A mixed isogeometric analysis and control volume approach for heat transfer analysis of nonuniformly heated plates

References

• N. Liu, P. Plucinsky, and A. E. Jeffers, “Combining load-controlled and displacement-controlled algorithms to model thermal-mechanical snap-through instabilities in structures,” J. Eng. Mech., vol. 143, no. 8, pp. 04017051, 2017. DOI:10.1061/(ASCE)EM.1943-7889.0001263.
   Web of Science ®Google Scholar
• K. B. McGrattan, and G. P. Forney Fire dynamics simulator (version 4). Washington, DC: National Institute of Standards and Technology, 2014. Available: http://dx.doi.org/10.6028/nist.sp.1019.
   Google Scholar
• K. S. Surana and P. Kalim, “Isoparametric axisymmetric shell elements with temperature gradients for heat conduction,” Comput. Struct., vol. 23, no. 2, pp. 279–289, 1986. DOI:10.1016/0045-7949(86)90219-1.
   Web of Science ®Google Scholar
• K. S. Surana and R. K. Phillips, “Three dimensional curved shell finite elements for heat conduction,” Comput. Struct., vol. 25, no. 5, pp. 775–785, 1987. DOI:10.1016/0045-7949(87)90169-6.
   Web of Science ®Google Scholar
• K. S. Surana and N. J. Orth, “Axisymmetric shell elements for heat conduction with p-approximation in the thickness direction,” Comput. Struct., vol. 33, no. 3, pp. 689–705, 1989. DOI:10.1016/0045-7949(89)90243-5.
   Web of Science ®Google Scholar
• K. S. Surana and G. Abusaleh, “Curved shell elements for heat conduction with p-approximation in the shell thickness direction,” Comput. Struct., vol. 34, no. 6, pp. 861–880, 1990. DOI:10.1016/0045-7949(90)90357-8.
   Web of Science ®Google Scholar
• K. S. Surana and N. J. Orth, “Three-dimensional curved shell element based on completely hierarchical p-approximation for heat conduction in laminated composites,” Comput. Struct., vol. 43, no. 3, pp. 477–494, 1992. DOI:10.1016/0045-7949(92)90282-5.
   Web of Science ®Google Scholar
• J. H. Liu and K. S. Surana, “Piecewise hierarchical p-version axisymmetric shell element for geometrically nonlinear behavior of laminated composites,” Comput. Struct., vol. 55, no. 1, pp. 67–84, 1995. DOI:10.1016/0045-7949(94)00500-3.
   Web of Science ®Google Scholar
• A. K. Noor and W. S. Burton, “Steady-state heat conduction in multilayered composite plates and shells,” Comput. Struct., vol. 39, no. 1-2, pp. 185–193, 1991. DOI:10.1016/0045-7949(91)90086-2.
   Web of Science ®Google Scholar
• N. Mukherjee, and P. K. Sinha, “A comparative finite element heat conduction analysis of laminated composite plates,” Comput. Struct., vol. 52, no. 3, pp. 505–510, 1994. DOI:10.1016/0045-7949(94)90236-4.
   Web of Science ®Google Scholar
• J. Noack, R. Rolfes, and J. Tessmer, “New layerwise theories and finite elements for efficient thermal analysis of hybrid structures,” Comput. Struct., vol. 81, no. 26-27, pp. 2525–2538, 2003. DOI:10.1016/S0045-7949(03)00300-6.
   Web of Science ®Google Scholar
• A. E. Jeffers, “Heat transfer element for modeling the thermal response of non-uniformly heated plates,” Finite Elem. Anal. Des., vol. 63, pp. 62–68, 2013. DOI:10.1016/j.finel.2012.08.009.
   Web of Science ®Google Scholar
• A. E. Jeffers, “Triangular shell heat transfer element for the thermal analysis of nonuniformly heated structures,” J. Struct. Eng., vol. 142, no. 1, pp. 04015084, 2016. DOI:10.1061/(ASCE)ST.1943-541X.0001335.
   Web of Science ®Google Scholar
• A. E. Jeffers and P. A. Beata, “Generalized shell heat transfer element for modeling the thermal response of non-uniformly heated structures,” Finite Elem. Anal. Des., vol. 83, pp. 58–67, 2014. DOI:10.1016/j.finel.2014.01.003.
