Fundamental frequency maximization of orthotropic shells using a free-form optimization method

In this study, a free-form optimization method is proposed that maximizes the fundamental frequencies of the orthotropic shells to avoid vibrational resonance. The negative fundamental vibrational eigenvalue is employed as the objective function, which is minimized by subjecting to the governing equation of the natural frequency analysis and area constraint. In the free-form optimization process, the natural frequency analysis of the orthotropic shells is performed to calculate the shape gradient function. The shape gradient function is then applied to the velocity analysis for determining the optimal shape variation. The repeated eigenvalues are considered by converting the fundamental eigenvalue to a summation form of the repeated eigenvalues. The proposed optimization method is validated using three examples of the orthotropic shells. The numerical results show that the optimized shapes of the orthotropic shells are smooth, and their fundamental frequencies are significantly enhanced using the proposed free-form optimization method.