholar
• Nejad, M. Z., A. Hadi, and A. Farajpour. 2017. Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials. International Journal of Engineering Science 63 (2):161–9. doi:10.12989/sem.2017.63.2.161.
   Google Scholar
• Nejad, M. Z., A. Hadi, A. Omidvari, and A. Rastgoo. 2018. Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen’s non-local elasticity theory. International Journal of Engineering Science 67 (4):417–25. doi:10.12989/sem.2018.67.4.417.
   Google Scholar
• Nejad, M. Z., M. Jabbari, and A. Hadi. 2017. A review of functionally graded thick cylindrical and conical shells. Journal of Computational Applied Mechanics 48 (2):357–70. doi:10.22059/JCAMECH.2017.247963.220.
   Web of Science ®Google Scholar
• Nemat-Alla, M. M., M. H. Ata, M. R. Bayoumi, and W. Khair-Eldeen. 2011. Powder metallurgical fabrication and microstructural investigations of aluminum/steel functionally graded material. Materials Sciences and Applications 2 (12):1708. doi:10.4236/msa.2011.212228.
   Google Scholar
• Noda, N. 1999. Thermal stresses in functionally graded materials. Journal of Thermal Stresses 22 (4–5):477–512. doi:10.1080/014957399280841.
   Web of Science ®Google Scholar
• Peng, X. L., and X. F. Li. 2010. Thermal stress in rotating functionally graded hollow circular disks. Composite Structures 92 (8):1896–904. doi:10.1016/j.compstruct.2010.01.008.
   Web of Science ®Google Scholar
• Shaffer, B. W., and R. N. House. 1955. The elastic-plastic stress distribution within a wide curved bar subjected to pure bending. ASME Transactions of the Journal of Applied Mechanics 22:305.
   Google Scholar
• Shaffer, B. W., and R. N. House. 1957. Displacements in a wide curved bar subjected to pure elastic-plastic bending. ASME Transactions of the Journal of Applied Mechanics 24:447–52.
   Google Scholar
• Shao, Z. S. 2005. Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length. International Journal of Pressure Vessels and Piping 82 (3):155–63. doi:10.1016/j.ijpvp.2004.09.007.
   Web of Science ®Google Scholar
• She, G. L., Y. R. Ren, and K. M. Yan. 2019. On snap-buckling of porous FG curved nanobeams. Acta Astronautica 161:475–84. doi:10.1016/j.actaastro.2019.04.010.
   Web of Science ®Google Scholar
• She, G. L., F. G. Yuan, and Y. R. Ren. 2017. Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory. Applied Mathematical Modelling 47:340–57. doi:Org/10.1016/j.apm.2017.03.014. doi:10.1016/j.apm.2017.03.014.
   Web of Science ®Google Scholar
• Shishesaz, M., M. Hosseini, K. N. Tahan, and A. Hadi. 2017. Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory. Acta Mechanica 228 (12):4141–68. doi:10.1007/s00707-017-1939-8.
   Web of Science ®Google Scholar
• Sobczak, J. J., and L. Drenchev. 2013. Metallic functionally graded materials: A specific class of advanced composites. Journal of Materials Science & Technology 29 (4):297–316. doi:10.1016/j.jmst.2013.02.006.
   Web of Science ®Google Scholar
• Timoshenko, S. P., and J. N. Goodier. 1970. Theory of elasticity. 3rd ed. New York: McGraw-Hill.
   Google Scholar
• Tsiptsis, I. N., and E. J. Sapountzakis. 2018. Isogeometric analysis for the dynamic problem of curved structures including warping effects. Mechanics Based Design of Structures and Machines 46 (1):66–84. doi:10.1080/15397734.2016.1275974.
   Web of Science ®Google Scholar
• Tufekci, E., U. Eroglu, and S. A. Aya. 2016. Exact solution for in-plane static problems of circular beams made of functionally graded materials. Mechanics Based Design of Structures and Machines 44 (4):476–94. doi:10.1080/15397734.2015.1121398.
   Web of Science ®Google Scholar
• Tutuncu, N., and M. Ozturk. 2001. Exact solutions for stresses in functionally graded pressure vessels. Composites Part B: Engineering 32 (8):683–6. doi:10.1016/S1359-8368(01)00041-5.
   Web of Science ®Google Scholar
• Wang, X., X. Liang, and C. Jin. 2017. Accurate dynamic analysis of functionally graded beams under a moving point load. Mechanics Based Design of Structures and Machines 45 (1):76–91. doi:10.1080/15397734.2016.1145060.
   Web of Science ®Google Scholar
• Wang, M., and Y. Liu. 2013. Elasticity solutions for orthotropic functionally graded curved beams. European Journal of Mechanics - A/Solids 37:8–16. doi:10.1016/j.euromechsol.2012.04.005.
   Web of Science ®Google Scholar
• Wang, W.,. Y. Zhou, C. Li, H. Wang, and Y. Zhang. 2019. Dynamic reliability analysis of a cantilever beam during a deterioration process. Mechanics Based Design of Structures and Machines 47 (1):87–101. doi:10.1080/15397734.2018.1525992.
   Web of Science ®Google Scholar
• Zimmerman, R. W., and M. P. Lutz. 1999. Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder. Journal of Thermal Stresses 22 (2):177–88. doi:10.1080/014957399280959.
   Web of Science ®Google Scholar