Premium
An algorithm based on the boundary element method for problems in engineering mechanics
Author(s) -
Vable Madhukar
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210906
Subject(s) - boundary element method , mathematics , line integral , simple (philosophy) , singular integral , boundary (topology) , function (biology) , product (mathematics) , element (criminal law) , mathematical analysis , boundary knot method , singular boundary method , line (geometry) , algorithm , integral equation , finite element method , geometry , philosophy , physics , epistemology , evolutionary biology , biology , political science , law , thermodynamics
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.