Computational Geometry Contributions Applied to Additive Manufacturing

This Doctoral Thesis develops novel articulations of Computation Geometry for applications on Additive Manufacturing, as follows:

(1) Shape Optimization in Lattice Structures. Implementation and sensitivity analysis of the SIMP (Solid Isotropic Material with Penalization) topology optimization strategy. Implementation of a method to transform density maps, resulting from topology optimization, into surface lattice structures. Procedure to integrate material homogenization and Design of Experiments (DOE) to estimate the stress/strain response of large surface lattice domains.

(2) Simulation of Laser Metal Deposition. Finite Element Method implementation of a 2D nonlinear thermal model of the Laser Metal Deposition (LMD) process considering temperature-dependent material properties, phase change and radiation. Finite Element Method implementation of a 2D linear transient thermal model for a metal substrate that is heated by the action of a laser.

(3) Process Planning for Laser Metal Deposition. Implementation of a 2.5D path planning method for Laser Metal Deposition. Conceptualization of a workflow for the synthesis of the Reeb Graph for a solid region in ℝ" denoted by its Boundary Representation (B-Rep). Implementation of a voxel-based geometric simulator for the LMD process. Conceptualization, implementation, and validation of a tool for the minimization of the material over-deposition at corners in LMD. Implementation of a 3D (non-planar) slicing and path planning method for the LMD-manufacturing of overhanging features in revolute workpieces.

The aforementioned contributions have been screened by the international scientific community via Journal and Conference submissions and publications.