| Summary: | 碩士 === 國立臺灣科技大學 === 營建工程系 === 91 === The thesis discusses the numerical errors caused by boundary element method in treating the thermal loading problem. The thermal loading problem is equivalent to the body force problem. For the body force problems, the complete solution can be split into homogeneous and particular solutions. In this study, the particular solution is evaluated first by expanding the equivalent body force into Fourier series, and then the boundary conditions of the homogeneous problem can be specified. After the homogeneous solution is obtained by the boundary element method, the complete solution then is evaluated by summing the homogeneous and particular solutions.
Body force presented by thermal loading is related to the internal temperature gradient in elastic body. This thesis applies the boundary element method to calculate the inner temperature gradient. However, due to the singular integration equation existing in boundary element analysis, numerical errors is arise when an internal point is very close to the boundary. Moreover, the body forces cannot be efficiently simulates at the ends of the region when expanded by Fourier series. Therefore, in boundary element analysis, the error mainly due to (1) the temperature gradient of inner point close to the boundary, (2) the error of Fourier series expanding. The linear extrapolated method is used to improve the present problems in this work.
Results show that (1) the linear extrapolated method could be useful in the boundary element method to obtain accurate results; (2) when the body force function is known, we can enlarge expand the region of Fourier series expanding to eliminate errors.
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