By John A Goldak,Mehdi Akhlaghi,SpringerLink (Online service)

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The issue is to reduce the computational cost to acceptable levels for meshes that achieve useful accuracy. The principal tools are optimizing the mesh and creating efficient solvers. In 3 0 analysis, brick elements are preferred because they tend to be more accurate and easier to use and interpret than tetrahedral elements. However, it is more difficult to grade a mesh with small brick elements near the welding arc to capture the rapid changes in temperature and with large brick elements far from the arc where the temperature varies slowly.

However, for high power density sources such as the laser or electron beam, it ignores the digging action of the arc that transports heat well below the surface of the weld pool. In such cases a hemispherical Gaussian distribution of power density ( w / m 3 )would be a step toward a more realistic model. The power density distribution for a hemispherical volume source can be written as: where q(x,y, 5 )is the power density (w/rn3). Eq. (2-5) is a special case of the more general ellipsoidal formulation developed in the next section.

It requires a special transition element to join shell and 3 0 brick elements. Computational Welding Mechanics 0 to be 0 nodes constrained bottom corner real nodes Figure 2-15: The transformation of a brick element to a transition element is shown. In particular, the relation between the transition node j and its top and bottom nodes is shown [67]. Gu in [67] presents a method to connect a three-dimensional element to the shell element. Figure 2-15 shows brick and shell elements and the transformation of a brick element to a transition element.

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