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

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

Cracked bars

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

Green’s identity First Green’s identity Secend Green’s identity

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

Torsion rigidity Method 4

Torsion rigidity

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

Dual boundary integral equations Governing equation: Boundary conditions:

Dual boundary integral equations where

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

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

The end Thank your attention