Topology Optimization of 2D shapes - MATLAB

Project done as part of the course 24-785 (Engineering Optimization) at Carnegie Mellon University (Fall 2023)

This project explored the use of topology optimization (TO) for designing compliant mechanisms. Topology Optimization is a computational method that iteratively removes material from a design space to achieve a desired performance, such as maximizing stiffness or minimizing weight. This computational approach holds significant promise in reshaping engineering design by determining optimal material distributions within defined spaces, thereby enhancing structural performance, thermal conductance, and fluid flow. Compliant mechanisms use flexibility instead of joints to achieve desired motion, making them lightweight and compact. Responsible for loading cases and comparison with expected results.

The project utilized a 99-line MATLAB code to implement the SIMP (Solid Isotropic Material with Penalization) method for Topology Optimization. Two loading cases were considered: a cantilever beam with a fixed left end and a simply supported beam with fixed ends. The objective function was to minimize compliance (i.e., maximize stiffness) for each case. A meticulous evaluation process was considered, covering node number calculations, stiffness matrix considerations, and comprehensive analyses of loading scenarios and boundary conditions. The systematic approach to parameter tuning, sensitivity analysis, and convergence criteria enriches the understanding of the optimization algorithm's behavior under diverse conditions.

Different load scenarios and boundary conditions were applied to assess the robustness and adaptability of the optimization algorithm. The convergence criteria were based on the change in volume for each iteration. The results showed that the optimized designs varied significantly depending on the loading conditions and boundary constraints. In some cases, the convergence rate was sensitive to the minimum relative density parameter. A convergence study revealed that a larger minimum relative density value resulted in smoother convergence and less sharp features in the optimized designs. 

Loading Case (a) - Top node load

Loading Case (b) - Center node load

Loading Case (c) - Bottom node load

The project demonstrated the potential of Topology Optimization for designing compliant mechanisms. However, limitations were identified, such as the potential for checkerboard artifacts and the sensitivity of convergence to specific parameters. Future work could explore more advanced filtering techniques and investigate the influence of mesh density and material properties on the optimization process. Overall, the project provided valuable insights into the use of Topology Optimization for designing compliant mechanisms and highlighted its potential for various engineering applications.