Certain problems of an arbitrarily oriented stringer in a composite an isotropic plane

Krivoi, A. F.; Popov, G. Ya.; Radiollo, M. V.

doi:10.1016/0021-8928(86)90012-2

Cited by 7 publications

(5 citation statements)

References 2 publications

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“…3 ) to the matrix equation ( 6). Thus, by using equalities (7), conditions (8), and the results obtained in [7,13,14,16,17,[19][20][21][22], for…”

Section: Construction Of the Fundamental Solutionmentioning

confidence: 99%

“…The functions w kj ± ∈ ′ ℑ (! ± 3 ) admit an analytic representation [7,13,14,16] with respect to the variable α 3 and, therefore, Eq. ( 9) is the boundary condition of the matrix Riemann problem in the variable α 3 .…”

Section: Construction Of the Fundamental Solutionmentioning

confidence: 99%

“…( 9) is the boundary condition of the matrix Riemann problem in the variable α 3 . By using the properties of generalized functions applying using the methods proposed in [7,13,14,16,17,[19][20][21][22], we represent the boundary conditions (9) in the form…”

Section: Construction Of the Fundamental Solutionmentioning

confidence: 99%

“…In [2, 9-12, 15, 18], the nonsymmetric problems of elasticity and thermoelasticity for interface stress concentrators, such as cracks or rigid inclusions in piecewise-homogeneous transversely isotropic spaces, were reduced to systems of two-dimensional singular integral equations (SIE) by the method of singular integral relations (SIR) [29], and a method for their solution was proposed. A similar approach was applied in [8,13,14,[20][21][22] to solve the problems of interface and internal defects in piecewise-homogeneous anisotropic media.…”

mentioning

confidence: 99%

“…3 ) of generalized tempered functions proves to be an efficient method for the solution of the indicated problem. In particular, in [16,17], the problem of construction of the fundamental solutions for piecewise homogeneous two-dimensional anisotropic media was reduced to the matrix Riemann problem for a part of variables in the space ′ ℑ (! 3 ), and an approach to its solution was proposed.…”

mentioning

confidence: 99%

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Fundamental Solutions for a Piecewise-Homogeneous Transversely Isotropic Elastic Space

Kryvyi¹,

Morozov

2023

J Math Sci

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The problem of construction of the fundamental solutions for a piecewise-homogeneous transversely isotropic space is reduced to a matrix Riemann problem in the space of slowly increasing distributions. We propose a method for the solution of this problem. As a result, in the explicit form, we obtain expressions for the components of the vector of fundamental solution and simple representations for the components of the stress tensor and the vector of displacements in the plane of joint of transversely isotropic elastic half spaces subjected to the action of concentrated normal and tangential forces. We study the fields of stresses and displacements in the plane of joint of the half spaces. In particular, for some combinations of materials, we present the numerical values of the coefficients of influence of concentrated forces on the stresses and displacements. We also establish conditions under which the normal displacements are absent in the plane of joint of transversely isotropic elastic half spaces.

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