| The dissertation is to address the need, in contact mechanics, of efficient and effective solutions to certain 3-D contact problems. The solutions developed here are based on underlying analytical solutions to pyramidal loading elements. This feature, along with other characteristics, distinguishes this method from other numerical solutions. The research work is logically divided into three subsequent parts, each of which addresses a particular aspect of the project: (1) Developed analytical solution sets in closed form to pyramidal loading profiles. First, a set of Boussinesq-Curruti equations to linear/bilinear distribution of normal and tangential loading over a triangular area are derived and evaluated. Second, solution sets to normal and tangential surface loading pyramids are constructed. The work provides a solution set to a basic loading element, which is the foundation of the development of effective and efficient semi-analytical solutions to 3-D contact problems with general geometry and loading profile. (2) Developed a semi-analytical approach (non-incremental algorithm) to 3-D normal contact problems with friction. This approach treats normal contact (indentation) phenomenon as a static problem. Based on fully coupled governing equations, the algorithm of contact detecting and stick/slip partitioning is designed as nested iterations, to fulfill contact boundary conditions. The computation shows that it is an efficient algorithm. Numerical examples are presented to show the accuracy and efficiency of the method. (3) Developed a semi-analytical approach (incremental algorithm) to 3-D contact problems with friction. This approach treats contact as a dynamic problem. The general dynamic models are simplified into quasi-static models in many practical cases that inertial force can be ignored. The incremental algorithm is designed to solve the quasi-static problems. The computation shows that the algorithm works very well for cases featuring both similar and dissimilar materials. Results are favorably compared with Mindlin's analytical solution, Munisamy's approach for axisymmetric contact subject to shear forces. Nowell's analytical approach for 2-D case is used for comparison in an analogous manner.; Computational practice shows that the semi-analytical approaches are efficient and robust, yielding very good results. They have wide range of potential applications. |
