Abstract
In this paper, we propose a non-parametric material orientation optimization method for vibrational eigenvalue problem of laminated shell structures composed of orthotropic CFRP materials. This optimal design problem that maximizes in arbitrarily specified vibrational eigenvalue is formulated as a distributed parameter optimization problem based on the variational method where an objective function based on the KS function is employed to solve duplicated eigenvalue problem. The sensitivity function with respect to the variation of the material orientation is theoretically derived, and the optimal material orientation distribution is determined by the H1 gradient method for scalar variable. Specifically, the sensitivity function is fictitious to internal heat generation and given to the entire region as the Robin condition of Poisson's equation in order to obtain a smooth material orientation distribution. Then, the temperature distribution obtained there is deemed the optimal smooth material orientation distribution. Numerical analysis examples show the effectiveness of the proposed method for obtaining the optimal material orientation distribution that maximizes arbitrarily specified vibrational eigenvalue.
