Vibrations of prestressed variable stiffness composite aerospace structures by ritz approach

With the introduction of the variable stiffness concept, the design space for high-performance lightweight composite structures has expanded significantly. A larger design space, in particular, allows designers to find more effective solutions with higher overall stiffness and fundamental frequency when considering prestressed dynamically excited aerospace components. In this context, an efficient and versatile Ritz method for the transient analysis of prestressed variable stiffness laminated doubly-curved shell structures is presented. The considered theoretical framework is the first-order shear deformation theory without further assumptions on the shallowness or on the thinness of the structure. A rational Bézier surface representation is adopted for the description of the shell allowing general orthogonal surfaces to be represented. General stacking sequences are considered and the unknown displacement field is approximated by Legendre orthogonal polynomials. Stiffened variable angle tow shell structures are modelled as an assembly of shell-like domains and penalty techniques are used to enforce the displacement continuity of the assembled multi-domain structure and the kinematical boundary conditions. For the transient analysis of prestressed variable stiffness structures, classical Rayleigh damping is considered and solutions are obtained through the Newmark integration scheme. The proposed approach is validated by comparison with literature and finite elements results and original solutions are presented for prestressed free and forced vibrations of VS stiffened shell structure, proving the ability of the present method in dealing with the analysis of complex aerospace structures.