Modified trapezoidal quadratures and accurate potential evaluation for numerical solutions of S.I.E's on the unit circle
✍ Scribed by E. N. Theotokoglou
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 755 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0029-5981
No coin nor oath required. For personal study only.
✦ Synopsis
Plane elasticity problems that can be reduced to singular integral equations over the unit circle are considered, the method of using a dislocation density function 4.) is adopted. First, the trapezoidal approximation is modified for the evaluation of the contour integral $? [w(a)/(.-z)]da at the complex field point z; extra correction terms for known singularities of w(z) can easily be determined from the error expression. Based on the quadratures obtained, expressions for the accurate evaluation of the potentials are derived using their analyticity properties. The numerical techniques proposed are used for the solution of the problem of an infinite plate weakened by a circular hole and subjected to a dislocation.