Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Professor M.A. Dokainish


A corotational finite element formulation for flexible multibody systems which are subjected to frictional impact is developed in this thesis. The formulation can predict the motion of the system, the contact forces, the velocities, the accelerations, the duration of impact and the associated deformations.

First, a corotational finite element formulation is developed for the dynamic analysis of flexible multibody systems without impact. A numerical algorithm is developed along the lines of the incremental-iterative method of the Newmark direct integration and Newton-Raphson methods.

Frictional impact is then included in the formulation. The prediction of contact establishment and separation is achieved using an event predictor. Point impact is assumed and Coulomb's friction law is used to model the friction forces.

Two multibody-oriented approaches are used to model the frictional impact. The first approach is based on a modified momentum balance model. An energy-based method is developed to resolve the problem of energy mismatch which arises with the use of Newton's impact law or Poisson's hypothesis. The concept of the coefficient of restitution is used and a new technique is developed to calculate the contact forces in some special cases. In general, it is assumed that multiple impulses occur during the contact period. An automatic time stepping algorithm is developed for numerical solutions.

The second approach is based on the Lagrange multiplier method. The model exactly satisfies the geometric compatibility conditions during contact. It also allows the direct evaluation of the contact forces. Both sliding and sticking modes are considered. The proposed scheme overcomes the problem of high dimensionality in the traditional Lagrange multiplier models in structural dynamics.

The applicability and accuracy of the formulation and the numerical technique are demonstrated. Simulation of various mechanical systems, which are subjected to impact loads, are presented.

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