| Summary: | 碩士 === 國立臺灣海洋大學 === 河海工程學系 === 96 === In this thesis, we employ the addition theorem and superposition technique to derive the Green function of the concentrated forces and screw dislocation problems. By using the superposition technique, the problems can be decomposed into two parts. One is the problem of the fundamental solution and the other is a typical boundary value problem (BVP). The fundamental solution is expanded into the degenerate kernel by using the addition theorem. The angle-type fundamental solution of the screw dislocation problem has not been expanded into the degenerate form before to our best knowledge. Following the success of null-filed integral formulation for solving the typical BVP with Fourier boundary densities in the NTOU/MSV group, the second part boundary condition can be easily obtained by introducing the superposition technique and addition theorem. After superposing the two solutions, the Green function can be obtained. Convergence rate using various numbers of terms for Fourier series is also examined. Finally, some concentrated force and screw dislocation problems with circular boundaries, including holes and inclusions, were demonstrated to see the validity of present method. Five disadvantages, (1) calculation of principal value, (2) ill-posed model, (3) boundary-layer effect, (4) linear convergence and (5) mesh generation, can be avoided by using the present approach in comparison with the conventional BEM.
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