Applied Mathematics and Mechanics

, Volume 24, Issue 12, pp 1390–1397

Equivalent boundary integral equations with indirect variables for plane elasticity problems

• Zhang Yao-ming
• Wen Wei-dong
• Zhang Zuo-quan
• Sun Huan-chun
• Lü He-xiang
Article

Abstract

The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle. Based on this, the equivalent boundary integral equations (EBIE) with direct variables, which are equivalent to the original boundary value problem, were deduced rigorously. The conventionally prevailing boundary integral equation with direct variables was discussed thoroughly by some examples and it is shown that the previous results are not EBIE.

Key words

variational principle exterior problem equivalent boundary integral equation (EBIE)

O342

74S15 74K99

References

1. [1]
SUN Huan-chun, ZHANG, Yao-ming, SU Jiang,et al. Nonsingular Boundary Element Method [M]. dalian University of Technology Press, 1999. (in Cihinese)Google Scholar
2. [2]
YU De-hao.The Mathematical Theory of Nature Boundary Element Method[M]. Beijing: Science Press, 1993. (in Chinese)Google Scholar
3. [3]
Schmidt G, Stress H. The convergence of a direct, BEM for the plane mixed boundary value problems of the Laplacian[J].Numer Math, 1988,54(1):145–165.
4. [4]
Ciaret P G.The Finite Element Method for Elliptic Problems[M]. Amsterdam: North-Holland, 1978.Google Scholar
5. [5]
WANG Ming, ZHANG Hong-qing. Generalized Konr-Poincare inequality and Applications[J].Science Exploration, 1982,2(3):83–92. (in Chinese)
6. [6]
Zeb A, Elliot L, Ingham D B,et al. The boundary element method for solution of Stokes equation in two-dimensional domains[J].Eng Anal Boundary Element, 1998,22(11):317–326.
7. [7]
ZHANG Yao-ming, SUN Huan-chun, YANG Jia-xin. Equivalent boundary integral equations with indirect variables for thin elastic plate bending theory[J].Applied Mathematics and Mechanics (English Edition), 2000,21(11):1246–1255.
8. [8]
ZHANG Yao-ming, SUN Huan-chun. Plane Laplace problems[J].J Comput Mech, 2001,18(2): 162–166. (in Chinese)Google Scholar

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

• Zhang Yao-ming
• 1
• Wen Wei-dong
• 1
• Zhang Zuo-quan
• 2
• Sun Huan-chun
• 3
• Lü He-xiang
• 3
1. 1.College of energy & Power EngineeringNanjing University of Aeronautics and AstronauticsNanjingP. R. China
2. 2.School of Mathematics and PhysicsNorthern Jiaotong InstituteBeijingP. R. China
3. 3.Department of MechanicsDalian University of TechnologyDalianP. R. China