Surface crack problems in plates

Joseph, Paul; Erdoğan, F.

doi:10.1007/bf00018480

Cited by 61 publications

(26 citation statements)

References 21 publications

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“…For Reissner plate theory, the solutions were obtained using the Fourier cosine/sine transform [3, 4, 5] and solving the integral equations [4,6,8] or minimizing the potential energy [5]. The stress intensity factors tabulated in I-5, 6] were adopted and are shown in Table !…”

Section: Reference Solutionsmentioning

confidence: 99%

“…Similarly, the relationship between G] R~ and KI R) for Reissner plate can be found using near-tip expressions (1), (4) and (5) which give From the stress intensity factors given in [5] and [6], the strain energy release rate can easily be found. However, in order to get the limiting expression of the strain energy release rate, the approach is made to utilize the potential energy given in [5].…”

Section: G~c)-3 +~V Ehmentioning

confidence: 99%

“…In order to satisfy three stress-free boundary conditions along the crack face, i.e. normal bending moment, twisting moment and transverse shear force must be zero; many researchers investigated the cracked plate problems using Reissner plate theory [3][4][5][6][7][8][9][10]. Their results show that near-tip bending and shearing stresses are inversely proportional to the square root of the distance from the crack tip.…”

Section: Introductionmentioning

confidence: 99%

“…Both the crack opening displacement and the stress intensity factors are shown to be smaller than the non-closure solutions. Joseph and Erdogan [6] employed a line spring model to investigate the closure effect. The contact zone and stress intensity factors are found to be dependent on the ratio of plate thickness to crack size.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose is to compare the two plate theories and also to see the difference between the line contact model and the line spring model [6]. The approach employs the Fourier transform technique used in [5] and includes the membrane component to satisfy the compatibility conditions along the crack face at the compressive side.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

Young

Sun

1993

Int J Fract

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For a through-the-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment, the strain energy release rate is determined using the virtual crack extension and the variation of potential energy. It is shown that the strain energy release rate for the Reissner's plate approaches the classical plate solution as the ratio of plate thickness to crack size becomes infinitesimally small. By using this result, the limiting expression of the stress intensity factor can be explicitly obtained. For general problems, the modified crack closure method is shown to be an efficient tool for evaluating the strain energy release rates from which the stress intensity factor can be calculated. Both the classical plate element and the Mindlin plate element are investigated, and the applicability of the classical plate element is evaluated.Because the stress-free conditions along the crack face lead to inter-penetration of the plate, a line contact model is assumed to investigate the closure effect using Reissner plate theory. Closure at the compressive side is shown to reduce crack opening displacement and consequently the stress intensity factors. When closure is considered, the strain energy rate based on the Reissner plate theory converges to the classical plate solution. This is similar to the nonclosure case.

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Section: Reference Solutionsmentioning

confidence: 99%

Section: G~c)-3 +~V Ehmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

Young

Sun

1993

Int J Fract

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Enrichment of Finite Elements With Numerical Solutions for Singular Stress Fields

Pageau

Biggers

1997

Int. J. Numer. Meth. Engng.

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SUMMARYEnriched 2-D and 3-D finite elements are formulated for analysis of solids having multi-material junction and wedge configurations that create singular stress fields due to the material and/or geometric discontinuities. The order and angular variation of the displacements associated with the singular fields are determined from a separate special finite element eigenanalysis and used in the enrichment process. The use of these numerically determined singular fields allows enriched elements to be developed for complex configurations for which analytical fields are not available. In addition to this added flexibility of application, the current formulation applies to elements that may or may not be in direct contact with the singular point. This allows multiple layers of enriched elements to be used around the singular point and traditional mesh refinement studies to be carried out in the enriched element region. Previous enriched formulations have not provided this important capability. For cases where analytical fields are available, such as cracked solids, the performance of elements developed with the current approach is shown to be equivalent to that obtained using analytically enriched elements. Mesh refinement techniques using enriched elements are described that allow accurate stress distributions and generalized stress intensity factors to be directly determined. The importance of high-order numerical integration, use of multiple layers of enriched elements, and proper choice of the size of the enriched region are demonstrated by comparison to existing solutions for solids with cracks. Application of enriched element modelling to a 2-D bi-material wedge and a 3-D stepped-thickness anisotropic composite laminate is demonstrated.1997 by John Wiley & Sons, Ltd.

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Conducting Material Systems and Structures

Shindo

2015

Electromagneto‐Mechanics of Material Systems and Structures

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Surface crack problems in plates

Cited by 61 publications

References 21 publications

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

Enrichment of Finite Elements With Numerical Solutions for Singular Stress Fields

Conducting Material Systems and Structures

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