Some Properties of J-Integral in Plane Elasticity

2001 ◽  
Vol 69 (2) ◽  
pp. 195-198 ◽  
Author(s):  
Y. Z. Chen ◽  
K. Y. Lee
Keyword(s):  
Function Method ◽  
Infinite Plate ◽  
Scalar Function ◽  
Plane Elasticity ◽  
Reciprocal Theorem ◽  
J Integral ◽  
Large Circle ◽  
Complex Variable Function ◽  
Variable Function ◽  
Complex Variable Function Method

Some properties of the J-integral in plane elasticity are analyzed. An infinite plate with any number of inclusions, cracks, and any loading conditions is considered. In addition to the physical field, a derivative field is defined and introduced. Using the Betti’s reciprocal theorem for the physical and derivative fields, two new path-independent D1 and D2 are obtained. It is found that the values of Jkk=1,2 on a large circle are equal to the values of Dkk=1,2 on the same circle. Using this property and the complex variable function method, the values of Jkk=1,2 on a large circle is obtained. It is proved that the vector Jkk=1,2 is a gradient of a scalar function Px,y.

scholarly journals Mode Stresses for the Interaction between an Inclined Crack and a Curved Crack in Plane Elasticity

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
N. M. A. Nik Long ◽  
M. R. Aridi ◽  
Z. K. Eshkuvatov
Keyword(s):  
Integral Equations ◽  
Function Method ◽  
Quadrature Rule ◽  
Plane Elasticity ◽  
Mode Iii ◽  
Inclined Crack ◽  
Complex Variable Function ◽  
Curved Crack ◽  
Variable Function ◽  
Complex Variable Function Method

The interaction between the inclined and curved cracks is studied. Using the complex variable function method, the formulation in hypersingular integral equations is obtained. The curved length coordinate method and suitable quadrature rule are used to solve the integral equations numerically for the unknown function, which are later used to evaluate the stress intensity factor. There are four cases of the mode stresses; Mode I, Mode II, Mode III, and Mix Mode are presented as the numerical examples.

scholarly journals Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Hongmei Wu
Keyword(s):  
Wave Scattering ◽  
Radial Stress ◽  
Function Method ◽  
Dynamic Stress ◽  
Analytic Solutions ◽  
Interface Effect ◽  
Sh Wave ◽  
Complex Variable Function ◽  
Variable Function ◽  
Complex Variable Function Method

This paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is given, and the infinite algebraic equations are established to solve the unknown coefficients of the scattered and refracted wave solutions. The analytic solutions of the stress field are obtained by using the orthogonality of trigonometric function. Finally, the dynamic stress concentration factor and the radial stress of a circular nanoinclusion are analyzed with some numerical results. The numerical results show that the interface effect weakens the dynamic stress concentration but enhances the radial stress around the nanoinclusion; further, we prove that the analytic solutions are correct.

The Analysis of the Effect of Surface Stresses at Nanoscale

2015 ◽  
Vol 1102 ◽  
pp. 169-172
Author(s):  
Zhi Ying Ou ◽  
Ya Wen Wu
Keyword(s):  
Contact Problem ◽  
Elasticity Theory ◽  
Function Method ◽  
Classical Elasticity ◽  
Complex Variable Function ◽  
Surface Stresses ◽  
Variable Function ◽  
Complex Variable Function Method ◽  
Classical Elasticity Theory ◽  
Effect Of Surface

Based on classical elasticity theory, the effects of surface stresses on the nanosized contact problem in an elastic half-plane which contains a nanocylindrical hole are analyzed. Meanwhile, the effects of surface energy of the contact nanosized surface are considered. The complex variable function method is applied to derive the fundamental solution of the contact problem. As example, the deformation induced by a distributed traction of cosine function on the nanosized surface is analyzed in detail. The results tell some interesting characteristics in contact mechanics, which are different from those in classical elasticity theory.

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