Mykola Makhorkin, Tetiana Makhorkina

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Abstract. In this paper, the possibility of constructing the analytical expressions to determine the order of the stress singularities in multi-wedge composites of the most prevalent geometric configurations for the case of antiplane deformation is considered. Particularly, the
analytical solutions of the corresponding characteristic equations are constructed for three-wedge systems whose components have such geometric characteristics: α1=π/2, α2=π, α3=α1=π/2is а half-plane and attached to it wedges with the such apical angles: α1=π/2 (in the
presence and absence of a slit); α1=π/4 , α2=π, α3=3π/4 is а half-plane and attached to it wedges with such apical angles: α1=π/4 , α2=3π/4 (in the presence and absence of the slit with outlet angle α=π/4 to the linear materials interface); α1=π/4 , α2=π, α3=π/4
is а half-plane and attached to it wedges with such apical angles: α1= α2=π/4 . The analytical solutions of characteristic equations for composite wedges composed of n = 3, 4 elements with identical apical angles are constructed as well. Additional studies, the results of
which have not been included in the materials of the article due to their inconvenience, indicate to that there are analytical solutions of the characteristic equation for a composite of this type with more elements. The obtained results make it possible to study the stress-strain state in multi-wedge systems of the considered configurations not restricting ourselves only to the vicinity of the wedges convergence point. In addition, the use of analytical solutions of characteristic equations in systems with a large number of wedges having the same apical angles gives the additional possibilities for analysis the angularly functionally graded materials.

Key words: multi-wedge system, antiplane deformation, order of the stress singularities, analytical solutions, composite wedge.

# Analytical determination of the order of stress field singularity in some configurations of multiwedge systems for the case of antiplane deformation

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