Laser Powder Bed Fusion (LPBF) has emerged as an influential metal additive manufacturing technology capable of producing geometrically complex, high-performance components. However, the process is governed by extremely high thermal gradients, rapid solidification, and repeated thermal cycles, all of which strongly influence microstructure formation, defect generation, and final part quality. Accurate part-scale thermal simulation is therefore essential for predicting process outcomes and guiding process-parameter optimization. This thesis advances the semi-analytical thermal modeling framework for LPBF, addressing limitations in existing semi-analytical methods and demonstrating its applicability to melt-pool prediction, overheating mitigation, and microstructural evolution analysis.

Conventional Finite Element Method (FEM)–based part-scale models face a fundamental challenge due to the multiscale nature of LPBF. The small laser spot size and associated steep temperature gradients require a fine Finite Element (FE) mesh near the heat source, while the large build volume demands computationally efficient discretization. Adaptive remeshing strategies alleviate part of this difficulty but incur high computational cost because the mesh must be updated frequently as the laser traverses the geometry. Semi-analytical methods provide an alternative by employing closed-form thermal solutions for moving point or line heat sources in a semi-infinite medium, thereby capturing the steep temperature gradients analytically without requiring local mesh refinement. However, the state-of-the-art semi-analytical formulations were limited to simple geometries with straight boundaries.

This thesis first extends the semi-analytical method by introducing a generalized image-source formulation capable of handling curved boundaries. Image sources offset the boundary heat flux induced by the regular heat sources, thereby enforcing appropriate boundary conditions, while decoupling the mesh size from the characteristic length scale dictated by laser spot size. Image source positions and power modulation factors are derived using local boundary curvature, supported by NURBS representations of arbitrary geometries, enabling the use of image sources for complex shapes. Numerical examples confirm that the modulated image-source approach dramatically reduces boundary heat-flux error and enables accurate temperature prediction with significantly coarser meshes. This advancement marks an important step in extending semi-analytical approaches to realistic part geometries.

The second methodological development replaces the FEM-based complementary field computation with isogeometric analysis (IGA) in a semi-analytical thermal modeling framework. IGA employs NURBS basis functions that exactly represent geometry, allowing the simulation of realistic parts with complex geometries. In addition, with the exact geometric representation and higher-order continuity of NURBS basis functions, the numerical complementary field can be resolved with significantly fewer degrees of freedom. Comparative studies show that the IGA-based formulation reduces computational cost by an order of magnitude while maintaining accuracy, making it highly attractive for large-scale LPBF simulations.

The semi-analytical thermal modeling framework is then applied to study overheating phenomena in LPBF of magnesium alloy. Using a triangular prism part geometry, the study reveals how geometric constraints—particularly decreasing scan vector length toward the tip of a triangular layer—lead to reduced cooling time, rapid heat accumulation, and significant increases in melt-pool depth. However, extremely short vectors experience insufficient heating duration, causing a sudden drop in melt-pool depth. Two mitigation strategies are proposed: extending zero-power ghost vectors and adjusting laser power based on vector length. Both numerical predictions and experimental results validate their effectiveness in homogenizing melt-pool depth and reducing porosity.

Finally, the semi-analytical thermal model is employed to investigate phase transformations in Ti-6Al-4V during LPBF under varying volumetric energy densities. Higher energy densities promote greater decomposition of martensite due to reheating from subsequent layers, whereas layers built at the end of the process contain a higher percentage of martensite phase because rapid cooling favors martensite formation. The semi analytical model successfully captures the thermal transients required to drive these phase-transformation predictions. Besides, the effects of laser scanning strategies and the number of scanning lasers are also investigated, showing little influence on the overall phase fractions.

In summary, this thesis advances the semi-analytical modeling framework for LPBF and demonstrates its strong potential for predicting melt-pool behavior, mitigating defects, and understanding microstructural evolution.

Part-scale thermal process simulations play an important role in improving the part quality of the Laser Powder Bed Fusion (LPBF) process. The semi-analytical simulation method relies on the superposition of analytical fields to represent laser-induced heat sources in a semi-infinite space and a complementary temperature field to enforce boundary conditions. So far, boundary conditions have been imposed by analytical image fields for straight boundaries and numerically for non-straight boundaries. The latter requires considerable refinement on the spatial discretization, at least near the boundaries, and compromises the computational efficiency of the simulations. In this paper, we derive a closed-form solution for the image fields that can accurately enforce the boundary conditions for non-straight boundaries. A geometrically complex part boundary is represented by B-splines, and with the aid of an offset method and reparameterization, the positions of the image sources are determined. The image field's closed-form expression is then found using the boundary's local curvature calculated from the local tangent lines. Numerical examples on different levels of complexity revealed that the net heat lost along an adiabatic boundary vanishes when the novel image source solutions are used, and the thermal evolution of complex parts can be accurately predicted with high computational efficiency. Simulations involving multiple lasers can also be performed with no extra computational cost.