Hybrid Trefftz finite element method for heat conduction in cylindrical composite laminates

References

• I. H. Akcay and I. Kaynak, “Analysis of multilayered composite cylinders under thermal loading,” J. Reinf. Plast. Comp., vol. 24, no. 11, pp. 1169–1179, 2005. DOI: 10.1177/0731684405048840.
   Web of Science ®Google Scholar
• B. Yang and S. Liu, “Closed-form analytical solutions of transient heat conduction in hollow composite cylinders with any number of layers,” Int. J. Heat Mass Tran., vol. 108, pp. 907–917, 2017. DOI: 10.1016/j.ijheatmasstransfer.2016.12.020.
   Web of Science ®Google Scholar
• M. Norouzi, A. A. Delouei and M. Seilsepour, “A general exact solution for heat conduction in multilayer spherical composite laminates,” Compos. Struct., vol. 106, pp. 288–295, 2013. DOI: 10.1016/j.compstruct.2013.06.005.
   Web of Science ®Google Scholar
• A. K. Mishra and S. Chakraborty, “Development of a finite element model updating technique for estimation of constituent level elastic parameters of FRP plates,” Appl. Math. Comput., vol. 258, pp. 84–94, 2015. DOI: 10.1016/j.amc.2015.02.003.
   Web of Science ®Google Scholar
• S. Kundu, A. Kumari and S. Gupta, “Three-dimensional Green’s function approach for analysis of dispersion and attenuation curve in fibre-reinforced heterogeneous viscoelastic layer due to a point source,” Appl. Math. Comput., vol. 338, pp. 387–399, 2018. DOI: 10.1016/j.amc.2018.04.011.
   Web of Science ®Google Scholar
• M. R. Kulkarni and R. P. Brady, “A model of global thermal conductivity in laminated carbon/carbon composites,” Compos. Sci. Technol., vol. 57, no. 3, pp. 277–285, 1997. DOI: 10.1016/S0266-3538(96)00116-9.
   Web of Science ®Google Scholar
• Suneet, Singh, Prashant K., Jain, Rizwan-uddin, Rizwan-uddin, Analytical solution to transient heat conduction in polar coordinates with multiple layers in radial direction. Int. J. Therm. Sci., 3. 47:261–273 (2008). DOI: 10.1016/j.ijthermalsci.2007.01.031.
   Web of Science ®Google Scholar
• M. H. Kayhani, M. Shariati, M. Nourozi and M. K. Demneh, “Exact solution of conductive heat transfer in cylindrical composite laminate,” Heat Mass Transf., vol. 46, no. 1, pp. 83–94, 2009. DOI: 10.1007/s00231-009-0546-1.
   Web of Science ®Google Scholar
• M. H. Kayhani, M. Norouzi and A. A. Delouei, “A general analytical solution for heat conduction in cylindrical multilayer composite laminates,” Int. J. Therm. Sci., vol. 52, pp. 73–82, 2012. DOI: 10.1016/j.ijthermalsci.2011.09.002.
   Web of Science ®Google Scholar
• M. Norouzi, S. M. R. Niya, M. H. Kayhani, M. Shariati, M. K. Demneh and M. S. Naghavi, “Exact solution of unsteady conductive heat transfer in cylindrical composite laminates,” Heat Mass Tran., vol. 46, pp. 83–94, 2012.
   Google Scholar
• A. A. Delouei, M. H. Kayhani and M. Norouzi, “Exact analytical solution of unsteady axi-symmetric conductive heat transfer in cylindrical orthotropic composite laminates,” Int. J. Heat Mass Tran., vol. 55, no. 15-16, pp. 4427–4436, 2012. DOI: 10.1016/j.ijheatmasstransfer.2012.04.012.
   Web of Science ®Google Scholar
• N. D. Milošević and M. Raynaud, “Analytical solution of transient heat conduction in a two-layer anisotropic cylindrical slab excited superficially by a short laser pulse,” Int. J. Heat Mass Tran., vol. 47, no. 8-9, pp. 1627–1641, 2004. DOI: 10.1016/j.ijheatmasstransfer.2003.10.023.
   Web of Science ®Google Scholar
• D. Chakravorty, J. N. Bandyopadhyay and P. K. Sinha, “Finite element free vibration analysis of point supported laminated composite cylindrical shells,” J. Sound Vib., vol. 181, no. 1, pp. 43–52, 1995. DOI: 10.1006/jsvi.1995.0124.
   Web of Science ®Google Scholar
• B. P. Patel, K. K. Shukla and Y. Nath, “Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells,” Compos. Struct., vol. 71, no. 1, pp. 101–114, 2005. DOI: 10.1016/j.compstruct.2004.09.030.
   Web of Science ®Google Scholar
• L. Zhang, J. M. Zhao and L. H. Liu, “Finite element approach for radiative transfer in multi-layer graded index cylindrical medium with Fresnel surfaces,” J. Quant. Spectrosc. RA., vol. 111, no. 3, pp. 420–432, 2010. DOI: 10.1016/j.jqsrt.2009.09.011.
   Web of Science ®Google Scholar
• J. Jirousek and N. Leon, “A powerful finite element for plate bending,” Comput. Method. Appl. Mech., vol. 12, no. 1, pp. 77–96, 1977. DOI: 10.1016/0045-7825(77)90052-4.
   Web of Science ®Google Scholar
• M. R. Akella and G. R. Kotamraju, “Trefftz indirect method applied to nonlinear potential problems,” Eng. Anal. Bound. Elem., vol. 24, no. 6, pp. 459–465, 2000. DOI: 10.1016/S0955-7997(00)00023-0.
