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A modified boundary-element method is proposed to analyze the stress-strain state of a plate with a multilayer inclusion of arbitrary shape. The two-dimensional approximation of displacements on each boundary element makes it possible to determine all the stress/strain components at the interface between the inclusion and each layer. The stress state of a plate with an elliptical and a rectangular multilayer inclusion under unidirectional tension (a load uniformly distributed along the edges) is analyzed as numerical examples. The numerical examples demonstrate high accuracy and computational efficiency of the method Keywords: plate, stress-strain state, multi-layer inclusion, modified boundary-element method, unidirectional tensionThe stress distribution around fibers in fibrous composites plays an important role in strength analysis. Solid mechanics reduces such problems to a stress analysis of an elastic matrix with holes or inclusions. A fundamental contribution to the study of stress concentration around curvilinear holes was made by G. N. Savin [5,6].The stress-strain state of plates and shells with holes and inclusions of different stiffness was addressed in [7,10,11,13,16]. This paper is concerned with the stress-strain state of laminated composites with multilayer fibers that are in a plane strain state. The problem is reduced to a stress-strain analysis of a matrix with a multilayer inclusion inside it and is solved by a modified [2-4] boundary-element method [17, 18].

Integral representations of the components of the displacement vector and the stress tensor and the corresponding system of boundary integral equations are derived for a piecewise-homogeneous body. A numerical scheme is developed that allows for the specific behavior of the stress fields in the neighborhood of the comer points of the inclusions. As an example, we consider the thermally stressed state of an elastic halfplane with inclusions of various shapes.

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