| Existing Finite Element codes rely on the use of the variational approach to formulate contact problems. In this context, contact elements are developed and are assembled within the original FE code. This approach suffers from serious convergence and accuracy problems, which are governed by user defined parameters. It is thus the objective of this thesis to overcome these difficulties by using a mathematically rigorous and consistent variational inequalities approach. In this case, traditional structural finite elements are used in conjunction with the explicit imposition of the kinematic contact constraints, so as to eliminate the need for contact elements.; Consequently, this work is devoted to the development and implementation of a new variational inequalities approach for treating the general quasistatic frictional contact problem. The developed formulations are capable of describing the elastic and elasto-plastic behavior of solids. In the elasto-plastic case, an updated Lagrangian formulation is adopted to develop a new incremental variational inequality representing the time variation of the solution. In addition, the Jaumann objective stress rate is incorporated to account for finite rotations and Coulomb's friction was used to model friction forces.; In order to account for history effects, the load was applied incrementally in a newly developed two step algorithm. In the first step, the technique of Quadratic Programming is used to predict the actual contact surface and the stresses acting on it. In the second, the techniques of Lagrange multipliers and Non-Differential Optimization were used to calculate the field variables.; The use of the two step algorithm allows the determination of contact stresses and the actual contact surface between the contacting bodies, the explicit imposition of the active kinematic contact constraints, and the decomposition of the original complex problem into simpler sub-problems. In order to establish the validity of the developed techniques and formulations, test cases were examined and compared with existing solutions.; Finally, a number of engineering case studies, involving elastic and elasto-plastic behavior of solids, have been carefully examined. These cases include the analysis of: (i) spur gears, (ii) robotic dextrous grippers and (iii) the deep drawing process. The selection of these cases was governed by their practical importance to the engineering industry, their complexity and the role played by contact stresses in determining the failure of such systems. The treated cases also highlight the versatility and robustness of the developed approach. |
