Heat conduction analysis for irregular functionally graded material geometries using the meshless weighted least-square method with temperature-dependent material properties

References

• J. N. Reddy and C. D. Chin, “Thermomechanical analysis of functionally graded cylinders and plates,” J. Thermal Stresses, vol. 21, no. 6, pp. 593–626, 1998. DOI:10.1080/01495739808956165.
   Web of Science ®Google Scholar
• H. V. Tung, “Nonlinear thermomechanical stability of shear deformable FGM shallow spherical shells resting on elastic foundations with temperature dependent properties,” Compos. Struct., vol. 114, pp. 107–116, 2014. DOI:10.1016/j.compstruct.2014.04.004.
   Web of Science ®Google Scholar
• H. Bagheri, Y. Kiani, and M. R. Eslami, “Asymmetric thermal buckling of temperature dependent annular FGM plates on a partial elastic foundation,” Comput. Math. Appl., vol. 75, no. 5, pp. 1566–1581, 2018. DOI:10.1016/j.camwa.2017.11.021.
   Web of Science ®Google Scholar
• V. N. V. Do and C.-H. Lee, “Thermal buckling analyses of FGM sandwich plates using the improved radial point interpolation mesh-free method,” Compos. Struct., vol. 177, pp. 171–186, 2017. DOI:10.1016/j.compstruct.2017.06.054.
   Web of Science ®Google Scholar
• H.-S. Shen, “Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties,” Int. J. Mech. Sci., vol. 49, no. 4, pp. 466–478, 2007. DOI:10.1016/j.ijmecsci.2006.09.011.
   Web of Science ®Google Scholar
• A. Moosaie and H. Panahi-Kalus, “Thermal stresses in an incompressible FGM spherical shell with temperature-dependent material properties,” Thin Wall. Struct., vol. 120, pp. 215–224, 2017. DOI:10.1016/j.tws.2017.09.005.
   Web of Science ®Google Scholar
• Y. Ootao and M. Ishihara, “Transient thermal stress problem of a functionally graded magneto-electro-thermoelastic hollow cylinder due to a uniform surface heating,” J. Thermal Stresses, vol. 35, no. 6, pp. 517–533, 2012. DOI:10.1080/01495739.2012.674781.
   Web of Science ®Google Scholar
• M. D. Demirbas, “Thermal stress analysis of functionally graded plates with temperature-dependent material properties using theory of elasticity,” Compos. Part B, vol. 131, pp. 100–124, 2017. DOI:10.1016/j.compositesb.2017.08.005.
   Web of Science ®Google Scholar
• I. A. Abbas, “Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties,” Meccanica, vol. 49, no. 7, pp. 1697–1708, 2014. DOI:10.1007/s11012-014-9948-3.
   Web of Science ®Google Scholar
• K. Yang, H.-F. Peng, J. Wang, C.-H. Xing, and X.-W. Gao, “Radial integration BEM for solving transient nonlinear heat conduction with temperature-dependent conductivity,” Int. J. Heat Mass Transf., vol. 108, pp. 1551–1559, 2017. DOI:10.1016/j.ijheatmasstransfer.2017.01.030.
   Web of Science ®Google Scholar
• K. Yang, J. Wang, J.-M. Du, H.-F. Peng, and X.-W. Gao, “Radial integration boundary element method for nonlinear heat conduction problems with temperature-dependent conductivity,” Int. J. Heat Mass Transf., vol. 104, pp. 1145–1151, 2017. DOI:10.1016/j.ijheatmasstransfer.2016.09.015.
   Web of Science ®Google Scholar
• K. Yang, W-z Feng, J. Wang, and X-w Gao, “RIBEM for 2D and 3D nonlinear heat conduction with temperature dependent conductivity,” Eng. Anal. Boundary Elements, vol. 87, pp. 1–8, 2018. DOI:10.1016/j.enganabound.2017.11.001.
   Web of Science ®Google Scholar
• M. Cui, B. B. Xu, W. Z. Feng, Y. W. Zhang, X. W. Gao, and H. F. Peng, “A radial integration boundary element method for solving transient heat conduction problems with heat sources and variable thermal conductivity,” Numer. Heat Transf. Part B, vol. 73, no. 1, pp. 1–18, 2018. DOI:10.1080/10407790.2017.1420319.
   Web of Science ®Google Scholar
• A. Karageorghis and D. Lesnic, “Steady-state nonlinear heat conduction in composite materials using the method of fundamental solutions,” Comput. Methods Appl. Mech. Eng., vol. 197, no. 33-40, pp. 3122–3137, 2008. DOI:10.1016/j.cma.2008.02.011.
   Web of Science ®Google Scholar
• A. Karageorghis and D. Lesnic, “The method of fundamental solutions for steady-state heat conduction in nonlinear materials,” Commun. Comput. Phys., vol. 4, pp. 417–421, 2008.
   Web of Science ®Google Scholar
• S. Jafari Mehrabadi and B. Sobhani Aragh, “On the thermal analysis of 2-D temperature-dependent functionally graded open cylindrical shells,” Compos. Struct., vol. 96, pp. 773–785, 2013. DOI:10.1016/j.compstruct.2012.09.036.
   Web of Science ®Google Scholar
• M. Sobhy, “Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations,” Int. J. Appl. Mech., vol. 07, no. 06, pp. 1550082, 2015. DOI:10.1142/S1758825115500829.
