| Summary: | 碩士 === 國立成功大學 === 機械工程學系碩博士班 === 93 === Owing to the improvements of the processing technology, there exist a lot of micro-scale problems during the fabrication, such as thermal stress and phase change of materials etc.. Under the assumption of the Fourier’s law, the speed of the thermal wave in a body is infinite. But this speed can be finite, such as the problem in a very short time. Under this circumstance, the generalized thermoelectric theorem can be introduced to analyze such problems. The main purpose is to investigate the effects of temperature and displacement on the thermal stress in a very short time. Therefore, Generalized thermoelectric theorem is used to investigate the temperature, the displacement, and the stress distribution in piezoelectricity material.
The governing differential equations and boundary conditions are transformed by using the Laplace transform method and then the control volume method is used to discrete the resulting differential equations. The hyperbolic shape functions. As introduced in order to overcome the numerical oscillations in the from Jump discontinuities Finally, the numerical inversion of the Laplace transform is used to obtained the temperature, the displacement and the stresses.
In order to evidence the accuracy of the numerical scheme, a comparison of the numerical results and the analytical solution is made for a semi-finite problem conditions is used to get the distributions of temperature, displacement, and stress, then compare with the analytical results.
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