Problem of an anisotropic plate weakened by curvilinear cracks and reinforced by stiffeners

Maksimenko, V. N.

doi:10.1007/bf00911019

Cited by 8 publications

(7 citation statements)

References 4 publications

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“…For λ = 0.001, the elliptic hole degenerates into a rectilinear cut. In this case, the calculation results agree with those given in[2] for the problem of an anisotropic plate with cuts reinforced by thin elastic ribs [for the normalized stiffness parameter of the ribs…”

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Stress-strain state of an anisotropic plate with an elliptic hole and thin rigid inclusions

Maksimenko

Zorin

2007

J Appl Mech Tech Phys

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The stress-strain state of an anisotropic plate containing an elliptic hole and thin, absolutely rigid, curvilinear inclusions is studied. General integral representations of the solution of the problem are constructed that satisfy automatically the boundary conditions on the elliptic-hole contour and at infinity. The unknown density functions appearing in the potential representations of the solution are determined from the boundary conditions at the rigid inclusion contours. The problem is reduced to a system of singular integral equations which is solved by a numerical method. The effects of the material anisotropy, the degree of ellipticity of the elliptic hole, and the geometry of the rigid inclusions on the stress concentration in the plate are studied. The numerical results obtained are compared with existing analytical solutions.Let an infinite rectilinearly anisotropic plate of thickness h be weakened by an elliptic hole with the contour L 0 = {(x/a) 2 + (y/b) 2 = 1} and a set of thin, absolutely rigid inclusions shaped like smooth open curves L j (j = 1, k ). The curves do not intersect each other and the contour L 0 . For each contour L j , we determine the normal vector n(t) (t ∈ L j ) directed to the right when passing from the points a j to the points b j (Fig. 1). The plate is loaded by external forces X n + iY n at the hole contour and the forces σ ∞ x , σ ∞ y , and τ ∞ xy at infinity. Each inclusion can perform rigid-body translations and rotations:Here c j is a complex constant and ε j is the unknown or specified rotation of the rigid inclusion L j . The plus and minus signs refer to the left and right faces of the inclusion, respectively. It is assumed that a generalized plane stress state occurs in the plate and the rotation vanishes at infinity. The stresses in the plate can be expressed in terms of two analytical functions Φ ν (z ν ) (ν = 1, 2):(z ν = x + μ ν y and μ ν are the roots of the corresponding characteristic equation with positive imaginary parts [1]). We write the functions Φ ν (z ν ) (ν = 1, 2) as

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“…(the coefficients A * ν depend on the magnitude and direction of the point force [1]) and using the superposition principle [2], we seek the functions Φ ν2 (z ν ) in the form…”

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confidence: 99%

Stress-strain state of an anisotropic plate with an elliptic hole and thin rigid inclusions

Maksimenko

Zorin

2007

J Appl Mech Tech Phys

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“…For the stress field around cracks, a complex potential <lJv 1 (zv) was given by the following expression in the form of Cauchy type integral with an unknown integrand roy (1) [6];…”

Section: B Complex Potential For E D Ge Crack Aroun D Elliptical Holementioning

confidence: 99%

Complex potential method for stress intensity analysis in stringer bonded composite panel with impact damage

Jung-Ho

Pavchok

2010

International Forum on Strategic Technology 2010

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“…The deformation of an unbounded plate reinforced by a regular system of ribs of narrow rectangular cross sections has been the subject of extensive research (see, for example, [1][2][3][4]). Considerable attention has been given to the analysis of the fracture of a plate stiffened by a regular system of stringers [5][6][7][8][9]. In all indicated papers, the consideration was confined to a Griffith crack.…”

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Crack initiation in a stiffened plate

Mir-Salim-zade

2007

J Appl Mech Tech Phys

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UDC 539.375 M. V. Mir-Salim-zadeThe fracture mechanics problem of crack initiation in a stiffened plate is considered. The crack nucleus is modeled by a prefracture zone with bonds between the crack faces, which is treated as a region of weakened interparticle bonds of the material. The boundary-value problem of the equilibrium of a stiffened plate with a crack nucleus reduces to a nonlinear singular integrodifferential equation with a Cauchy type kernel. The strains in the crack initiation zone are found by solving this equation. The case of the stress state of the plate with a periodic system of prefracture zones is considered.

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Problem of an anisotropic plate weakened by curvilinear cracks and reinforced by stiffeners

Cited by 8 publications

References 4 publications

Stress-strain state of an anisotropic plate with an elliptic hole and thin rigid inclusions

Stress-strain state of an anisotropic plate with an elliptic hole and thin rigid inclusions

Complex potential method for stress intensity analysis in stringer bonded composite panel with impact damage

Crack initiation in a stiffened plate

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