scholarly journals Moving Griffith crack in an orthotropic strip with punches at boundary faces

2005 ◽  
Vol 2005 (19) ◽  
pp. 3157-3167
Author(s):  
S. Mukherjee ◽  
S. Das
Keyword(s):  
Constant Pressure ◽  
Integral Transform ◽  
Finite Thickness ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Griffith Crack ◽  
Orthotropic Strip ◽  
Finite Hilbert Transform ◽  
Integral Transform Technique ◽  
State Propagation

Integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of a Griffith crack centrally situated along the midplane of orthotropic strip of finite thickness2hand subjected to point loading with centrally situated moving punches under constant pressure along the boundaries of the layer. The problem is reduced to the solution of a pair of simultaneous singular integral equations with Cauchy-type singularities which have finally been solved through the finite Hilbert transform technique. For largeh, analytical expression for the stress intensity factor at the crack tip is obtained. Graphical plots of the numerical results are also presented.

Local Buckling of a Circular Interface Delamination Between a Layer and a Substrate With Finite Thickness

1999 ◽  
Vol 67 (3) ◽  
pp. 590-596 ◽  
Author(s):  
R. Sburlati ◽  
E. Madenci ◽  
I. Guven
Keyword(s):  
Integral Equations ◽  
Mixed Boundary ◽  
Finite Thickness ◽  
Local Buckling ◽  
Singular Integral Equations ◽  
Mixed Boundary Conditions ◽  
Homogeneous System ◽  
Theory Of Elasticity ◽  
Cauchy Type ◽  
The Stability

An analytical study investigating the local buckling response of a circular delamination along the interface of an elastic layer and a dissimilar substrate with finite thickness is presented. The solution method utilizes the stability equations of linear theory of elasticity under axisymmetry conditions. In-plane loading and the presence of mixed boundary conditions on the bond-plane result in a homogeneous system of coupled singular integral equations of the second kind with Cauchy-type kernels. Numerical solution of these integral equations leads to the determination of local buckling stress and its sensitivity to geometric parameters and material properties. [S0021-8936(00)01503-8]

Response of Finite-Thickness Gardon Heat-Flux Sensors

1972 ◽  
Vol 94 (2) ◽  
pp. 244-245 ◽  
Author(s):  
Robert H. Kirchhoff
Keyword(s):  
Heat Flux ◽  
Aspect Ratio ◽  
Integral Transform ◽  
Finite Thickness ◽  
Time Response ◽  
Heat Flux Sensor ◽  
Heat Flux Sensors ◽  
Temperature Time ◽  
Integral Transform Technique ◽  
Flux Sensor

The temperature–time response of a Gardon heat-flux sensor of finite thickness has been calculated by the integral-transform technique. Through the introduction of the aspect ratio, results are presented which characterize the response of a finite-thickness probe compared to a probe of zero thickness.

Load Buckling of a Layer Bonded to a Half-Space With an Interface Crack

1995 ◽  
Vol 62 (1) ◽  
pp. 64-70 ◽  
Author(s):  
Wen-Xue Wang ◽  
Yoshihiro Takao
Keyword(s):  
Half Space ◽  
Interface Crack ◽  
Integral Transform ◽  
Local Buckling ◽  
Compressive Load ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Theory Of Elasticity ◽  
Layered System ◽  
Cauchy Type

An analytical solution is presented for local buckling of a model of delaminated composites, that is, a layer bonded to a half-space with an interface crack. The layered system is subjected to compressive load parallel to the free surface. Basic stability equations derived from the mathematical theory of elasticity are employed to study this local buckling behavior. They are different from the conventional buckling equations used in most previous studies and based on the classical structural mechanics of beams and plates. A system of homogeneous Cauchy-type singular integral equations of the second kind is formulated by means of the Fourier integral transform and is solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for the buckling load and shape are presented for various delamination geometries and material properties of both the layer and half-space.

scholarly journals A pair of arbitrarily-oriented coplanar cracks in an anisotropic elastic slab

