We study the problem of determination of the stress–strain state of a thin elastic orthotropic plate with orthotropic inclusions of any shape under loads applied to its edges. To solve the problem, we propose a modified direct boundary-element method capable of the simultaneous determination of all necessary quantities on the contact surfaces of each inclusion with the matrix by using a two-dimensional approximation of the components of the vector of displacements and stress tensor in every element of the discretization. The governing input relations are obtained for all components of the vector of displacements and stress tensor on the boundary and at inner points of the body under consideration.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 4, pp. 110–117, October–December, 2013.
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Lavrenyuk, M.V. Application of a Modified Boundary-Element Method to Problems of the Elasticity Theory in Piecewise Homogeneous Anisotropic Media. J Math Sci 208, 400–408 (2015). https://doi.org/10.1007/s10958-015-2454-x
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DOI: https://doi.org/10.1007/s10958-015-2454-x