   Web of Science ®Google Scholar
• K. Y. Wang, L. Q. Zhang and P. C. Li, “A four-node hybrid-Trefftz annular element for analysis of axisymmetric potential problems,” Finite Elem. Anal. Des., vol. 60, pp. 49–56, 2012. DOI: 10.1016/j.finel.2012.06.002.
   Web of Science ®Google Scholar
• Z. N. Xia, K. Y. Wang and F. Y. Ge, “Special hole elements for simulating the heat conduction in two-dimensional cellular materials,” Compos. Struct., vol. 246, pp. 112383, 2020. DOI: 10.1016/j.compstruct.2020.112383.
   Web of Science ®Google Scholar
• J. C. Zhou, K. Y. Wang, P. C. Li and X. D. Miao, “Hybrid fundamental solution based finite element method for axisymmetric potential problems,” Eng. Anal. Bound. Elem., vol. 91, pp. 82–91, 2018. DOI: 10.1016/j.enganabound.2018.03.009.
   Web of Science ®Google Scholar
• J. C. Zhou, K. Y. Wang and P. C. Li, “Hybrid fundamental solution based finite element method for axisymmetric potential problems with arbitrary boudnary conditions,” Comput. Struct., vol. 212, pp. 72–85, 2019. DOI: 10.1016/j.compstruc.2018.10.012.
   Web of Science ®Google Scholar
• J. Jirousek and A. Venkatesh, “Hybrid Trefftz plane elasticity elements with p-method capabilities,” Int. J. Numer. Meth. Eng., vol. 35, no. 7, pp. 1443–1472, 1992. DOI: 10.1002/nme.1620350705.
   Web of Science ®Google Scholar
• J. T. Chen, Y. T. Lee and S. C. Shieh, “Revisit of two classical elasticity problems by using the Trefftz method,” Eng. Anal. Bound. Elem., vol. 33, no. 6, pp. 890–895, 2009. DOI: 10.1016/j.enganabound.2008.12.003.
   Web of Science ®Google Scholar
• C. O. D. Souza, “A hybrid-Trefftz formulation for plane elasticity with selective enrichment of the approximations,” Int. J. Numer. Method Biomed. Eng., vol. 27, pp. 785–804, 2011. DOI: 10.1002/cnm.1334.
   Web of Science ®Google Scholar
• A. Maciąg, “Solving thermoelasticity problems by means of Trefftz functions,” Comput. Assist. Mech. Eng. Sci., vol. 16, pp. 193–208, 2017.
   Google Scholar
• Q. H. Qin, “Hybrid Trefftz finite-element approach for plate bending on an elastic foundation,” Appl. Math. Model., vol. 18, no. 6, pp. 334–339, 1994. DOI: 10.1016/0307-904X(94)90357-3.
   Web of Science ®Google Scholar
• P. L. Bishay and S. N. Atluri, “Trefftz-Lekhnitskii Grains (TLGs) for efficient direct numerical simulation (DNS) of the micro/meso mechanics of porous piezoelectric materials,” Comput. Mater. Sci., vol. 83, pp. 235–249, 2014. DOI: 10.1016/j.commatsci.2013.10.038.
   Web of Science ®Google Scholar
• P. L. Bishay, A. Alotaibi and S. N. Atluri, “Multi-region Trefftz collocation grains (MTCGs) for modeling piezoelectric composite and porous materials in direct and inverse problems,” J. Mech. Mater. Struct., vol. 9, no. 3, pp. 287–312, 2014. DOI: 10.2140/jomms.2014.9.287.
   Web of Science ®Google Scholar
• P. L. Bishay, L. Dong and S. N. Atluri, “Multi-physics computational grains (MPCGs) for direct numerical simulation (DNS) of piezoelectric composite/porous materials and structures,” Comput. Mech., vol. 54, no. 5, pp. 1129–1139, 2014. DOI: 10.1007/s00466-014-1044-y.
   Web of Science ®Google Scholar
• H. Wang and Q. H. Qin, “A new special coating/fiber element for analyzing effect of interface on thermal conductivity of composites,” Appl. Math. Comput., vol. 268, pp. 311–321, 2015. DOI: 10.1016/j.amc.2015.06.077.
   Web of Science ®Google Scholar
• Z. She, K. Y. Wang and P. C. Li, “Hybrid Trefftz polygonal elements for heat conduction problems with inclusions/voids,” Comput. Math. Appl., vol. 78, no. 6, pp. 1978–1992, 2019. DOI: 10.1016/j.camwa.2019.03.032.
   Web of Science ®Google Scholar
• Z. She, K. Y. Wang and P. C. Li, “Thermal analysis of multilayer coated fiber-reinforced composites by the hybrid Trefftz finite element method,” Compos. Struct., vol. 224, pp. 110992, 2019. DOI: 10.1016/j.compstruct.2019.110992.
   Web of Science ®Google Scholar
• S. Natarajan, A. K. R. Kumar, S. Bordas and E. Atroshchenko, “Trefftz polygonal finite element for linear elasticity: convergence, accuracy, and properties,” Asia. Pac. J. Comput. Eng., vol. 4, pp. 1–17, 2017.
   Google Scholar
• T. B. Lewis and L. E. Nielsen, “Dynamic mechanical properties of particulate-filled polymers,” J. Appl. Polym. Sci., vol. 14, no. 6, pp. 1449–1471, 1970. DOI: 10.1002/app.1970.070140604.
   Web of Science ®Google Scholar
• Z. W. Zhang, “Transient Bioheat Transfer Analysis in Biological Tissues by Fundamental-Solution-Based Numerical Methods,” Master Thesis, 2015. The Australian National University, Melbourne, VIC.
   Google Scholar