   Google Scholar
• M. Mierzwiczak, W. Chen, and Z.-J. Fu, “The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity,” Int. J. Heat Mass Transf., vol. 91, pp. 205–217, 2015. DOI:10.1016/j.ijheatmasstransfer.2015.07.051.
   Web of Science ®Google Scholar
• K. R. Bagnall, Y. S. Muzychka, and E. N. Wang, “Application of the Kirchhoff transform to thermal spreading problems with convection boundary conditions,” IEEE Trans. Compon. Packag. Manufact. Technol., vol. 4, no. 3, pp. 408–420, 2014. DOI:10.1109/TCPMT.2013.2292584.
   Web of Science ®Google Scholar
• A. Khosravifard, M. R. Hematiyan, and L. Marin, “Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method,” Appl. Math. Modelling, vol. 35, no. 9, pp. 4157–4174, 2011. DOI:10.1016/j.apm.2011.02.039.
   Web of Science ®Google Scholar
• A. Singh, I. V. Singh, and R. Prakash, “Meshless analysis of unsteady-state heat transfer in semi-infinite solid with temperature-dependent thermal conductivity,” Int. Commun. Heat Mass Transfer, vol. 33, no. 2, pp. 231–239, 2006. DOI:10.1016/j.icheatmasstransfer.2005.10.008.
   Web of Science ®Google Scholar
• A. Singh, I. V. Singh, R. Prakash, “Numerical solution of temperature-dependent thermal conductivity problems using a meshless method,” Numer. Heat Transf. Part A, vol. 50, no. 2, pp. 125–145, 2006. DOI:10.1080/10407780500507111.
   Web of Science ®Google Scholar
• M. H. Shojaeefard and A. Najibi, “Nonlinear transient heat conduction analysis of hollow thick temperature-dependent 2D-FGM cylinders with finite length using numerical method,” J. Mech. Sci. Technol., vol. 28, no. 9, pp. 3825–3835, 2014. DOI:10.1007/s12206-014-0846-3.
   Web of Science ®Google Scholar
• D.-S. Yang et al., “Calculating the multi-domain transient heat conduction with heat source problem by virtual boundary meshfree Galerkin method,” Numer. Heat Transf. Part B, vol. 74, no. 1, pp. 465–479, 2018. DOI:10.1080/10407790.2018.1505091.
   Web of Science ®Google Scholar
• M. Shariyat, M. Khaghani, and S. M. H. Lavasani, “Nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick FGM cylinders with temperature-dependent material properties,” Eur. J. Mech. A Solids, vol. 29, no. 3, pp. 378–391, 2010. DOI:10.1016/j.euromechsol.2009.10.007.
   Web of Science ®Google Scholar
• F. Mohebbi and M. Sellier, “Identification of space- and temperature-dependent heat transfer coefficient,” Int. J. Thermal Sci., vol. 128, pp. 28–37, 2018. DOI:10.1016/j.ijthermalsci.2018.02.007.
   Web of Science ®Google Scholar
• N. Afrin, Z. C. Feng, Y. Zhang, and J. K. Chen, “Inverse estimation of front surface temperature of a locally heated plate with temperature-dependent conductivity via Kirchhoff transformation,” Int. J. Thermal Sci., vol. 69, pp. 53–60, 2013. DOI:10.1016/j.ijthermalsci.2013.02.004.
   Web of Science ®Google Scholar
• D. G. Yang, X. X. Yue, and Q. B. Yang, “Virtual boundary element method in conjunction with conjugate gradient algorithm for three-dimensional inverse heat conduction problems,” Numer. Heat Transf. Part B, vol. 72, no. 6, pp. 421–430, 2017. DOI:10.1080/10407790.2017.1409525.
   Web of Science ®Google Scholar
• Y. Liu, X. Zhang, and M. W. Lu, “Meshless least-squares method for solving the steady-state heat conduction equation,” Tsinghua Sci. Technol., vol. 10, no. 1, pp. 61–66, 2005. DOI:10.1016/S1007-0214(05)70010-9.
   Google Scholar
• Y. Liu, X. Zhang, and M. W. Lu, “A meshless method based on least-squares approach for steady-and unsteady-state heat conduction problems,” Numer. Heat Transf. Part B, vol. 47, no. 3, pp. 257–275, 2005. DOI:10.1080/10407790590901648.
   Web of Science ®Google Scholar
• H. M. Zhou, Z. G. Liu, and B. H. Lu, “Heat conduction analysis of heterogeneous objects based on multi-color distance field,” Mater. Des., vol. 31, pp. 3331–3338, 2010. DOI:10.1016/j.matdes.2010.02.001.
   Web of Science ®Google Scholar
• H. M. Zhou, W. H. Zhou, G. Qin, Z. Y. Wang, and P. M. Ming, “Transient heat conduction analysis for distance-field-based irregular geometries using the meshless weighted least-square method,” Numer. Heat Transf. Part B, vol. 71, no. 5, pp. 456–466, 2017. DOI:10.1080/10407790.2016.1265332.
   Web of Science ®Google Scholar
• G. Kirchhoff, Vorlesungen Uber die Theorie der Varme. Leipzig, Germany: Teubner, 1894, pp. 1–13.
   Google Scholar
• Z.-J. Fu, W. Chen, and Q. Qin, “Three boundary meshless methods for heat conduction analysis in nonlinear FGMs with Kirchhoff and Laplace transformation,” Adv. Appl. Math. Mech., vol. 4, pp. 519–542, 2012. DOI:10.4208/aamm.10-m1170.
   Web of Science ®Google Scholar