Titolo della tesi: A Novel Design Methodology for Heterogeneous Beam-based Lattices
This thesis investigates the use of heterogeneous lattice structures from an optimization perspective. A novel design methodology was developed to concurrently optimize both the macroscopic topology and the microscopic infill distribution, enabling the creation of spatially varying lattice architectures tailored to specific performance objectives. The proposed framework integrates multiscale modeling, numerical homogenization, and gradient-based optimization within a unified formulation, allowing efficient exploration of the design space while maintaining manufacturability constraints. A novel geometrical algorithm was proposed to enable continuous topology changes within the lattice while preserving manufacturability. This algorithm allows smooth transitions between different lattice configurations, ensuring cell interconnection and avoiding discontinuities that could hinder fabrication. By coupling this geometrical adaptability with the optimization framework, the method supports the generation of structurally efficient and manufacturable heterogeneous lattices, bridging the gap between computational design and practical realization. To accelerate computations, a new optimization strategy based on gradient-based algorithms was introduced. It leverages a piecewise definition of the design variables to construct a multigrid representation of the design space, enabling efficient refinement and coarsening during the optimization process. The numerical model is discretized using a fine mesh for physical accuracy, while the design variables are kept constant within each lattice cell, limiting their number and improving computational efficiency. This hierarchical structure allows the algorithm to capture both global and local features of the solution with reduced computational cost, improving convergence speed while maintaining accuracy in the final optimized lattice design. Overall, this work contributes a unified and computationally efficient methodology for the design of heterogeneous lattices. It bridges the gap between high-fidelity numerical optimization and practical 3D printing constraints, offering a foundation for future developments in multiscale and multifunctional design.