THERMO-MECHANICAL OPTIMIZATION OF MATERIALS AND STRUCTURES

This thesis presents a comprehensive investigation into topology optimization (TO) and its applications to structural and thermal systems. It spans theoretical developments, computational implementations, and practical validations, with a focus on enhancing efficiency, accuracy, and versatility in addressing complex engineering challenges. The development and application of the Immersed Level-Set Topology Optimization (ILSTO) framework, which decouples the finite element (FE) mesh from the level-set (LS) grid, enabling precise boundary representations without the computational burden of adaptive meshing is the central novelty of the thesis. The research is organized into three thematic areas: (1) the design and characterization of advanced lattice and metamaterial structures, including Triply Periodic Minimal Surface geometries and porous metaplates (2) a critical review and development of numerical approaches in TO, highlighting the potential of LS-based methods and their integration into multi-physics frameworks; and (3) applications of ILSTO in thermo-mechanical TO, addressing problems involving conflicting objectives such as minimizing structural compliance and thermal transport simultaneously. Key contributions include novel strategies for mapping field variables between the FE mesh and LS grid, enhanced convergence criteria, and innovative interpolation schemes to balance computational cost and solution accuracy. The findings demonstrate the robustness of the ILSTO framework in solving complex TO problems while maintaining flexibility for extensions to nonlinear material models thus soft robotics applications, multi-scale designs, and integration into commercial FEM software. This work not only bridges theoretical and practical advancements in TO but also lays the foundation for future developments in high-performance structural design, offering insights into optimizing multi-functional materials and systems for engineering applications.