Influence of a thin isotropic coating on the edge effect zone in isotropic and transversely isotropic materials

Bystrov, V. M.; Kokhanenko, Yu. V.

doi:10.1007/s10778-008-0010-9

Cited by 3 publications

(1 citation statement)

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“…The edge effect on the edge where the external load acts has not been studied sufficiently. In [2,6,7], such a problem is investigated using the finite-difference method. In [16], an analytical method for investigation of such a problem is proposed.…”

Section: Introductionmentioning

confidence: 99%

Stress distribution in multilayered composites near loaded edges

Soyucok

Soyuçok

2008

Int Appl Mech

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The edge effect in layered composite material is studied using the piecewise-homogeneous body model and the exact equations of the theory of elasticity. It is assumed that continuously distributed normal forces act at the edges of the reinforcing layers. A plain strain state is considered and the stresses are expressed in terms of the solutions of a system of dual singular integral equations. The singularity of the stresses is determined by the solution procedure. The concentration of the reinforcing layers is assumed low and the interaction between them is not taken into account. A numerical algorithm is developed and numerical results on the stress distribution are presented Keywords: edge effects, composite material, singularity, stress distribution 1. Introduction. The investigation of edge effects in layered and fibrous composites is of significant practical and theoretical importance. In this field, many studies were carried out in various numerical and analytical approximations [2-7, 12, 13, 15, 18, 19]. Most of these studies are reviewed in the recently published papers [9,10]. In most of these papers, the edge effect is studied mainly in the edge plane that is parallel to the direction of external loading. Moreover, in some of these investigations emphasis is placed on the determination of the order of stress singularities. The edge effect on the edge where the external load acts has not been studied sufficiently. In [2, 6, 7], such a problem is investigated using the finite-difference method. In [16], an analytical method for investigation of such a problem is proposed. The present paper employs this method to study a concrete problem on the edge effect in layered composites. The concentration of the reinforcement layers is assumed low and the interaction between these layers is not taken into account. In other words, the plane-strain elasticity problem in an isotropic half-space containing a different isotropic layer loaded at the edge surface is considered (Fig. 1). The stresses are determined from the solutions of a system of dual singular integral equations. The singularity of the stresses is determined by the solution procedure. Fourier expansions in terms of Jacobi polynomials and generalized Laguerre polynomials for two unknown functions are used to obtain numerical results of the integral equations for some boundary loadings and material data. The normal stresses in the planes parallel to the free surface and normal and shear stresses at the interface between the two materials are presented by graphs. The results are compared with the classical results for a homogeneous half-plane loaded by the same surface forces.2. Formulation and Solution of the Problem. The governing equations of the linear theory of elasticity for each material in Fig. 1 are

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Section: Introductionmentioning

confidence: 99%

Stress distribution in multilayered composites near loaded edges

Soyucok

Soyuçok

2008

Int Appl Mech

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Studying edge effects near rectangular mine workings weakened by a crack

Zelenskii

2008

Int Appl Mech

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Edge effects in a rock mass near a system of periodic mine workings crossed by a crack (fold fault) are considered. The stress state near the mine workings is determined by solving an elastic problem using the piecewise-homogeneous medium model. The original differential problem is reduced to a discrete problem based on the concept of a base scheme. Methods are proposed to solve the discrete problem, and the issue of optimizing the numerical analysis is discussed. The stress distribution around mine workings is analyzed. The stress isolines that represent the boundaries of edge effect zones and indicate their maximum decay length are plotted Keywords: edge effect, periodic system of mine workings, crack (fold fault), discrete problem, numerical methodIntroduction. The determination of the stress-strain state near mine workings is one of the main problems in rock mechanics. Cracks (faults) in a rock mass greatly affect its strength near a mine working. It is of practical interest to analyze and allow for this factor in developing construction-and technology-related measures that ensure trouble-free mining operations. The edge effects near a system of parallel horizontal mine workings of rectangular cross-section were analyzed in [3]. In [4], edge effects are determined using a difference approach that employs the concept of base factors to set up difference equations and formulate a discrete problem. A real rock mass was considered there. The isolines of stress s 22 defining the boundaries of edge effect zones with prescribed accuracy r% were plotted as an example. Such an approach was used in [7-10] to study edge effects in structural members made of layered and fibrous composites.Continuing the study [3], the present paper determines the edge effect in a rock mass containing a periodic system of deep horizontal mine workings. The workings are aligned along the Îx 3 -axis, are parallel to the Ox 1 -axis, and are crossed by a crack symmetric about the Ox 2 -axis (Fig. 1). The analysis of the edge effect is reduced to the determination and analysis of the stress-strain state near a mine working, analysis of the geometry of the edge effect zone, and the determination of its decay length with prescribed accuracy.

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