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

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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.