Study of numerical tools for the design of lightweight structures when considering mode analysis

The design of lightweight and stiff structures is crucial, especially for the aeronautical industry. One of the approaches that can accomplish the design of these structures is topology optimization, a numerical technique that seeks the optimal design with certain requirements. The main objective of this project is to develop an in-house MATLAB algorithm able to propose optimal structures under the condition of maximizing the natural frequency of vibration of the structure, that is, solving the modal analysis eigenvalue problem. For this purpose, the project begins with the resolution of the classical eigenvalue problem of the optimal design of columns maximizing the critical buckling load, and ends with the optimal design of the topology of a structure maximizing the first vibration frequency. The presented problems are solved with different optimization solvers, such as the Method of Moving Asymptotes (MMA), Augmented Lagrangian or Function Minimizer Constrained (fmincon). In addition, in the eigenfrequency maximization problem, it is discuss the influence of different material interpolation scheme (SIMP and SIMPALL) over the results.