1991 ◽  
Vol 32 (3) ◽  
pp. 284-295 ◽  
Author(s):  
W. T. Ang
Keyword(s):  
Integral Equations ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Finite Part ◽  
Fourier Integral Transform ◽  
Anisotropic Elastic ◽  
Elastic Slab ◽  
Integral Transform Technique ◽  
Coplanar Cracks

AbstractThe problem of an anisotropic elastic slab containing two arbitrarily-oriented coplanar cracks in its interior is considered. Using a Fourier integral transform technique, we reduce the problem to a system of simultaneous finite-part singular integral equations which can be solved numerically. Once the integral equations are solved, relevant quantities such as the crack energy can be readily computed. Numerical results for specific examples are obtained.

scholarly journals Plane Elastostatic Solution in an Infinite Functionally Graded Layer Weakened by a Crack Lying in the Middle of the Layer

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
R. Patra ◽  
S. P. Barik ◽  
M. Kundu ◽  
P. K. Chaudhuri
Keyword(s):  
Integral Transform ◽  
Crack Opening ◽  
Crack Problem ◽  
Functionally Graded ◽  
Internal Crack ◽  
Cauchy Type ◽  
Elastic Parameters ◽  
Concentrated Force ◽  
Functionally Graded Layer ◽  
Integral Transform Technique

This paper is concerned with an internal crack problem in an infinite functionally graded elastic layer. The crack is opened by an internal uniform pressure p0 along its surface. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitude P/2 with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. Elastic parameters λ and μ are assumed to vary along the normal to the plane of crack. The problem is solved by using integral transform technique. The solution of the problem has been reduced to the solution of a Cauchy-type singular integral equation, which requires numerical treatment. The stress-intensity factors and the crack opening displacements are determined and the effects of graded parameters on them are shown graphically.

On the receding contact between a graded and a homogeneous layer due to a flat-ended indenter

2021 ◽  
pp. 108128652110431
Author(s):  
Rui Cao ◽  
Changwen Mi
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Integral Equations ◽  
Singular Integral ◽  
Functional Dependence ◽  
Singular Integral Equations ◽  
Homogeneous Layer ◽  
Cauchy Type ◽  
Receding Contact ◽  
Contact Pressures

This paper solves the frictionless receding contact problem between a graded and a homogeneous elastic layer due to a flat-ended rigid indenter. Although its Poisson’s ratio is kept as a constant, the shear modulus in the graded layer is assumed to exponentially vary along the thickness direction. The primary goal of this study is to investigate the functional dependence of both contact pressures and the extent of receding contact on the mechanical and geometric properties. For verification and validation purposes, both theoretical analysis and finite element modelings are conducted. In the analytical formulation, governing equations and boundary conditions of the double contact problem are converted into dual singular integral equations of Cauchy type with the help of Fourier integral transforms. In view of the drastically different singularity behavior of the stationary and receding contact pressures, Gauss–Chebyshev quadratures and collocations of both the first and the second kinds have to be jointly used to transform the dual singular integral equations into an algebraic system. As the resultant algebraic equations are nonlinear with respect to the extent of receding contact, an iterative algorithm based on the method of steepest descent is further developed. The semianalytical results are extensively verified and validated with those obtained from the graded finite element method, whose implementation details are also given for easy reference. Results from both approaches reveal that the property gradation, indenter width, and thickness ratio all play significant roles in the determination of both contact pressures and the receding contact extent. An appropriate combination of these parameters is able to tailor the double contact properties as desired.

scholarly journals Interaction between line cracks in an orthotropic layer

2002 ◽  
Vol 29 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Subir Das
Keyword(s):  
Fourier Transform ◽  
Stress Intensity ◽  
Finite Thickness ◽  
Intensity Factors ◽  
Orthotropic Layer ◽  
Finite Hilbert Transform ◽  
Crack Tips ◽  
The Fourier Transform ◽  
Analytical Expressions ◽  
Elastostatic Problem

We deal with the interaction between three coplanar Griffith cracks located symmetrically in the mid plane of an orthotropic layer of finite thickness2h. The Fourier transform technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have been solved by using the finite Hilbert transform technique and Cooke's result. The analytical expressions for the stress intensity factors at the crack tips are obtained for largeh. Numerical values of the interaction effect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to each other and crack tip spacing as well as the thickness of the layer.

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