| This dissertation is based on two major computational methods for solving problems in mechanics, both of which arise from the boundary integral equation formulation. The first method is the boundary element method (BEM), which is especially useful for fracture mechanics problems, and the second is the fast Fourier transform method (FFT), which is useful for contact mechanics problems.; The fracture mechanics application of the BEM led to the solution of the inverse problem of earthquake location for the main shock of the June 26, 1989, magnitude M6.1 earthquake near Kalapana, Hawaii. The successful result of this study was the finding that part of the discrepancy between the geodetically and seismically inferred hypocenter depth could be attributable to the observed lateral variation in the material properties of the Earth's crust.; The contact mechanics application of the FFT solved tribological problems related to frictional heating. The method uses Fourier transformed Green's functions (frequency response functions), which are found in closed form. A fast and effective method was developed for the calculation of the normal surface displacement of an elastic halfspace due to arbitrary transient surface heating. |
