A quadratic boundary element for potential problems in 2D with no numerical integration
✍ Scribed by Verhoeven, N. A. ;Morgan, K.
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 448 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1069-8299
No coin nor oath required. For personal study only.
✦ Synopsis
Both the logarithmic and derivative kernel integrations for potential problems, solved with quadratic isoparametric boundary elements, contain quartic functions of the integration parameter. It is shown that such functions can be written as the product of two quadratic functions with real coefficients. The derivative kernel integration is then represented as the s u m of two integrals, which can be evaluated analytically. The logarithmic kernel integration can be similarly split but needs a Taylor series expansion of the Jacobian of the integration to enable analytical integration. The use of this Taylor series expansion means that the method presented is limited to problems involving weakly curved elements.
KEY WORDS boundary element method; two-dimensional potential problems; logarithmic kemel; derivative kemal J ( t ) is the Jacobian of the transformation from actual to parametric space, n(t) is the unit