On the Interior Stress Problem for Elastic Bodies-Reference-Cited by-同舟云学术

On the Interior Stress Problem for Elastic Bodies

Published:2000-05-10 Issue:4 Volume:67 Page:658-662
ISSN:0021-8936
Container-title:Journal of Applied Mechanics
language:en
Short-container-title:

Author:

Helsing J.¹

Affiliation:

1. Department of Solid Mechanics and NADA, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

Abstract

The classic Sherman-Lauricella integral equation and an integral equation due to Muskhelishvili for the interior stress problem are modified. The modified formulations differ from the classic ones in several respects: Both modifications are based on uniqueness conditions with clear physical interpretations and, more importantly, they do not require the arbitrary placement of a point inside the computational domain. Furthermore, in the modified Muskhelishvili equation the unknown quantity, which is solved for, is simply related to the stress. In Muskhelishvili’s original formulation the unknown quantity is related to the displacement. Numerical examples demonstrate the greater stability of the modified schemes. [S0021-8936(00)01304-0]

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

http://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/67/4/658/5467667/658_1.pdf

Reference13 articles.

1. Sherman, D. I. , 1940, “Sur la Solution du Second Proble`me Fondamental de la The´orie Statique Plane de l’E´lasticite´,” Comptes Rendus (Doklady) l’Acad. Sci. l’URSS, 28, pp. 25–32.

2. Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Ltd., Groningen.

3. Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York.

4. Mikhlin, S. G., 1957, Integral equations, Pergamon Press, London.

5. Parton, V. Z., and Perlin, P. I., 1982, Integral Equation Methods in Elasticity, MIR, Moscow.

Cited by 10 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the Stability of the Nyström Method for the Muskhelishvili Equation on Contours with Corners;SIAM Journal on Numerical Analysis;2013-01

2. Features of the Nyström Method for the Sherman-Lauricella Equation on Piecewise Smooth Contours;East Asian Journal on Applied Mathematics;2011-11

3. Stability of the Nyström Method for the Sherman–Lauricella Equation;SIAM Journal on Numerical Analysis;2011-01

4. Efficient algorithm for edge cracked geometries;International Journal for Numerical Methods in Engineering;2006-06-11

5. Laplace’s equation and the Dirichlet–Neumann map: a new mode for Mikhlin’s method;Journal of Computational Physics;2005-01