1. 二維反平面力學與穩態熱傳問題之 理論解析 編 號 ： NSC 97-2221-E-218-018 執行期限： 97 年 08 月 01 日至 98 年 07 月 31 日 執行機構：南台科技大學機械系 主持人 ：林 儒 禮 E-mail ： ruli@mail.stut.edu.tw

2. Heat Conduction V.S. Anti-Plane Shear Deformation Heat Conduction Anti-Plane Shear Deformation Governing Eq. Heat FluxShear Stress

3. The Relations Between Heat Conduction And Anti-plane Shear Deformation Heat conduction (Symbol)Anti-plane deformation (Symbol) Temperature ( T )Displacement ( w ) Coefficient of thermal conductivity ( k ) Shear modulus (  ) Heat flux along x-direction ( -q x ) Shear stress (  xz ) Heat flux along y-direction ( -q y ) Shear stress (  yz ) Concentrated heat source ( q 0 )Concentrated force ( f z ) Uniform distributed temperate ( T 0 )Dislocation ( b z ) Thermal isolation ( q = 0 ) Traction free (  = 0 ) Isothermal ( T = 0 )Fixed ( w = 0 )

4. Conformal Mapping MAPPING FUNCTION x - y domain (layered media) u – v domain (circular media) Governing Eq. Finite Layered Media Finite Wedge Finite Layered Media with Periodic Boundary Condition Annular Media

5. Fundamental Solution The temperature (displacement) field for a layered media where The temperature (displacement) field for a wedge by conformal mapping where

6. The temperature (displacement) field for a layered media with periodic boundary condition The temperature (displacement) field for a infinite circular media (infinite plane) by conformal mapping

7. Method of Image

8. Numerical Result of Finite Layered media

9. Numerical Result of Finite Wedge

10. Numerical Result of Annular Media

11. Solution of Composite Layer Media

12. Solution of Composite Layer media with Periodic Boundary Condition

13. Numerical results

14. Solution of Composite layer media

15. Solution of Composite Layer with Periodic Boundary Condition

16. Numerical results

17. A complete analysis of a concentrated loading applied in isotropic composite layer, wedge and circular media is presented. Conclusion Just only the fundamental solutions of layered media are solved mathematically. The solutions of the original layer medium are converted to wedge or circular problem, without resolving the correspondent problems. The explicit solutions presented in this project with explicit simple forms are easy to use for numerical investigations and theoretical analysis.

18. R.L. Lin, “Explicit Full Field Analytic Solutions for Two Dimensional Heat Conduction Problems with Finite Dimensions ”, International Journal of Heat and Mass Transfer, revised. Achievement R.L. Lin, “The Image Force of Screw Dislocation for Layered media, wedge and circular media”, Int. J. Solids and Structures.

19. Thanks for your attention