Two-Dimensional Rosenthal Moving Heat Source Analysis Using the Meshless Element Free Galerkin Method

REFERENCES

• D. Rosenthal , Mathematical Theory of Heat Distribution in Welding and Cutting , Welding J. , vol. 20 , no. 5 , pp. 220 – 234 , 1941 .
   Google Scholar
• D. Rosenthal , The Theory of Moving Source of Heat And its Applications to Metal Treatments , Trans. of the American Society of Mechanical Engineers , vol. 68 , pp. 849 – 865 , 1946 .
   Google Scholar
• N. Christensen , V. de L. Davies , and K. Gjermundsen , Distribution of Temperatures in Arc Welding , British Welding J. , vol. 12 , no. 54 , pp. 54 – 75 , 1965 .
   Google Scholar
• R. Weichert and K. Schonert , Temperature Distribution Produced by a Moving Heat Source , Mech. Appl. Math. , vol. 31 , pt. 3 , pp. 363 – 379 , 1978 .
   Web of Science ®Google Scholar
• T. W. Eager and N. S. Tsai , Temperature Fields Produced by Traveling Distributed Heat Sources , Welding J. , vol. 62 , no. 12 , pp. 346 – 355 , 1983 .
   Google Scholar
• J. Goldak , A. Chakravarti , and M. Bibby , A New Finite Element Model for Welding Heat Sources , Metallurgical Trans. B , vol. 15B , pp. 299 – 305 , 1994 .
   Google Scholar
• N. T. Nguyen , A. Ohta , K. Matsuoka , N. Suzuki , and Y. Maeda , Analytical Solutions for Transient Temperature of Semi-Infinite Body Subjected to 3-D Moving Heat Sources , Supplement to the Welding J. , pp. 265 – 274 , 1999 .
   Google Scholar
• R. Komaduri , and Z. B. Hou , Thermal Analysis of the Arc Welding Process: Part I. General Solutions , Metallurgical and Materials Trans. B , vol. 31 , no. 6 , pp. 1353 – 1370 , 2000 .
   Google Scholar
• R. Komaduri , and Z. B. Hou , Thermal Analysis of the Arc Welding Process: Part II. Effect of Variation of Thermophysical Properties with Temperature , Metallurgical and Materials Trans. B , vol. 32 , no. 3 , pp. 483 – 499 , 2001 .
   Google Scholar
• J. Ascough , A Single Step Finite Element Analysis of the Temperature Distribution around a Moving Laser Heat Source , Optics and Laser in Engi. , vol. 6 , pp. 137 – 143 , 1985 .
   Google Scholar
• C.-Y. Yang , The Determination of Two Moving Heat Sources in Two-Dimensional Inverse Heat Problem , Applied Mathematical Modelling , vol. 30 , pp. 278 – 292 , 2006 .
   Web of Science ®Google Scholar
• A. Nisar , M. J. J. Schmidt , M. A. Sheikh , and L. Li , Three-Dimensional Transient Finite Element Analysis of the Laser Enamelling Process and Moving Heat Source and Phase Change Considerations , Proc. of the Institution of Mechanical Engineers (Proc. Instn. Mech. Engrs.), Part B: J. of Engi. Manufacture , vol. 217 , pp. 753 – 764 , 2003 .
   Google Scholar
• J. J. Monaghan , An Introduction to SPH , Comput. Phys. Commn. , vol. 48 , pp. 89 – 96 , 1988 .
   Web of Science ®Google Scholar
• J. J. Monaghan , Simulating Free Surface Flows with SPH , J. Comput. Phys. , vol. 110 , pp. 399 – 406 , 1994 .
   Web of Science ®Google Scholar
• P. W. Cleary and J. J. Monaghan , Conduction Modelling using Smoothed Particle Hydrodynamics , J. of Computational Physics , vol. 148 , pp. 227 – 264 , 1999 .
   Web of Science ®Google Scholar
• L. D. Libersky , A. G. Petschek , T. C. Carney , J. R. Hipp , and F. A. Allahadi , High Strain Lagrangian Hydrodynamics , J. Comput. Phys. , vol. 109 , pp. 67 – 75 , 1993 .
   Web of Science ®Google Scholar
• W. Benz and E. Asphaug , Simulation of Brittle Solid using Smoothed Particle Hydrodynamics, Comput. Phys. Comm. , pp. 253–65, 1995.
   Google Scholar
• J. P. Gray , J. J. Monaghan , and R. P. Swift , SPH Elastic Dynamics , Comput. Methods Appl. Mech. Eng. , vol. 190 , pp. 6641 – 6662 , 2001 .
   Web of Science ®Google Scholar
• M. Shibahara and S. N. Atluri , The Meshless Local Petrov-Galerkin Method for the Analysis of Heat Conduction due to a Moving Heat Source in Welding , Int. J. of Therm. Sci. , vol. 50 , pp. 984 – 992 , 2011 .
   Web of Science ®Google Scholar
• et al. . Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Element , Comput. Mech. , vol. 10 , pp. 307 – 318 , 1992 .
   Google Scholar
• et al. . Element-Free Galerkin Methods , Int. J. Numer. Meth. Eng. , vol. 37 , pp. 229 – 256 , 1994 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• T. Sophy , A. Da Silva , and A. Kribèche , 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 .
   Web of Science ®Google Scholar
• I. V. Singh , K. Sandeep , and R. Prakash , Heat Transfer Analysis of Two-Dimensional Fins using Meshless Element Free Galerkin Method , Numer. Heat Transfer A , vol. 44 , pp. 73 – 84 , 2003 .
   Web of Science ®Google Scholar
• I. V. Sigh , Meshless EFG method in Three-Dimensional Heat Transfer Problems: A Numerical Comparison, Cost and Error Analysis , Numer. Heat Transfer A , vol. 46 , pp. 199 – 220 , 2004 .
   Google Scholar
• A. Singh , I. V. Singh , and R. Prakash , Numerical Solution of Temperature-Dependent Thermal Conductivity Problems using a Meshless Method , Numer. Heat Transfer A , vol. 50 , pp. 125 – 145 , 2006 .
   Web of Science ®Google Scholar
• et al. . The Finite Element Method in Heat Transfer Analysis , pp. 1 – 13 , John Wiley & Sons , 1996 .
   Google Scholar
• H. S. Carslaw and J. C. Jaeger , Conduction of Heat in Solids , pp. 6 – 8 , Oxford , 1959 .
   Google Scholar
• P. Lancaster and K. Salkauskas , Surface Generated by Moving Least Squares Methods , Math. Comput. , vol. 37 , no. 155 , pp. 141 – 158 , 1981 .
   Web of Science ®Google Scholar
• G. R. Liu , Mesh Free Methods: Moving Beyond The Finite Element Method chapt. 5 , pp. 83 – 161 , CRC Press, Boca Raton , 2003 .
   Google Scholar