Accurate Response of Wing Structures to Free-Vibration, Load Factors, and Nonstructural Masses

Based on the Carrera unified formulation, this work extends variable kinematic finite beam elements to include load factors and nonstructural masses for the static and vibration analyses of complex, metallic wing structures. According to the Carrera unified formulation, variable kinematic beam theories are formulated in an automatic and hierarchical manner by expressing the displacement field as an arbitrary expansion through generic cross-sectional functions. Both Taylor-like and Lagrange polynomials are used in this paper to develop refined beam kinematics, and the related theories are referred to as Taylor expansion and Lagrange expansion, respectively. The generalized unknowns of Taylor expansion models are the beam axis displacements and the N-order displacement derivatives, with N being a free parameter of the analysis. Classical beam theories are clearly particular cases of the linear (N=1) Taylor expansion model. On the other hand, Lagrange expansion models have only pure translational displacements as unknowns. By exploiting this characteristic of Lagrange expansion, a componentwise approach is implemented and used for the analysis of multicomponent reinforced-shell structures. Numerical applications are developed by classical finite element procedures, and both static response and free vibration analyses are addressed. Various configurations of a benchmark wing are considered, and the capabilities of the present methodologies when dealing with higher-order effects due to deformable cross sections and geometrical discontinuities (for example, underside windows) are evaluated. The attention is focused on the applicability of the present refined beam models to problems involving complex, external inertial loadings. The results are compared to finite element solutions from commercial tools, including full three-dimensional models and models obtained by assembling two-dimensional shell and one-dimensional finite elements.