Reduced Structural Modeling of Integrally-Strained Slender Wings

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77134/1/AIAA-2004-2038-697.pd

XII-Apologies

A one-dimensional theory of slender structures with heterogeneous anisotropic materials is presented. It expands Cosserats description of beam kinematics by allowing deformation of the beam cross sections. For that purpose, a Ritz approximation is introduced on the cross-sectional warping field, which defines additional elastic degrees of freedom (finitesection modes) in the 1-D model. This results in an extended set of beam dynamic equations that includes direct measures of both the large global displacement and rotations of a certain reference line, and the small local deformations of the cross sections. Two situations of interest are then studied in which this approach provides a simpler alternative to nonlinear shell models: First, we look at the detailed structural response of thin-walled composite beams with distributed loads. In particular, the case of a composite construction with embedded piezoelectric actuators is considered. Second, this methodology is applied to study the low-frequency response characterization of a thin-walled composite beam. Numerical results are presented in both cases, in which a reduced set of finite-section modes allows a full characterization of the actual 3-D structure within a strictly 1-D framework solution.Published versio

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

In the presented paper the equations of motion of a rotating composite Timoshenko beam are derived by utilising the Hamilton principle. The nonclassical effects like material anisotropy, transverse shear and both primary and secondary cross-section warpings are taken into account in the analysis. As an extension of the other papers known to the authors a nonconstant rotating speed and an arbitrary beam’s preset (pitch) angle are considered. It is shown that the resulting general equations of motion are coupled together and form a nonlinear system of PDEs. Two cases of an open and closed box-beam cross-section made of symmetric laminate are analysed in details. It is shown that considering different pitch angles there is a strong effect in coupling of flapwise bending with chordwise bending motions due to a centrifugal force. Moreover, a consequence of terms related to nonconstant rotating speed is presented. Therefore it is shown that both the variable rotating speed and nonzero pitch angle have significant impact on systems dynamics and need to be considered in modelling of rotating beams

A refined structural model for static aeroelastic response and divergence of metallic and composite wings

A refined beam model with hierarchical features is in this work extended to the static aeroelastic analysis of lifting surfaces made of metallic and composite materials. The refined structural one-dimensional (1D) theory is based on the Carrera Unified Formulation and it permits to take into account any cross-section deformation, including warping effects. The vortex lattice method is employed to provide aerodynamic loadings along the two in-plane wing directions (wing span and wing cross-section). Applications are obtained by developing a coupled aeroelastic computational model which is based on the finite element method. The accuracy of the proposed 1D model is shown by a number of applications related to various wings made of metallic and composite materials. The effect of the cross-section deformation is evaluated on the aeroelastic static response and divergence of the considered wings. The need of higher-order expansions is underlined as well as the limitations of beam results which are based on classical theories. Comparison with results obtained by existing plate/shell aeroelastic models shows that the present 1D model could result less expensive from the computational point of view with respect to shell cases. The beneficial effects of aeroelastic tailoring in the case of wings made of composite anisotropic materials are also confirmed by the present analysis