Journal of Mathematical Sciences

, Volume 86, Issue 6, pp 3123–3128 | Cite as

A system of boundary integral equations for orthotropic shells of positive curvature with slits and holes

  • E. N. Dovbnya


We propose a method of constructing a system of boundary integral equations for the problem of the stress state of an orthotropic shell with slits and holes. Using the theory of distributions and the two-dimensional Fourier transform, we reduce the problem to a system of boundary integral equations. In the solution obtained the kernels of the system of integral equations do not contain the direction cosines of the unit outward normal vector explicitly. There are no extra-integral terms. The matrix of the kernels is symmetric. The kernels are regular or have a logarithmic singularity. Two figures. Bibliography: 6 titles.


Fourier Fourier Transform Stress State Integral Equation Normal Vector 
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Literature Cited

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    V. K. Khizhnyak and V. P. Shevchenko, “The stress state of orthotropic shells weakened by cracks,” in:Proceedings of the Third National Congress on Theoretical and Applied Mechanics, Varna 1977 [in Bulgarian], Sofiya (1977), Vol. 1, 604–609.Google Scholar
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    V. P. Shevchenko and E. N. Dovbnya, “On the solution of boundary-value problems of the theory of orthotropic shells with slits and holes of arbitrary configuration,”Dop. Akad. Nauk Ukr., Ser. A, No. 4, 44–47 (1995).Google Scholar
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    V. P. Shevchenko,Integral Transforms in the Theory of Plates and Shells [in Russian], Course materials, Donetsk (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

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  • E. N. Dovbnya

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