# An algorithm based on the boundary element method for problems in engineering mechanics

An algorithm based on the boundary element method for problems in engineering mechanics The solution to a two‐dimensional problem using the boundary element method requires the evaluation of a line integral over the boundary. The integrand ot this line integral is a product of a known Green's function and an unknown function. A large number of Green's functions for two‐dimensional problems can be represented by a linear combination of four singular functions. By approximating the unknown function by a linear combination of known polynomials, integrals are generated whose integrand is a product of the polynomiais and one of the four singular functions. To evaluate these integrals analytically, the boundary is approximated by a sum of straight‐line segments. Recursive formulae are established which reduce the generality and the complexity of the integrands to simple expressions. Analytical forms for these simple expressions are found and are used for initiating the algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

# An algorithm based on the boundary element method for problems in engineering mechanics

16 pages

/lp/wiley/an-algorithm-based-on-the-boundary-element-method-for-problems-in-DPyz4cFHxb
Publisher
Wiley
ISSN
0029-5981
eISSN
1097-0207
D.O.I.
10.1002/nme.1620210906
Publisher site
See Article on Publisher Site

### Abstract

The solution to a two‐dimensional problem using the boundary element method requires the evaluation of a line integral over the boundary. The integrand ot this line integral is a product of a known Green's function and an unknown function. A large number of Green's functions for two‐dimensional problems can be represented by a linear combination of four singular functions. By approximating the unknown function by a linear combination of known polynomials, integrals are generated whose integrand is a product of the polynomiais and one of the four singular functions. To evaluate these integrals analytically, the boundary is approximated by a sum of straight‐line segments. Recursive formulae are established which reduce the generality and the complexity of the integrands to simple expressions. Analytical forms for these simple expressions are found and are used for initiating the algorithm.

### Journal

International Journal for Numerical Methods in EngineeringWiley

Published: Sep 1, 1985

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