A Nonlinear Beam Finite Element with Bending–Torsion Coupling Formulation for Dynamic Analysis with Geometric Nonlinearities

Abstract

Vibration analysis of wing-box structures is a crucial aspect of the aeronautic design to avoid aeroelastic effects during normal flight operations. The deformation of a wing structure can induce nonlinear couplings, causing a different dynamic behavior from the linear counterpart, and nonlinear effects should be considered for more realistic simulations. Moreover, composite materials and aeroelastic tailoring require new simulation tools to include bending–torsion coupling effects. In this research, a beam finite element with bending–torsion coupling formulation is used to investigate the effects of the deflection of beam structures with different aspect ratios. The nonlinear effects are included in the finite element formulation. The geometrical effect is considered, applying a deformation dependent transformation matrix. Stiffness effects are introduced in the stiffness matrix with Hamilton’s Principle and a perturbation approach. The results obtained with the beam finite element model are compared with numerical and experimental evidence.

Keywords

• nonlinear modal analysis
• beam finite element
• bending–torsion coupling