Development of a New General Solution for Elastic Quarter-space Problems Based on Matrix Formulation

Elastic quarter-space problems are quite common in practical mechanical systems such as rail-wheel contact or contacts in gears, and roller bearings. They have a common feature that a vertical free surface is close to the contact region. The free surface would affect the determination of the elastic stress and displacement fields under applied surface loadings. Theoretical solutions to quarter-space problems are complicated. Thus, numerical methods, typically FEM, are required to obtain approximate solutions. However, the processes are very time-consuming, and not easy to apply to real applications. Particularly, for those engineering problems which require the convergence of iterative calculations to obtain the solutions such as elastohydrodynamic lubrication (EHL) analyses, a more efficient approach is crucial.The aim of this project is thus to develop an efficient way to solve the elastic quarter-space problems, which can shorten significantly the calculation time and be more convenient to apply to practical engineering.