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Torsion cracked bar problem using BIEM

This study explores the torsion problems of cracked bars, employing advanced Boundary Integral Equation Methods (BIEM). Key topics include the implementation of Green’s identities to analyze torsion rigidity and the formulation of dual boundary integral equations. Several new methodologies are introduced to tackle the challenges presented by cracked bars, focusing on both analytical and numerical approaches. The research demonstrates novel techniques for managing singular matrices using methods such as Lin, SVD, and Orthogonal methods, providing insightful solutions for engineers and researchers dealing with structural integrity.

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Torsion cracked bar problem using BIEM

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  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

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

  10. Dual boundary integral equations • Governing equation: • Boundary conditions:

  11. Dual boundary integral equations where

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

  13. New Methods Singular matrix: • Method 1: Lin • Method 2: SVD • Method 3: Orthogonal

  14. The end Thank your attention

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