Dynamics of variable stiffness composite shell structures using a Ritz approach

The design philosophy for high-performance lightweight composite structures has broadened significantly since the introduction of variable stiffness composites. Indeed, by tailoring stiffness distributions, variable stiffness composites have been shown to improve buckling performance and dynamic stability, as well as to modify dynamic response. When considering prestressed dynamically excited aerospace components, efficient linear analysis tools play a significant role in the early design of variable stiffness structures, allowing designers to identify many viable solutions with higher overall stiffness and fundamental frequency.

In light of this, a single and multi-domain Ritz method for buckling, eigenfrequency, transient, and dynamic instability analysis of hygro-thermal and mechanically prestressed, variable stiffness, laminated, doubly-curved shell structures is presented. Sanders-Koiter based shell kinematics, within a first-order shear deformation theory framework, allows general orthogonal surfaces to be modelled without making any additional assumptions about the structure’s shallowness or thinness. The proposed Ritz method is efficient because it uses Legendre orthogonal polynomials as displacement trial functions, while the flexibility in modelling and design is provided by penalty techniques that allow stiffened variable angle tow shell structures to be modelled as an assembly of shell-like domains. The proposed approach is verified against published benchmark results and finite element solutions, showing excellent accuracy with approximately 65% fewer variables. Original parametric studies are carried out for cylindrical, spherical and variable?curvature shells, showing the flexibility that the variable stiffness concept provides for finding trade-off solutions for prestressed shell components. Then, original solutions for a prestressed, stiffened, variable angle tow shell structure are reported, demonstrating the reliability of the current approach in modelling the dynamic analysis of multi-part aerospace structures. Moreover, the dynamic behaviour of variable angle tow fairing shell geometries subject to hygro-thermomechanical prestress is examined, illustrating the validity of the variable stiffness concept in greatly improving the dynamic stability of critical doubly-curved variable-curvature components such as launch vehicle payload fairings.