| To develop a deeper understanding of contact problems, the axisymmetric contact of an elastic structure such as a plate pressed into an isotropic elastic half-space under a variety of boundary-interracial conditions, including stick, slip and separation possibilities between the two elastic bodies is considered in the theory of elasticity. By means of one-dimensional integral equations, it is shown that a simple but rigorous mathematical formulation is possible for this class of boundary value problems. With it as the theoretical basis, a versatile numerical method with high accuracy and efficiency is developed with the aid of a newly developed finite element paradigm.; Because of the nonlinearities inherent in contact problems such as those with limited frictional capacity and the requirement of non-tensile contact between the plate and half-space, iterative procedures are needed to delineate the different contact zones of the problem domain. Both conforming contact problems, such as a rigid punch pressed into an elastic half-space, and non-conforming contact problems such as the action of a conical indenter can be treated using the numerical method implemented in this thesis. Results for a variety of rigid indenters and flexible plates are provided as illustrations. |
