Friction-based complementarity models for nonlinear dynamic contact interaction in multi-flexible body systems with damping

This dissertation is concerned with frictional contact analysis of multi-flexible body systems undergoing constrained motion. The research consists of 3 sections: modeling of multi-flexible body systems undergoing large motion, modeling of multi-flexible body systems undergoing dynamic contact interaction with friction and damping, and modeling of tire-soil interaction based on an incremental form of Bekker equation.; In the first section, a multi-flexible body model capable of handling large translations and rotations is developed. Hamilton equation-based finite elements for the dynamic analysis of flexible beams are formulated. A symplectic algorithm is employed to integrate the resulting equations. Three examples are solved to demonstrate the procedure. No solution blowup is observed despite using fairly large timesteps in long-term dynamic simulation runs. It appears that the proposed symplectic finite elements are capable of producing accurate and robust simulation in the dynamics modeling of multi-flexible body systems with large overall motions.; In the second section, a general formulation for capturing the effects of frictional contact interactions in the constrained motion of multi-flexible bodies is developed. The frictional contacts are described via a set of nonlinear complementarity equations which are converted into a series of linear complementarity problems for solution using the Lemke algorithm. To demonstrate the formulation the motion of a flexible beam bouncing off a damped elastic; foundation with friction is studied. Comparisons with published results are provided.; In the third section, an incremental form of Bekker model is proposed to overcome the difficulties in the traditional modeling of tire-soil interaction problems. The method involves formulating the contact dynamics with a set of complementarity equations. This approach allows contact forces to be evaluated as part of the solution of the unknown kinematics, and the net result is enhanced computational accuracy and convergency. Two examples are solved to demonstrate the effectiveness of the proposed algorithm. Solutions for soil sinkage, drawbar pull, normal pressure, and shear stress for a tire interacting with 3 types of soil:, loose sand, soft soil and LETE sand are provided and compared with published results.