Numerical and experimental study on optimization of distributed material-orientation for frequency response of CFRP shell structures

Abstract

In this paper, we present a non-parametric material-orientation optimization method for frequency response, a dynamic design problem of a laminated shell structure composed of orthotropic carbon-fiber-reinforced plastic (CFRP) materials. The squared vibration displacements in the arbitrarily prescribed evaluation area are minimized at a given frequency or in a given frequency band. This optimal design problem to determine the optimal material-orientation distribution is formulated as a distributed-parameter system optimization problem based on the variational method, and the sensitivity function with respect to the variation of the material-orientation is theoretically derived. The optimal material-orientation distribution is determined by the H1 gradient method with Poisson’s equation. With this method, the objective function is minimized while controlling the smoothness and the curvature distribution of the material-orientation. Numerical results show the effectiveness of the proposed method for obtaining the optimal material-orientation distribution of each layer that minimizes the squared vibration displacements at the given frequency or in the given frequency band. Also, the prototypes for the initial and the optimized material-orientation distribution are fabricated by the tailored fiber placement technique (TFP), and the static stiffness and the frequency response are experimentally evaluated. The results are compared with the calculated ones and discussed.