Structural Topology Optimization with Volume and Natural Frequency Constraints by Using the TOBS Method

This study proposes to address the optimization challenge of minimizing compliance subjected to a volume and a natural frequency constraint for solid mechanics problems, employing the Topology Optimization of Binary Structures (TOBS) method as the optimization solver. The finite element method solves the linear elasticity equations and the eigenvalue problems considering a free vibration analysis. The modified SIMP model is proposed as the material interpolation model for obtaining compliance and natural frequency sensitivities. Modal Assurance Criterion (MAC)-based mode-tracking is implemented to observe the first three natural frequencies in each case, focusing on identifying modes crossing. Two bidimensional problems were studied to verify the algorithm’s efficacy - a biclamped beam and a tower subjected to a horizontal load. Different values of natural frequency constraints are examined to assess the final topology and modes crossing. Numerical results demonstrate that the TOBS method is well-suited for addressing the current problem, offering optimized layouts for structures exposed to vibrations while maintaining natural frequencies within specified levels established in the optimization problem.