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.

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]

On the Interaction at Anti-Flat Deformation of Stress Concentrators of the Type of Cracks and Stringers with Regard to the Layer Manufactured from Miscellaneous Materials

2019 ◽  
Vol 828 ◽  
pp. 81-88
Author(s):  
Nune Grigoryan ◽  
Mher Mkrtchyan
Keyword(s):  
Integral Transform ◽  
Composite Layer ◽  
Singular Integral Equations ◽  
Original System ◽  
Fourier Integral ◽  
Quadrature Formulas ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Tangential Forces

In this paper, we consider the problem of determining the basic characteristics of the stress state of a composite in the form of a piecewise homogeneous elastic layer reinforced along its extreme edges by stringers of finite lengths and containing a collinear system of an arbitrary number of cracks at the junction line of heterogeneous materials. It is assumed that stringers along their longitudinal edges are loaded with tangential forces, and along their vertical edges - with horizontal concentrated forces. In addition, the cracks are laden with distributed tangential forces of different intensities. The case is also considered when the lower edge of the composite layer is free from the stringer and rigidly clamped. It is believed that under the action of these loads, the composite layer in the direction of one of the coordinate axes is in conditions of anti-flat deformation (longitudinal shift). Using the Fourier integral transform, the solution of the problem is reduced to solving a system of singular integral equations (SIE) of three equations. The solution of this system is obtained by a well-known numerical-analytical method for solving the SIE using Gauss quadrature formulas by the use of the Chebyshev nodes. As a result, the solution of the original system of SIE is reduced to the solution of the system of systems of linear algebraic equations (SLAE). Various special cases are considered, when the defining SIE and the SLAE of the task are greatly simplified, which will make it possible to carry out a detailed numerical analysis and identify patterns of change in the characteristics of the tasks.

Effects of Interleaves on Fracture of Laminated Composites: Part I—Analysis

1990 ◽  
Vol 57 (1) ◽  
pp. 168-174 ◽  
Author(s):  
A. K. Kaw ◽  
J. G. Goree
Keyword(s):  
Composite Laminates ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Elastic Media ◽  
Two Dimensional ◽  
Shear Moduli ◽  
Fourier Integral Transform ◽  
Shaped Crack ◽  
Symmetric Crack

The influence of placing interleaves between fiber-reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as a two-dimensional, isotropic, linearly elastic media consisting of a damaged layer bonded between two half-planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. Fourier integral transform techniques are used to develop the solutions in terms of singular integral equations.

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.

Transfer Matrix Method of Wave Propagation in a Layered Medium With Multiple Interface Cracks: Antiplane Case

2000 ◽  
Vol 68 (3) ◽  
pp. 499-503 ◽  
Author(s):  
Y.-S. Wang ◽  
D. Gross
Keyword(s):  
Wave Propagation ◽  
Transfer Matrix ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Universal Method ◽  
Dynamic Stress Intensity Factors ◽  
Interface Cracks ◽  
Multiple Interface

The paper develops a universal method for SH-wave propagation in a multilayered medium with an arbitrary number of interface cracks. The method makes use of the transfer matrix and Fourier integral transform techniques to cast the mixed boundary value problem to a set of Cauchy singular integral equations of the first type which can be solved numerically. The paper calculates the dynamic stress intensity factors for some simple but typical examples.

Rapid Contact on a Prestressed Highly Elastic Half-Space: The Sliding Ellipsoid and Rolling Sphere

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Half Space ◽  
Contact Zone ◽  
Compressive Load ◽  
Reference Value ◽  
Singular Integral Equations ◽  
Elastic Half Space ◽  
Polar Coordinates ◽  
Rigid Sphere ◽  
Cauchy Stress ◽  
Specific Contact

A neo-Hookean half-space, in equilibrium under uniform Cauchy stress, undergoes contact by a sliding rigid ellipsoid or a rolling rigid sphere. Sliding is resisted by friction, and sliding or rolling speed is subcritical. It is assumed that a dynamic steady state is achieved and that deformation induced by contact is infinitesimal. Transform methods, modified by introduction of quasi-polar coordinates, are used to obtain classical singular integral equations for this deformation. Assumptions of specific contact zone shape are not required. Signorini conditions and the requirement that resultant compressive load is stationary with respect to contact zone stress give an equation for any contact zone span in terms of a reference value and an algebraic formula for the latter. Calculations show that prestress can significantly alter the ratio of spans parallel and normal to the direction of die travel, an effect enhanced by increasing die speed.

Size Effect of a Crack in a Micropolar Piezoelectric Medium

2009 ◽  
Vol 417-418 ◽  
pp. 525-528
Author(s):  
Gan Yun Huang ◽  
Shou Wen Yu
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Constitutive Relations ◽  
Electric Displacement ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Piezoelectric Medium ◽  
Intensity Factors

A crack problem in a micropolar piezoelectric solid is considered. By using simplified constitutive relations, the problem can be reduced to the solution of a set of Cauchy singular integral equations with the help of Fourier integral transform technique. Numerical results for stress intensity factors, couple stress intensity factors and electric displacement intensity factors show that micropolar theory can be expected to explain certain size effects in piezoelectric solids.

scholarly journals TRANSIENT PLANE WAVES IN MULTILAYERED HALF-SPACE

2013 ◽  
Vol 7 (1) ◽  
pp. 53-57
Author(s):  
Ihor Turchyn ◽  
Olga Turchyn
Keyword(s):  
Half Space ◽  
Normal Load ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Boundary Surface ◽  
Fourier Integral ◽  
Theory Of Elasticity ◽  
Mechanical Contact ◽  
Space Boundary ◽  
And Function

Abstract Considered the dynamic problem of the theory of elasticity for multilayered half-space. Boundary surface of inhomogeneous half-space loaded with normal load, and the boundaries of separation layers are in conditions of ideal mechanical contact. The formulation involves non-classical separation of equations of motion using two functions with a particular mechanical meaning volumetric expansion and function of acceleration of the shift. In terms of these functions obtained two wave equation, written boundary conditions and the conditions of ideal mechanical contact of layers. Using the Laguerre and Fourier integral transformations was obtained the solution of the formulated problem. The results of the calculation of the stress-strain state in the half-space with a coating for a local impact loading are presented.

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 An Elastic Half Space with a Moving Punch

2021 ◽  
Vol 16 ◽  
pp. 245-249
Author(s):  
Sandip Saha ◽  
Vikash Kumar ◽  
Apurba Narayan Das
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Integral Transform ◽  
Contact Region ◽  
Stress Component ◽  
Static Problem ◽  
Fourier Integral ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Dual Integral Equations

The dynamic problem of a punch with rounded tips moving in an elastic half-space in a fixed direction has been considered. The static problem of determining stress component under the contact region of a punch has also been solved. Fourier integral transform has been employed to reduce the problems in solving dual integral equations. These integral equations have been solved using Cooke’s [1] result (1970) to obtain the stress component. Finally, exact expressions for stress components under the punch and the normal displacement component in the region outside the punch have been derived. Numerical results for stress intensity factor at the punch end and torque applied over the contact region have been presented in the form of graph.

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