Abstract
In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When numerical computations are needed for the solution, the method proves to have high precision and fast convergency.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Мусхелшивили, Н.И., Some Basic Problems of Mathematical Theory of Elasticity, Noordhoff, Groningen Holland (1953).
Mikhlin, S.G., Integral Equations and their application to certain problems in mechanics, Mathematical Physics and Technology, Trans, from Russian (1964).
Idel's, L. V. and Solov'er, Yu.I., One form of the integral equations for the solution of plane problems of elasticity,Mechanics of Solids,16, 3(1981).
Idel's, L.V., and Solov'er, Yu.I., One form of the integral equations for solution of three-dimensional axismmetric problems of elasticity,Mechanics of Solids,18, 3(1983).
Hartranft, R.J. and Sih, G.C., Alternating method applied to edge and surface crack problems,Mechanics of Fracture, I, Ed. by G.C. Sih, Noordhoff International Publishing, Leyden (1973).
Aleksandrov, A.Ya., et al., Numerical, implementation of the method of integral equations for the solution of elasticity for orthotropic continuous bodies and with cuts,Mechanics of Solids,18, 6(1983).
Kosenyuk, V.K., Solution of plane problem of elasticity for orthotropic bodies by numerical implementation of the method of integral equations,Mechanics of Solids,15, 6(1980).
Chen Y.Z., Solution of multiple crack problems of a circular plate or an infinite plate containing a circular hole by using Fredholm integral equation approachInter. J. Frac. 25, (1984).
Yun T.Q., An integral equation method for problem of load acting perpendicularly on the surface of a half space with rigid horizontal level,Acta Mechanica Solida Sinica, 3(1983), (in Chinese).
Gecit, M.R., An integral equation approach for simutaneous solution of rectangular block problems,Int. J. Engng Sci.,21, 9(1983).
Tang Renji and Wang Yinbang. Problem of crack system with an elliptical hole.Acta Mechanica Sinica,16, 6(1984), (in Chinese).
Wang Liangguo and Lin Xiao. Problems on infinite plate with arbitrary collinear cracks.Acta Mechanica Sinica 17, 3(1985), (in Chinese).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Liangguo, W., Xiao, L. On the general expression of Fredholm Integral Equations Method in elasticity. Acta Mech Sinica 4, 138–145 (1988). https://doi.org/10.1007/BF02487715
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487715