A Study on Activation Algorithm of Finite Elements for Three-Dimensional Transient Heat Transfer Analysis of Directed Energy Deposition Process


Heat transfer finite element analysis (FEA) for directed energy deposition (DED) process is crucial to properly estimate the residual stress in the additive manufactured part. The material deposition of the DED process is generally simulated by activation of finite elements. However, the activation algorithm of inactive finite elements is complicated. Besides, existing element activation algorithm is not suitable for highly focused energy source. In order to overcome these discrepancies, an inactive element activation algorithm with two-element cross section has been proposed for simulating a DED process using a high intensity laser heat flux. The nodal temperature during the element activation has been evaluated. The proposed algorithm has been implemented into the heat transfer FEAs for multilayer and planar depositions to investigate the applicability of the proposed algorithm. Finally, the results of FEAs using the proposed algorithm have been compared to those of commercial software SYSWELD.

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xe :

Mesh size in direction of deposition


Radius of laser beam

tstep :

Step time


Relative velocity between heat source and substrate


x-Coordinate relative to moving frame of heat source

whalf :

Half width of deposited bead


y-Coordinate relative to moving frame of heat source

hb :

Height of deposited bead


z-Coordinate relative to moving frame of heat source


Volumetric heat flux


Efficiency of laser


Input power of laser

dp :

Penetration depth of laser beam


x-Coordinate of node

Vx :

Velocity in x-direction

tlayer :

Process time during the current deposition layer


y-Coordinate of node

Vy :

Velocity in y-direction


z-Coordinate of node


Nodal temperature


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This study was supported by research fund from Chosun University, 2017.

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Correspondence to Dong-Gyu Ahn.

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Chua, B., Lee, H., Ahn, D. et al. A Study on Activation Algorithm of Finite Elements for Three-Dimensional Transient Heat Transfer Analysis of Directed Energy Deposition Process. Int. J. Precis. Eng. Manuf. 20, 863–869 (2019). https://doi.org/10.1007/s12541-019-00118-9

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  • Element activation algorithm
  • Heat transfer analysis
  • Directed energy deposition
  • Finite element analysis