Variational theory of complex rays applied to shell structures: in-plane inertia, quasi-symmetric ray distribution, and orthotropic materials
Recently, interest of aerospace and automotive industries on medium-frequency vibrational behavior of composite shell structures has grown due to their high specific stiffness and fatigue resistance. Conventional methods such as the finite element method and the statistical energy analysis are not suitable for the medium-frequency bandwidth. Conversely, the variational theory of complex rays (VTCR) is taking place as an ad-hoc technique to tackle such frequency band. It is a Trefftz method based on a weak variational formulation. Equilibrium equations are met using exact solutions as shape functions. The variational problem imposes boundary conditions in weak form. The present paper extends VTCR to orthotropic shell structures. Moreover, several new enhancements are introduced. Now, we use a quasi-symmetric ray distribution which can greatly reduce computational costs, and addresses in-plane inertia which was neglected in previous works. Some relevant numerical examples are presented to show the strategy and results are compared with a FEM reference to study performances.