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.

Partial slip contact analysis for a monoclinic half plane

2020 ◽  
pp. 108128652096283
Author(s):  
İ Çömez ◽  
Y Alinia ◽  
MA Güler ◽  
S El-Borgi
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Normal Load ◽  
Fibrous Composite ◽  
Singular Integral Equations ◽  
Contact Stresses ◽  
Partial Slip

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

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.

Thermal Response of Rolling Components Under Mixed Boundary Conditions: An Analytical Approach

1993 ◽  
Vol 115 (4) ◽  
pp. 857-865 ◽  
Author(s):  
P. Ulysse ◽  
M. M. Khonsari
Keyword(s):  
Temperature Distribution ◽  
Peclet Number ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Order Approximation ◽  
Thermal Response ◽  
Fourier Integral ◽  
Cylinder Surface ◽  
Péclet Number ◽  
Special Cases

An analytical solution for the steady-state temperature distribution in a cylinder undergoing uniform heating and nonuniform cooling is presented. The method of solution is a Fourier integral transform technique. The analysis shows that the Neumann series resulting from an integral equation can be well represented by a first-order approximation when the Peclet number is large. Furthermore, it is shown that the ratio of the Biot number to the square root of the Peclet number of the cooling zones is found to play an important role in governing the thermal response of the cylinder surface. The predicted results for the circumferential temperature distribution are compared to published experimental measurements for hot rolling and also existing analytical solutions for special cases. The agreement is found to be very good. By an appropriate superposition technique, the analysis presented may be easily extended to various heat sources and convective cooling zones at different locations of the cylinder surface.

On the dynamic interaction between a microdefect and a main crack

1995 ◽  
Vol 448 (1934) ◽  
pp. 449-464 ◽  
Keyword(s):  
Incident Wave ◽  
Main Crack ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Building Blocks ◽  
Dynamic Interaction ◽  
Dynamic Stress Intensity Factors ◽  
Plane Incident Wave ◽  
Incident Waves ◽  
Non Destructive

A generalized theoretical approach is presented for the dynamic interaction between an arbitrarily located and oriented microdefect and a finite main crack subjected to a plane incident wave. The analysis is based upon the use of integral transform techniques and an appropriate superposition procedure. The resulting dynamic stress intensity factors ( K * I and K * II ) at the main crack are obtained by solving the appropriate singular integral equations, using Chebyshev polynomi­als, for different incident waves. The resulting solution is verified by comparison with existing results, and numerical examples are provided to show the effect of the location and orientation of the microdefect and the frequency of the incident wave upon K * I and K * II of the main crack. The results advanced here can be used as building blocks in the fields of micromechanics, damage and non-destructive characterization of defects in solids.

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.

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 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.

On the Mechanical Modeling of Functionally Graded Interfacial Zone With a Griffith Crack: Anti-Plane Deformation

2003 ◽  
Vol 70 (5) ◽  
pp. 676-680 ◽  
Author(s):  
Y.-S. Wang ◽  
G.-Y. Huang ◽  
D. Dross
Keyword(s):  
Integral Transform ◽  
Mixed Boundary ◽  
Plane Deformation ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Interfacial Zone ◽  
Griffith Crack ◽  
Elastic Solids ◽  
Fourier Integral Transform ◽  
Graded Interfacial Zone

An analytical model is developed for a functionally graded interfacial zone between two dissimilar elastic solids. Based on the fact that an arbitrary curve can be approached by a continuous broken line, the interfacial zone with material properties varying continuously in an arbitrary manner is modeled as a multilayered medium with the elastic modulus varying linearly in each sublayer and continuous on the interfaces between sublayers. With this new multilayered model, we analyze the problem of a Griffith crack in the interfacial zone. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a Cauchy singular integral equation. The stress intensity factors are calculated. The paper compares the new model to other models and discusses its advantages.

Sliding Frictional Contact of Functionally Graded Magneto-Electro-Elastic Materials Under a Conducting Flat Punch

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Ju Ma ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang
Keyword(s):  
Frictional Contact ◽  
Integral Transform ◽  
Contact Region ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Flat Punch ◽  
Coupled Equations ◽  
Fourier Integral Transform ◽  
Coulomb Type

This paper presents the two-dimensional sliding frictional contact between a rigid perfectly conducting flat punch and a functionally graded magneto-electro-elastic material (FGMEEM) layered half-plane. The electric potential and magnetic potential of the punch are assumed to be constant within the contact region. The magneto-electro-elastic (MEE) material properties of the FGMEEM layer vary as an exponential function along the thickness direction, and the Coulomb type friction is adopted within the contact region. By using the Fourier integral transform technique, the problem is reduced to coupled Cauchy singular integral equations of the first and second kinds for the unknown surface contact pressure, electric charge, and magnetic induction. An iterative method is developed to solve the coupled equations numerically and obtain the surface MEE fields. Then, the interior MEE fields are also obtained according to the surface MEE fields. Numerical results indicate that the gradient index and friction coefficient affect both the surface and interior MEE fields significantly.

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