Abstract
This paper investigates the degenerate scale problem for plane elasticity in a multiply connected region with an outer elliptic boundary. Inside the elliptic boundary, there are many voids with arbitrary configurations. The problem is studied on the relevant homogenous boundary integral equation. The suggested solution is derived from a solution of a relevant problem. It is found that the degenerate scale and the non-trivial solution along the elliptic boundary in the problem are same as in the case of a single elliptic contour without voids. The present study mainly depends on integrations of several integrals, which can be integrated in a closed form.
Similar content being viewed by others
References
Rizzo F.J.: An integral equation approach to boundary value problems in classical electrostatics. Q. J. Appl. Math. 25, 83–95 (1967)
Cruse T.A.: Numerical solutions in three-dimensional electrostatics. Int. J. Solids Struct. 5, 1259–1274 (1969)
Jaswon M.A., Symm G.T.: Integral Equation Methods in Potential Theory and Elastostatics. Academic Press, London (1977)
Brebbia C.A., Telles T.C.F., Wrobel L.C.: Boundary Element Techniques—Theory and Applications in Engineering. Springer, Heidelberg (1984)
Cheng A.H.D., Cheng D.S.: Heritage and early history of the boundary element method. Eng. Anal. Boundary Elements 29, 286–302 (2005)
Christiansen S.: On two methods for elimination of non-unique solutions of an integral equation with logarithmic kernel. Appl. Anal. 13, 1–18 (1982)
Chen J.T., Lin S.R., Chen K.H.: Degenerate scale problem when solving Laplace’s equation by BEM and its treatment. Int. J. Numer. Mech. Eng. 62, 233–261 (2005)
Vodicka R., Mantic V.: On invertibility of elastic single-layer potential operator. J. Elast. 74, 147–173 (2004)
Vodicka R., Mantic V.: On solvability of a boundary integral equation of the first kind for Dirichlet boundary value problems in plane elasticity. Comput. Mech. 41, 817–826 (2008)
Chen Y.Z., Wang Z.X., Lin Z.X.: Numerical examination for degenerate scale problem for ellipse-shaped ring region. Int. J. Numer. Methods Eng. 71, 1208–1230 (2007)
Chen J.T., Shen W.C.: Degenerate scale for multiply connected Laplace problems. Mech. Res. Commun. 34, 69–77 (2007)
Chen Y.Z., Lin Z.X., Wang Z.X.: Evaluation of the degenerate scale for BIE in plane elasticity and antiplane elasticity by using conformal mapping. Eng. Anal. Boundary Elements 33, 147–159 (2009)
Muskhelishvili N.I.: Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Groningen (1953)
Chen J.T., Kuo S.R., Lin J.H.: Analytical study and numerical experiments for degenerate scale problems in the boundary element method of two-dimensional elasticity. Int. J. Numer. Methods Eng. 54, 1669–1681 (2002)
Chen Y.Z., Wang Z.X., Lin Z.X.: A new kernel in BIE and the exterior boundary value problem in plane elasticity. Acta Mech. 206, 207–224 (2009)
Chen, Y.Z., Lin, Z.X., Wang, Z.X.: Numerical solution for degenerate scale problem for exterior multiply connected region. Eng. Anal. Boundary Elements (2009, in press)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, Y.Z., Lin, X.Y. & Wang, Z.X. Degenerate scale problem for plane elasticity in a multiply connected region with outer elliptic boundary. Arch Appl Mech 80, 1055–1067 (2010). https://doi.org/10.1007/s00419-009-0357-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-009-0357-3