A symplectic analytical singular element for steady-state thermal conduction with singularities in composite structures

References

• M. F. Pernice, N. V. de Carvalho, J. G. Ratcliffe, and S. R. Hallett, Experimental Study on Delamination Migration in Composite Laminates, Compos, A Appl. Sci. Manuf., vol. 73, pp. 20–34, 2015.
   Web of Science ®Google Scholar
• G. C. Sih, Heat Conduction in the Infinite Medium with Lines of Discontinuities, J. Heat Transfer, vol. 87, pp. 293–298, 1965.
   Web of Science ®Google Scholar
• A. Y. Kuo, Interface Crack Between Two Dissimilar Half Spaces Subjected to a Uniform Heat Flow at Infinity-Open Crack, J. Appl. Mech., vol. 57, pp. 359–364, 1990.
   Web of Science ®Google Scholar
• C. K. Chao and M. H. Shen, Thermal Problem of Curvilinear Cracks in Bonded Dissimilar Materials, J. Appl. Phys., vol. 73, pp. 7129–7137, 1993.
   Web of Science ®Google Scholar
• C. K. Chao and L. Y. Kuo, Thermal Problem of Curvilinear Cracks in Bonded Dissimilar Materials with a Point Heat Source, Int. J. Heat Mass Transfer, vol. 36, pp. 4085–4093, 1993.
   Web of Science ®Google Scholar
• L. Marin, An Invariant Method of Fundamental Solutions for Two-dimensional Steady-state Anisotropic Heat Conduction Problems, Int. J. Heat Mass Transfer, vol. 94, pp. 449–464, 2016.
   Web of Science ®Google Scholar
• N. Hasebe and S. Kato, Solution of a Bonded Bimaterial Problem of Two Interfaces Subjected to Different Temperatures Arch. Appl. Mech., vol. 86, pp. 445–464, 2016.
   Web of Science ®Google Scholar
• J. Ling and D. S. Yang, Virtual Boundary Meshless with Trefftz Method for the Steady-state Heat Conduction Crack Problem, Numer. Heat Transfer B Fund., vol. 68, pp. 141–157, 2015.
   Web of Science ®Google Scholar
• Z. H. Zhou, C. H. Xu, X. S. Xu, and A. Y. T. Leung, Finite-element Discretized Symplectic Method for Steady-state Heat Conduction with Singularities in Composite Structures, Numer. Heat Transfer B Fund., vol. 67, pp. 302–319, 2015.
   Web of Science ®Google Scholar
• Z. Yosibash and B. Szabo, Numerical Analysis of Singularities in Two Dimensions Part 1: Computation of Eigenpairs, Int. J. Numer. Meth. Eng., vol. 38, pp. 2055–2082, 1995.
   Web of Science ®Google Scholar
• N. Omer, Z. Yosibash, M. Costabel, and M. Dauge, Edge Flux Intensity Functions in Polyhedral Domains and Their Extraction by a Quasidual Function Method, Int. J. Fract., vol. 29, pp. 97–130, 2004.
   Web of Science ®Google Scholar
• Z. Yosibash, Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation, Springer, New York, NY, pp. 73–96, 2012.
   Google Scholar
• S. Shannon, Z. Yosibash, M. Dauge, and M. Costabel, Extracting Generalized Edge Flux Intensity Functions with the Quasidual Function Method Along Circular 3-D Edges, Int. J. Fract., vol. 181, pp. 25–50, 2013.
   Web of Science ®Google Scholar
• J. Yvonnet, Q. C. He, Q. Z. Zhu, and J. F. Shao, A General and Efficient Computational Procedure for Modelling the Kapitza Thermal Resistance Based on XFEM, Comput. Mater. Sci., vol. 50, pp. 1220–1224, 2011.
   Web of Science ®Google Scholar
• W. A. Yao, W. X. Zhong, and C. W. Lim, Symplectic Elasticity, World Scientific, Singapore, 2009, pp. 181–223.
   Google Scholar
• X. F. Hu and W. A. Yao, A Novel Singular Finite Element on Mixed-mode Bimaterial Interfacial Cracks with Arbitrary Crack Surface Tractions, Int. J. Fract., vol. 172, pp. 41–52, 2011.
   Web of Science ®Google Scholar
• J. S. Wang and Q. H. Qin, Symplectic Model for Piezoelectric Wedges, and Its Application in Analysis of Electroelastic Singularities, Philos. Mag., vol. 87, pp. 225–251, 2007.
   Web of Science ®Google Scholar
• C. H. Xu, Z. H. Zhou, X. S. Xu, and A. Y. T. Leung, Electroelastic Singularities and Intensity Factors for an Interface Crack in Piezoelectric–Elastic Bimaterials, Appl. Math. Model., vol. 39, pp. 2721–2739, 2015.
   Web of Science ®Google Scholar
• H. W. Zhang and W. X. Zhong, Hamiltonian Principle Based Stress Singularity Analysis Near Crack Corners of Multi-material Junctions, Int. J. Solids Struct., vol. 40, pp. 493–510, 2003.
   Web of Science ®Google Scholar
• W. A. Yao and X. F. Hu, A Novel Singular Finite Element of Mixed-mode Crack Problems with Arbitrary Crack Tractions, Mech. Res. Commun., vol. 38, pp. 170–175, 2011.
   Web of Science ®Google Scholar
• X. F. Hu and W. A. Yao, A New Enriched Finite Element for Fatigue Crack Growth, Int. J. Fatigue, vol. 48, pp. 247–256, 2013.
   Web of Science ®Google Scholar
• W. A. Yao, Z. J. Zhang, and X. F. Hu, A Singular Element for Reissner Plate Bending Problem with V-shaped Notches, Theor. Appl. Fract. Mech., vol. 74, pp. 143–156, 2014.
   Web of Science ®Google Scholar
• W. A. Yao and X. F. Hu, A Novel Singular Finite Element on Mixed-mode Dugdale Model Based Crack, J. Eng. Mater. Technol., vol. 134, pp. 021003, 2012.
   Web of Science ®Google Scholar
• A. Y. T. Leung, X. S. Xu, and Z. H. Zhou, Hamiltonian Approach to Analytical Thermal Stress Intensity Factors—Part 1: Thermal Intensity Factor, J. Thermal Stress., vol. 33, pp. 262–278, 2010.
   Web of Science ®Google Scholar
• A. Y. T. Leung, X. S. Xu, and Z. H. Zhou, Hamiltonian Approach to Analytical Thermal Stress Intensity Factors—Part 2 Thermal Stress Intensity Factor, J. Thermal Stress., vol. 33, pp. 279–301, 2010.
   Web of Science ®Google Scholar