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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 68, 2015 - Issue 2
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Original Articles

Virtual Boundary Meshless with Trefftz Method for the Steady-State Heat Conduction Crack Problem

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Pages 141-157 | Received 12 Jan 2014, Accepted 08 Nov 2014, Published online: 29 May 2015

REFERENCES

  • Y. C. Shiah and Y. X. Shi Anisotropic Heat Conduction across an Interface Crack/Defect Filled with a Thin Interstitial Medium, Eng. Anal. Bound. Elem., vol. 30, pp. 325–337, 2006.
  • G. H. Paulino and A. Sutradhar The Simple Boundary Element Method for Multiple Cracks in Functionally Graded Media Governed by Potential Theory: a Three-Dimensional Galerkin Approach, Int. J. Numer. Meth. Eng., vol. 65, pp. 2007–2034, 2006.
  • A. A. Dobroskok and A. M. Linkov CV Dual Reciprocity BEM for Transient Flow in Blocky Systems with Singular Points and Lines of Discontinuities (vol. 34, pg. 238, 2010), Eng. Anal. Bound. Elem., vol. 35, pp. 156–156, 2011.
  • A. Ekhlakov, O. Khay, C. Zhang, J. Sladek, V. Sladek, and X. W. Gao Thermoelastic Crack Analysis in Functionally Graded Materials and Structures by a BEM, Fatigue Fract. Eng. Mater. Struct., vol. 35, pp. 742–766, 2012.
  • H. C. Sun, X. H. Li, and L. Z. Zhang Virtual Boundary Element-Collocation Method for Solving Problems of Elasticity, Chin. J. Comput. Mech., vol. 8, pp. 15–23, 1991 (in Chinese).
  • H. C. Sun, H. T. Yang, J. N. Wu, and H. X. Yang Virtual Boundary Element Method Application and Strategies for Solution, Chin. J. Appl. Mech., vol. 11, pp. 28–37, 1994 (in Chinese).
  • Q. Xu and Z. J. Zhang Virtual Boundary Element Method for Solving Uncoupled Thermo-Elastic Problems with Multi-Domain Combinations, J. Tongji Univ. (Nat. Sci.), vol. 38, pp. 1287–1292, 2010 (in Chinese).
  • L. K. Keppas and N. K. Anifantis Boundary Element Analysis of Cracked Homogeneous or Bi-Material Structures Under Thermo-Mechanical Cycling, Comput. Meth. Appl. Mech. Eng., vol. 199, pp. 3345–3355, 2010.
  • I. Herrera Trefftz Method, in C. A. Brebbia (ed.), Topics in Boundary Element Research, 1984, pp. 225–253.
  • Y. K. Cheung, W. G. Jin, and O. C. Zienkiewicz Direct Solution Procedure for Solution of Harmonic Problems Using Complete, Non-singular, Trefftz Functions, Commun. Appl. Numer. Meth., vol. 5, pp. 159–169, 1989.
  • S. C. Huang and R. P. Shaw The Trefftz Method as an Integral Equation, Adv. Eng. Software, vol. 24, pp. 57–63, 1995.
  • C. A. Wang, H. Sadat, and J. Y. Tan First-Order and Second-Order Meshless Formulations of The Radiative Transfer Equation: A Comparative Study, Numer. Heat. Transfer B, vol. 66, pp. 21–42, 2014.
  • C. A. Wang, H. Sadat, and J. Y. Tan Meshless Method for Solving Transient Radiative and Conductive Heat Transfer in Two-Dimensional Complex Geometries, Numer. Heat. Transfer B, vol. 65, pp. 518–536, 2014.
  • K. Luo, H. L. Yi, and H. P. Tan Coupled Radiation and Mixed Convection in an Eccentric Annulus Using The Hybrid Strategy of Lattice Boltzmann-Meshless Method, Numer. Heat. Transfer B, vol. 66, pp. 243–267, 2014.
  • X. T. Pham Two-Dimensional Rosenthal Moving Heat Source Analysis Using the Meshless Element Free Galerkin Method, Numer. Heat. Transfer A, vol. 63, pp. 807–823, 2013.
  • T. Sophy, A. Da Silva, and A. Kribeche A Space-Time Meshless Method That Removes Numerical Oscillations when Solving PDES with High Discontinuities, Numer. Heat. Transfer B, vol. 62, pp. 50–70, 2012.
  • C. Varanasi, J. Y. Murthy, and S. Mathur Numerical Schemes for The Convection-Diffusion Equation Using a Meshless Finite-Difference Method, Numer. Heat. Transfer B, vol. 62, pp. 1–27, 2012.
  • M. Li, C. S. Chen, and C. H. Tsai Meshless Method Based on Radial Basis Functions for Solving Parabolic Partial Differential Equations with Variable Coefficients, Numer. Heat. Transfer B, vol. 57, pp. 333–347, 2010.
  • 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 Stresses, vol. 33, pp. 279–301, 2010.
  • A. Portela and A. Charafi Trefftz Boundary Element Method for Domains with Slits, Eng. Anal. Bound. Elem., vol. 20, pp. 299–304, 1997.

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