Free Material orientation design for tailoring vibration eigenvalues of CFRP shell structures

Abstract

In this paper, we present a non-parametric material orientation optimization method for tailoring the vibration eigenvalues of laminated shell structures composed of orthotropic carbon-fiber-reinforced plastic (CFRP) materials. Both of the design problems to maximize an arbitrary vibration eigenvalue and to maximize the gap between arbitrarily specified the vibration eigenvalues are formulated as distribution parameter optimization problems based on the variational method. We introduce KS function to solve the multiple roots problem latent in the vibration eigenvalue optimization problem. The sensitivity functions derived are applied to the H1 gradient method for material orientation to determine the optimal material orientation of each layer. The effectiveness of the proposed method are confirmed by the numerical results of a cantilever plate and a three-layer rectangular shell structure. The proposed method makes it possible to tailor the vibration eigenvalues of laminated shell structures without design parametrization while maintaining the smooth material orientation.

Keywords

• eigenvalue
• natural frequency
• h1 gradient method
• laminated shell structure
• material orientation
• orthotropic
• optimization
• composite material
• cfrp
• optimization