Thermal Modeling of Metal Additive Manufacturing with Semi-analytical Isogeometric Analysis
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Accurate thermal simulations are essential for predicting the temperature histories of additively manufactured parts. Manufacturing parameters such as laser power, scanning speed, and layer thickness can be optimized based on the temperature histories. However, the multi-scale nature of the LPBF problem poses challenges for numerical simulations of additive manufacturing processes. Resolution of steep temperature gradients near a moving laser spot demands extremely fine spatial discretization on the order of the laser spot radius, typically tens of micrometers. Conventional Finite Element Methods (FEM) require highly refined, dynamically adaptive spatial discretization leading to prohibitive computational costs. Semi-analytical approaches mitigate this by decomposing the temperature field into an analytical point-source solution and a complementary numerical field that enforces boundary conditions. However, state-of-the-art implementations either necessitate extensive mesh refinement [1] near boundaries or rely on restrictive image-source techniques [2], limiting their efficiency and applicability to complex geometries. We present a novel reformulation of the semi-analytical framework using Isogeometric Analysis (IGA). Here, the laser heat input is captured by the analytical point-source solution in a half-infinite space. At the same time, the complementary correction field, which imposes boundary conditions, is solved using a spline-based IGA discretization. This approach leverages IGA’s key advantages: exact geometry representation, higher-order continuity, and superior accuracy per degree of freedom. These features unlock efficient thermal modeling of realistic parts with complex contours. Our strategy eliminates the need for scan-wise remeshing and robustly handles intricate geometric features, such as sharp corners and varying cross-sections. Additionally, multiple lasers can be simulated with no additional cost. Numerical examples demonstrate that the proposed semi-analytical IGA method delivers accurate temperature predictions and achieves substantial computational efficiency gains compared to standard FEM, establishing it as a powerful new tool for high-fidelity thermal simulation in laser powder bed fusion.
