The principles of the boundary integral equation (BIE) or boundary element method (BEM) are discussed in a non-mathematical way. The technique is compared with other numerical methods, particularly the finite element method (FEM), on the basis of computational efficiency, and the main advantages and disadvantages of the BIE approach are outlined.
Get full access to this article
View all access options for this article.
References
1.
BettessR.‘Operation counts for boundary integral and finite element methods’, Int. J. Numer. Methods Engng, 1981, 15, 306–308.
2.
FennerR.T.‘Boundary elements for stress problems’, Seminar on Finite Elements or Boundary Elements. organized by the Institution of Mechanical Engineers on 15 June 1982.
3.
JaswonM. A.‘Integral equation methods in potential theory I’, Proc. R. Soc. Lond.1963, A275, 23–32.
4.
SymmG. T.‘Integral equation methods in potential theory II’, Proc. R. Soc. Lond., 1963, A275, 33–46.
5.
RizzoF. J.‘An integral equation approach to boundary value problems of classical elastostatics’, Quart. appl. Maths, 1967, 25, 83–95.
6.
CruseT. A.‘Numerical solutions in three-dimensional elastostatics’. Int. J. Solids Structures, 1969, 5, 1259–1274.
7.
CruseT. A.‘Application of the boundary integral equation method to three-dimensional stress analysis’, Computers and Structures, 1973, 3, 509–527.
8.
CruseT. A.Van BurenW.‘Three-dimensional elastic stress analysis of a fracture specimen with an edge crack’, Int. J. Fracture Mech., 1971, 7, 1–16.
9.
CruseT. A.RizzoF. J.‘A direct formulation and numerical solution of the general transient elastodynamic problem: I’, J. Math. Anal. Appl., 1968, 22, 244.
10.
CruseT. A.RizzoF. J.‘A direct formulation and numerical solution of the general transient elastodynamic problem: II’. J. Math. Anal. Appl., 1968, 22, 341.
11.
SwedlowJ. L.CruseT. A.‘Formulation of boundary integral equations for three-dimensional elasto-plastic flow’, Int. J. Solids Structures, 1971, 7, 1673–1683.
12.
MendelsonA.‘Boundary integral methods in elasticity and plasticity’, NASA TN D7418, 1973.
13.
MendelsonA.AlbersL. U.‘Application of boundary integral equations to elasto-plastic problems’, Boundary integral equation method: Computational applications in applied mechanics, (Eds CruseT. A.RizzoF. J.), ASME Proc. AMD, 1975, 11.
14.
RiccardellaP. C.‘An implementation of the boundary integral technique for planar problems in elasticity and elastoplasticity’, Report SM 73–10, Mechanical Engineering Department, Carnegie-Mellon University, Pittsburgh, 1973.
15.
CruseT. A.‘An improved boundary integral equation method for three-dimensional elastic stress analysis’, Computers and Structures, 1974, 4, 741–754.
16.
BoissenotJ. M.LachatJ. C.WatsonJ. O.‘Etude par equations integrales d'une eprouvette C.T.15’, Rev. Phys. Appl., 1974, 9, 611–615.
17.
LachatJ. C.A further development of the boundary integral technique for elastostatics. PhD thesis, University of Southampton, 1975.
18.
LachatJ. C.WatsonJ. O.‘A second generation boundary integral equation program for three-dimensional elastic analysis’, Boundary integral equation method: Computational applications in applied mechanics. (Eds. CruseT. A.RizzoF. J.), ASME Proc. AMD11.
19.
LachatJ. C.WatsonJ. O.‘Effective numerical treatment of boundary integral equations’, Int. J. Numer. Methods Engng, 1976, 10, 991–1005.
20.
LachatJ. C.WatsonJ. O.‘Progress in the use of boundary integral equations, illustrated by examples’, Comp. Meths appl. Mech. Engng, 1977, 10, 273–289.
21.
RizzoF. J.ShippyD. J.‘An advanced boundary integral equation method for three-dimensional thermo-elasticity’, Int. J. Numer. Methods Engng, 1977, 11, 1753–1768.
22.
KermanidisT.‘A numerical solution for axially symmetrical elasticity problems’, Int. J. Solids Structures, 1975, 11, 493–500.
23.
MayrM.‘The numerical solution of axisymmetric elasticity problems using an integral equation approach’, Mech. Res. Communications, 1976, 3, 393–398.
24.
CruseT. A.SnowD. W.WilsonR. B.‘Numerical solutions in axisymmetric elasticity’, Computers and Structures, 1977, 7, 445–451.
25.
ShippyD. J.RizzoF. J.NigamR. K.‘A boundary integral equation method for axisymmetric elastostatic bodies under arbitrary surface loads’, Proc. 2nd International Symposium on Innovative Numerical Analysis in Applied Engineering Sciences, 1980 (University Press of Virginia) pp. 423–432.
26.
MayrM.DrexlerW.KuhnG.‘A semianalytical boundary integral approach for axisymmetric elastic bodies with arbitrary boundary conditions’, Int. J. Solids Structures, 1980, 16, 863–871.
27.
CathieD. N.BanerjeeP. K.‘Numerical solutions in axisymmetric elastoplasticity by the boundary element method’, Proc. 2nd International Symposium on Innovative Numerical Analysis in Applied Engineering Sciences, 1980 (University Press of Virginia) pp. 331–339.
28.
CruseT. A.‘Numerical evaluation of elastic stress intensity factors by the boundary integral equation method’, The surface crack: Physical problems and computational solutions, (Ed. SwedlowJ. L.) 1972 (ASME, New York) pp. 153–170.
29.
CruseT. A.‘Boundary integral equation method for three-dimensional elastic fracture mechanics analysis’, US Air Force Office of Scientific Research TR-75–0813, 1975.
30.
CruseT. A.MeyersG. J.‘Three-dimensional fracture mechanics analysis’, Proc. ASCE, J. Struct. Div., 1977, 103, 309–320.
31.
TanC. L.FennerR. T.‘Elastic fracture mechanics analysis by the boundary integral equation method’, Proc. R. Soc. Lond., 1979, A369, 243–260.
32.
WatsonJ. O.‘Hermitian cubic boundary elements for plane problems of fracture mechanics’, Res Mechanica, 1982, 4, 23 42.
