Analytical solutions of the thermal field induced by moving double-ellipsoidal and double-elliptical heat sources in a semi-infinite body

FACHINOTTI, V; ANCA, A.; CARDONA, A

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING

John Wiley & Sons

Lugar: Chichester; Año: 2011 vol. 27 p. 595 - 607

1069-8299

An analytical solution is computed for the thermal field induced in a semi-infinite body by a moving heat source whose shape was proposed by Goldak et al. for the simulation of welding processes. Due to its ability to accommodate a wide variety of welding techniques, this model is widely used. Throughout two semi-ellipsoidal volumes, corresponding to the front and the rear parts of the moving source, the heat power density is distributed using a Gaussian function.In the literature, Nguyen et al. have proposed an analytical solution to this problem that is however only correct when both semi-ellipsoids are equal (i.e., for a single-ellipsoidal model). The current work presents an extension of the analytical solution of Nguyen et al. to the double-ellipsoidal case. As a special case, the solution for the temperature field induced by a double-elliptical surface heat source is also developed. In order to validate the analytical solutions, the problem is solved using both two- and three-dimensional finite element models in several test-cases. Solutions for double-ellipsoidal and double-elliptical sources are numerically computed and compared to the analytical solutions, while clearly demonstrating the di®erences with respect to the solution of Nguyen et al. At the same time, the two-dimensional numerical approximation is evaluated in terms of accuracy and computational cost.