Advanced Boundary Element Methods pp 369-378 | Cite as

# Boundary Integral Equation Method of Higher Computational Accuracy

## Abstract

The boundary integral equation method presented in the paper features with the following: (11 no singular kernels, strong or weak, are involved, and computationally, no local “element” approximations are needed; (2) the integral equations are well conditioned, including the cases of the bounded and multiply-connected regions, and no iterative approximations are involved; (3) no post-solution differentiation is involved. These features provide for a higher computational efficiency. The method solves in full a number of engineering problems, and can be used for the stiffness matrix formulation in more complex situations.

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Nystrom, E.J., “On practical solution of integral equations with application to boundary value problems,” Acta Math., t. 54, pp. 185–204, 1930 (in German).MathSciNetCrossRefGoogle Scholar
- 2.Kantorovich, L.V., and Krylov, V. 1., Approximate Methods in Higher Analysis, Fizmatgiz, Moscow, 1962 (in Russian).Google Scholar
- 3.Mikhlin, S.G., Integral Equations, Pergamon, 1964.Google Scholar
- 4.Massonet, C.E., “Numerical use of integral procedures,” in Stress Analysis, ed. by: O.C. Zienkiewicz, G.S. Holister, Willey, pp. 198–235, 1965.Google Scholar
- 5.Jaswon, M.A., “Integral equation method in potential theory,” Proc. Roy. Soc., A, 275, pp. 23–32, 1963.Google Scholar
- 6.Rizzo, F.J., “An integral equation approach to boundary value problems of classical elastostatics,” Q. Appl. Math., 25, pp. 83–95, 1967.Google Scholar
- 7.Cruse, T.A., “Numerical solutions in three-dimensional elastostatics,” Int. J. Solids and Structs, 5, pp. 1259–1274, 1969.MATHCrossRefGoogle Scholar
- 8.Brebia, C.A., and Walker, S., Boundary Element Techniques in Engineering, NewnesButterworths, 1980.Google Scholar
- 9.Banerjee, P.K., and Batterfield, R., Boundary Element Method in Engineering Science, McGraw-Hill, 1981.Google Scholar
- 10.Stern, M., “Formulating nonsingular boundary integral equations in linear elasticity,” in Advanced Topics in Boundary Element Analysis, ed. by: T.A. Cruse, A.B. Pifko, H. Armen, ASME, pp. 213–223, 1985.Google Scholar
- 11.Ghosh, N., Rajiyah, H., Ghosh, S., Mukherjee, S., “A new boundary element method formulation for linear elasticity,” J. Appl. Mech., Trans. ASME, 53, pp. 67–76, 1986.MathSciNetGoogle Scholar
- 12.Tatur, G.K., and Rubenchik, V.Ya., “Stress calculations on elastic prismatic rods in torsion, ” V.stsi Acad. Navuk BSSR, Ser. Fiz.-Tekn. Navuk, n2, pp. 9–13, 1973 (in Russian).Google Scholar
- 13.Rubenchik, V.Ya., “Integral equations for calculating the stress at elastic part surface in the plane case,” Teor. Prik. Mekh. (Minsk), n. 3, Belorusskii Politekh. Inst., pp. 92–100, 1976 (in Russian).Google Scholar
- 14.Rubenchik, V.Ya., “Stress concentration close to grooves,” Russ. Eng. J., v55, n12, pp. 2123, 1975.Google Scholar
- 15.Rubenchik, V.Ya., and Supin, V.V., “On solution of torsion problem in simply and multiply-connected cross-sections by integral equation method,” Teor. Prik. Mekh. (Minsk), n 7, Belorusskii Politekh. Inst., pp. 72–77, 1980 (in Russian).Google Scholar
- 16.Rubenchik, V., “Boundary-integral equation method applied to gear strength rating,” J. Mech. Transm. Autom. Des., Trans. ASME, v105, nl, pp. 129–131, 1983.Google Scholar
- 17.Sherman, D.I., “Statical planar problems of elasticity theory,” Trudy Tbilis. Matem. Inst., v. 11, 1937 (in Russian).Google Scholar
- 18.Perlin, P.I., and Shalyukhin, Yu.N., “On numerical solution of integral equations of elasticity theory,” Izvestia Akad. Nauk Kaz. SSR, Ser. Fiz.-Mat., n. 1, 1976 (in Russian).Google Scholar
- 19.Parton, V.Z., and Perlin, P.I., Mathematical Methods of the Theory of Elasticity, Mir Publishers, Moscow, 1984.MATHGoogle Scholar