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 temperaturedependent 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 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.

Palabras clave

Geometría computacional, Fabricación aditiva, Impresión 3D