Lagrange Multiplier Method for Treatment of Nonlinear Multi Freedom Constraints in Dynamic Finite Element Analysis of Truss System Subjected to Harmonic Load

Quyen, Vu Thi Bich; Tien, Dao Ngoc; Van, Tran Thi Thuy; Dat, Pham Van

doi:10.1007/978-3-030-86001-1_34

Cited by 2 publications

(1 citation statement)

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“…Wang et al [14] assumed the deposited track formed by the powder to be in the shape of a rectangular prism. They established a more efficient thermodynamic model for the deposition of IN625 thin-walled components by combining the Lagrangian method [15] with the birth and death method. Manvatkar et al [16] improved the way to add mass based on the birth and death method, and utilized the fluid volume method (VOF) to track the free surface of the track and developed a transient heat transfer and fluid flow model for multi-tracks.…”

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confidence: 99%

Investigation of molten pool geometry and flow field based on powder scale modeling in laser directed energy deposition

Liu,

et al. 2024

Preprint

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Laser directed energy deposition (LDED) technology is currently facing challenges in controlling geometry accuracy of metal components. There is an urgent need to develop a numerical model that is more efficient and accurate compared to existing models and to analyze the dynamic behavior of the melt pool under the interaction of process parameters during LDED process to optimize parameters with fewer experimental studies to reduce costs. Therefore, a 3D powder scale multi-physics model is proposed during the single track LDED process in this study. The powder particles are added by a Lagrangian particle model in this model without the need for assuming that the powder particles entering the molten pool are added by the mass source term, which improves model accuracy and efficiency. The effect of Energy per Unit Mass (EUM, J/g), Mass per Unit Length (MUL, g/mm) and standoff distance (SD, mm) intensities on transient molten pool motion and flow field are comprehensively investigated. It is discovered that the proposed model is able to predict the single track height, width, depth and dilution rate, or less than 9% relative error from experimentation, providing a useful tool for track geometry to predict. Further, the flow velocity, width and depth of melt pool also gradually are improved with higher EUM, MUL and SD intensity and fluctuates within a small range. However, the height is improved and then decreases with higher SD intensity, and is improved with higher EUM or MUL. Overall, this study contributes to developing an optimizing process approach to improve formation accuracy for LDED manufacturing.

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confidence: 99%