1. Torsion cracked bar problem using BIEM S. K. Kao HR2-307/2008/01/21

2. Outline Cracked bars Green’s identity Torsion rigidity Dual boundary integral equations New Methods

3. Cracked bars

4. Outline Cracked bars Green’s identity Torsion rigidity Dual boundary integral equations New Methods

5. Green’s identity First Green’s identity Secend Green’s identity

6. Outline Cracked bars Green’s identity Torsion rigidity Dual boundary integral equations New Methods

7. Torsion rigidity Method 4

8. Torsion rigidity

10. Outline Cracked bars Green’s identity Torsion rigidity Dual boundary integral equations New Methods

11. Dual boundary integral equations Governing equation: Boundary conditions:

12. Dual boundary integral equations where

13. Outline Cracked bars Green’s identity Torsion rigidity Dual boundary integral equations New Methods

14. Singular matrix: Method 1: Lin Method 2: SVD Method 3: Orthogonal

15. The end Thank your attention