Nonlinear static and dynamic modelling of composite rotor blades including warping effects

A beam finite element formulation has been developed to model helicopter rotor blades constructed of composite materials. The present formulation takes into account the warping effects of composite beams undergoing large deflections. This formulation can handle static and free vibration analysis of both rotating and non-rotating composite beams. The new approach can model thin to moderately thick walled beams with complicated cross-sections, tapers, planforms and pretwists. The formulation allows transverse shear deformation. The warping displacement parallel to the beam axis in the deformed configuration is superimposed over the cross-section. The strain is assumed to vary linearly through the thickness of the wall. This allows analytical integration through the thickness direction for arbitrary ply layups. The Fixed or Total Lagrangian description is adopted for the large deflection analysis. A body fixed system is used to describe the finite rotations. The natural modes and frequencies of both rotating and non-rotating composite beams are calculated using a subspace iteration technique. A comparative study with more elaborate finite element models is presented as well as correlation with experimental observations. Many numerical tests are presented, showing various features of the present analysis. Beams involving the various structural couplings, bending-torsion, extension-torsion and extension-bending, are examined. The inclusion of warping is shown to have significant effects on the stiffness of beams, especially the torsional stiffness. Correlation of numerical tests with shell and three-dimensional solid element formulations, as well as experimental results, demonstrate the validity and effectiveness of the present approach. Agreement between results from the present formulation and experimental data ranges from good to excellent where as results from the present formulation are in excellent agreement with solutions from the shell and three-dimensional finite element formulations.