Green's Function for Thru-Crack Emanating From Fastener Holes

Hsu, T. M.; Rudd, JL

doi:10.1016/b978-0-08-022142-7.50032-6

Cited by 9 publications

(7 citation statements)

References 8 publications

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Section: Three-dimensional Applicationsmentioning

confidence: 99%

“…The stiffness would be K + SK and the nodal displacement vector would be u f Su. Assuming that SF = 0, the system of equations to be solved is then (9) Now, by using the fact that in the original solution, Ku = F, and ignoring the higher order term K~u = -SKU (10) This is extremely useful, for it shows that the perturbation in nodal displacements can be obtained from a second back-substitution through the already-factored initial stiffness matrix. The right-hand side is obtained from the initial displacements u and the perturbation of the stiffness matrix SK, which was also already calculated at the element level as a part of the determination of K I in equation (7).…”

Section: '($)+Sx'($)mentioning

confidence: 99%

“…Thus a local weighted average of the stress intensity factor can be obtained from separate nodal perturbations. Similarly, perturbations in nodal displacements associated with each crack advance can again be determined using (10). Now consider this loading, stress intensity factor distribution and set of displacement perturbations (one nodal vector 6u for each crack front perturbation Sl(s) in equation (12)) to be the 'starred' fields of equation ( Here t and f are again the continuum applied surface traction and body forces for the new, unstarred, loading system, 6u* = N6u" is the starred interpolated displacement perturbation, F is the equivalent nodal force vector for the new load system, and K~( s ) is the (to-be-determined) stress intensity factor distribution for the new load system.…”

Section: Three-dimensional Applicationsmentioning

confidence: 99%

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Weight functions from virtual crack extension

Parks¹,

Kamenetzky²

1979

Numerical Meth Engineering

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SUMMARYThe stiffness-derivative method of Parks' for calculating the linear elastic crack tip stress intensity factor for any symmetric crack configuration and a particular loading is extended to calculate the weight function vector fieldzB3 which serves as a Green's function for the stress intensity factor. The method, which combines the observations of Rice3 on the weight function and of Zienkiewicz4 on the differential stiffness method, permits very efficient determination of the weight function, requiring only one additional back-substitution on the already-factored stiffness matrix. Thus, the stress intensity factor for arbitrary loading of this configuration can subsequently be determined by quadrature alone. The promising extension of the method to three-dimensional configurations is outlined.While this manuscript was under review, the authors became aware of the recent work of Vanderglas,*' in which the same approach as ours is used to extend the stiffness-derivative method. The present work was then voluntarily revised in order to address further certain aspects of the topic of shape function perturbation, which Vanderglas noted.

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Section: Three-dimensional Applicationsmentioning

confidence: 99%

Section: '($)+Sx'($)mentioning

confidence: 99%

Section: Three-dimensional Applicationsmentioning

confidence: 99%

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Weight functions from virtual crack extension

Parks¹,

Kamenetzky²

1979

Numerical Meth Engineering

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“…-m2r4 sin (26 -2 a ) -3mr' sin 2a + sin (2a + 26) C = m3rb cos 29 -m2r4 cos 49 + 3mr' cos 29 -2m2r4 -1 D = m3r6 sin 28 -m2r4 sin 46 + my2 sin 28 E = m cos 28 + m2r2 -cos (28 + 21%) -mr' cos 2a F = m sin 28 -sin (28 + 2 a ) -my2 sin 2a G = 2mr4 cos 2a -m2r4 -2r' cos (21% + 28) + 1 H = m2r4 -2mr' cos 28 + 1 (7) If the plate is subjected to uniaxial stress S, (Fig. 3a), the stress distribution along the x axis, oyl (x), can be obtained from equation (7) Fig.…”

Section: Stress Distributionsmentioning

confidence: 99%

“…Hsu and Rudd [7], and Cartwright and Rooke [8] discussed the principle, which can be illustrated schematically from Fig. 1.…”

Section: Introductionmentioning

confidence: 98%

Stress Intensity Factors for Cracks in Notched Finite Plates Subjected to Biaxial Loading

Xiao¹,

Brown²,

Miller³

1985

Fatigue Fract Eng Mat Struct

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Stress intensity factors were calculated, based on Bueckner's principle for cracks in both infinite and finite plates with notches subjected to biaxial loading. Approximate Green's functions have been obtained by modifying two existing Green's functions, originally for unnotched plates. Values of stress intensity factors calculated using Bueckner's principle with the approximate Green's functions are in good agreement with published stress intensity factors for cracks in both infinite and finite plates containing a circular notch or an elliptical notch, previously found by the method of boundary collocation.

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Green's Functions in Fracture Mechanics

Cartwright¹,

Rooke²

1979

Fracture Mechanics

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Green's Function for Thru-Crack Emanating From Fastener Holes

Cited by 9 publications

References 8 publications

Weight functions from virtual crack extension

Weight functions from virtual crack extension

Stress Intensity Factors for Cracks in Notched Finite Plates Subjected to Biaxial Loading

Green's Functions in Fracture Mechanics

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