   Web of Science ®Google Scholar
• T. J. R. Hughes, J. A. Cottrell, and Y. Bazilevs, “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement,” Comput. Methods Appl. Mech. Eng., vol. 194, no. 39–41, pp. 4135–4195, 2005. DOI:10.1016/j.cma.2004.10.008.
   Web of Science ®Google Scholar
• N. Liu, and A. E. Jeffers, “Adaptive isogeometric analysis in structural frames using a layer-based discretization to model spread of plasticity,” Comput. Struct., vol. 196, pp. 1–11, 2018. DOI:10.1016/j.compstruc.2017.10.016.
   Web of Science ®Google Scholar
• N. Liu and A. E. Jeffers, “Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory,” Compos. Struct., vol. 176, pp. 143–153, 2017. DOI:10.1016/j.compstruct.2017.05.037.
   Web of Science ®Google Scholar
• N. Liu and A. E. Jeffers, “A geometrically exact isogeometric Kirchhoff plate: Feature-preserving automatic meshing and C1 rational triangular Bézier spline discretizations,” Int. J. Numer. Methods Eng., vol. 115, no. 3, pp. 395–409, 2018. DOI:10.1002/nme.5809.
   Web of Science ®Google Scholar
• Y. Bazilevs et al., “Isogeometric analysis using T-splines,” Comput. Methods Appl. Mech. Eng., vol. 199, no. 5-8, pp. 229–263, 2010. DOI:10.1016/j.cma.2009.02.036.
   Web of Science ®Google Scholar
• N. Liu and A. E. Jeffers, “Rational Bézier triangles for the analysis of isogeometric higher-order gradient damage models,” presented at 13th World Congress on Computational Mechanics (WCCM XIII) and 2nd Pan American Congress on Computational Mechanics (PANACM II), New York City, NY, USA, Jul. 22–27, 2018.
   Google Scholar
• N. Liu, “Non-uniform rational b-splines and rational Bezier triangles for isogeometric analysis of structural applications,” Ph.D. dissertation, University of Michigan, 2018.
   Google Scholar
• M. J. Borden, M. A. Scott, J. A. Evans, and T. Hughes, “Isogeometric finite element data structures based on Bézier extraction of NURBS,” Int. J. Numer. Methods Eng., vol. 87, no. 1–5, pp. 15–47, 2011. DOI:10.1002/nme.2968.
   Web of Science ®Google Scholar
• X. Yu and A. E. Jeffers, “A comparison of subcycling algorithms for bridging disparities in temporal scale between the fire and solid domains,” Fire Saf. J., vol. 59, pp. 55–61, 2013. DOI:10.1016/j.firesaf.2013.03.011.
   Web of Science ®Google Scholar
• P. A. Beata and A. E. Jeffers, “Spatial homogenization algorithm for bridging disparities in scale between the fire and solid domains,” Fire Saf. J., vol. 76, pp. 19–30, 2015. DOI:10.1016/j.firesaf.2015.05.008.
   Web of Science ®Google Scholar
• P. A. Beata, Computational Approaches to Fire-structure Interaction and Real-time Fire Monitoring, Ph.D. dissertation, University of Michigan, Ann Arbor, MI, USA, 2017.
   Google Scholar
• Q. Liu and P. Ming, “A high-order control volume finite element method for 3-D transient heat conduction analysis of multilayer functionally graded materials,” Numer. Heat Transf. Part B, vol. 73, no. 6, pp. 363–385, 2018. DOI:10.1080/10407790.2018.1470425.
   Web of Science ®Google Scholar
• D. P. Zielinski and V. R. Voller, “A control volume finite element method with spines for solutions of fractional heat conduction equations,” Numer. Heat Transf. Part B, vol. 70, no. 6, pp. 503–516, 2016. DOI:10.1080/10407790.2016.1230386.
   Web of Science ®Google Scholar
• E. O. B. Ogedengbe, K. L. Olaitan, and G. F. Naterer, “Tri-quadratic skew upwind scheme for scalar advection in a control-volume-based finite element method,” Numer. Heat Transf. Part B, vol. 71, no. 6, pp. 485–505, 2017. DOI:10.1080/10407790.2017.1309188.
   Web of Science ®Google Scholar