Nonlinear finite element based multi-body analysis for rotor dynamics

This thesis is concerned with the modeling and formulation of nonlinear elastic multi-body systems discretized using the finite element method. The formulation uses Cartesian coordinates to represent the position of each elastic body with respect to a single inertial frame. The kinematic constraints among the various bodies are enforced via a Lagrange multiplier technique. Finite element formulation enables the treatment of arbitrary topologies and all geometric and material nonlinearities. Resolving all unknowns in a single inertial system simplifies the kinetic energy and kinematic constraint expressions and requires no distinction between rigid and elastic motion. The methodology provides a framework for the development of computationally efficient, modular software for the analysis of nonlinear elastic multi-body systems.;Since multi-body systems involve various elastic bodies and kinematic constraints, the resulting equations of motion are stiff, nonlinear, differential-algebraic equations. The integration of these equations presents a real challenge, as most available techniques are either numerically unstable, or present undesirable high frequency oscillations of a purely numerical origin. An approach is proposed in which the equations of motion are discretized so that they imply an energy decay inequality of the elastic components of the system, whereas the forces of constraint are discretized so that the work they perform vanishes exactly. The combination of these two features of the discretization guarantees the stability of the numerical integration process for nonlinear elastic multi-body systems and provides high frequency numerical dissipation.;The adequate choice of the time step size is a critical issue in structural dynamic analysis, and more particularly in multi-body dynamic analysis. Robust local and global error measures based on energy arguments are proposed for a single degree of freedom problem, then extended to multi degrees of freedom problems. By using the local error measure, an adaptive time step methodology is proposed for the energy decaying scheme.;The proposed multi-body formulation is used to simulate several models in rotor dynamic applications. The first example deals with the dynamic response of the KAFLEX flexible coupling. Several simulations are performed: unloaded angular misalignment, and unloaded and loaded parallel offset misalignment. The second example deals with the dynamic analysis of drive shaft coupled with tail boom structures and tailrotor. The focus of the analysis is on a supercritical power drive shaft for the tailrotor. The last example deals with the aero-elastic response of a rotor with a detailed modeling of helicopter rotor comprising swash plates, scissor mechanism, and the pitching control linkages.