Solution of integral equation in curve crack problem by using curve length coordinate

Chen, Y.Z.

doi:10.1016/s0955-7997(03)00126-7

Cited by 15 publications

(10 citation statements)

References 7 publications

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“…The remote loading is s 1 x ¼ s 1 y ¼ p. A quadrature rule for the hypersingular integral equation proposed in [32] is used. In addition, the curve length coordinate technique is suggested in the solution [33]. Therefore, the hypersingular integral equation (107) can be solved numerically.…”

Section: A Numerical Example For a Curved Crack Using Hypersingular Imentioning

confidence: 99%

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

Chen

Lin

Wang

2010

Engineering Analysis with Boundary Elements

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Section: A Numerical Example For a Curved Crack Using Hypersingular Imentioning

confidence: 99%

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

Chen

Lin

Wang

2010

Engineering Analysis with Boundary Elements

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“…It was proved that the complex potentials for this field could be expressed as [Chen and Hasebe 1995]…”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

“…By substituting (20) and (21) into (14), letting the point z approach a point t o j ∈ L j on the j-th branch (see Figure 4b), and using the Plemelj formula for the Cauchy-type integral [Muskhelishvili 1953], one will find the following singular integral equation [Chen and Hasebe 1995]:…”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

Untitled

2009

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $600 a year (print and electronic); $460 a year (electronic only). Subscriptions, requests for back issues, and changes of address should be sent toThis paper investigates the singular integral equation method for examining the stress intensity factor and the T-stress in the asymptotic solution of a kinked crack with an infinitesimal kink length. A numerical technique for the branch crack problem is introduced, which depends upon distribution of dislocation along the crack face. The technique reduces the branch crack problem to the solution of a singular integral equation. The kinked cracked problem can be considered as a particular case of the branch crack, and this problem can be solved by using the suggested technique. It is found from the computed results that the available asymptotic solution can give qualitatively correct results for stress intensity factors and the T-stress. In addition, the available asymptotic solution can only give sufficiently accurate results in a narrow range of the length of the kinked portion and the inclined kink angle.Numerical procedures are developed for the homogenization and evaluation of the stress field in a composite as a consequence of the presence of embedded SMA (shape-memory alloy) wires. In particular, the elastic field developed at the end of the SMA wire self-strain process is studied, knowledge of which is necessary to evaluate the feasibility of such a hybrid composite.First, the numerical procedures are applied to the study of both a representative volume element (RVE) included in a theoretically infinite periodic medium and a RVE located near the medium free boundary, in order to evaluate the tangential stress field generated at the end of the fiber; then they are applied to the study of a plate able to bend after the effect of self-strain of the SMA wire.Observations are reported about the obtained results and about the similarities and the differences between the two problems.The Lyapunov exponent and moment Lyapunov exponent of two degree-of-freedom linear systems subjected to white noise parametric excitation are investigated. Through a perturbation method we obtain the explicit asymptotic expressions for these exponents in the presence of low intensity noise. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining the almostsure and moment stability of a stochastic dynamical system. As an example, we study the almost-sure and moment stability of the flexural-torsion stability of a thin elastic beam subjected to a stochastically fluctuating follower force. The validity of the approximate results for moment Lyapunov exponents is checked by a numerical Monte Carlo simulation for these stochastic systems.A method was devised to evaluate the adhesion between a film and a substrate. A front-end coated bullet is accelerated by a gas gun and hits the substrate of the specimen under test. The impact generates a compressive stre...

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“…In computation, the curve length coordinates method is used to solve the singular integral equation [Chen 2004]. The computed T-stresses is expressed as…”

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

Crack front position and crack back position techniques for evaluating theT-stress at crack tip using functions of a complex variable

Chen

Wang

Lin

2008

JOMMS

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In this paper, the crack front position and the crack back position techniques for evaluating the T-stress using complex variables are suggested. In the crack front technique, an expression for stress components in the crack front position is expressed through a complex variable. The limit value of the expression from the crack front position will give the T-stress. In the crack back technique, the other expression of stress components in the crack back position is expressed through the complex variable. The limit value of the expression from the crack back position will give the T-stress. The suggested techniques are used to evaluate T-stress in the arc crack and the curved crack problems. It is found from a detailed derivation that both techniques give the same result in the crack problem. Numerical examples are carried out for two problems: an elliptic crack with a central crack and a curved crack with parabolic configuration.

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Solution of integral equation in curve crack problem by using curve length coordinate

Cited by 15 publications

References 7 publications

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

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Crack front position and crack back position techniques for evaluating theT-stress at crack tip using functions of a complex variable

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