Sharif Digital Repository

Using Helmholtz's decomposition theorem, the laws of balance of linear and angular momenta are restated as surface integrals over the closed surface of an arbitrary subregion in a continuum. Newton's law of action and reaction and Cauchy's theorem for stress and couple-stress are proved as corollaries of these surface balance laws. © Sharif University of Technology  

A numerical method for solving Fredholm-Volterra Hammerstein integral equations is presented. This method is based on replacement of the unknown function by truncated series of well known Chebyshev expansion of functions.The quadrature formula which we use to calculate integral terms can be estimated by Fast Fourier Transform (FFT). The numerical examples and the number of operations show the advantages of this method to some other usual methods. © 2006 Elsevier Inc. All rights reserved  

Electromagnetic scattering from thin resistive strips is formulated using an integral equation approach. The formulation is then specialized to strips of constant curvature and arbitrary size allowing the employment of the method of moments to solve the scattering problem  

Electromagnetic scattering from thin resistive strips is formulated using an integral equation approach. Analytical expressions for the electric current density over wide and narrow strips are derived based on the physical optics and quasistatic approximation of the pertinent integral equations, respectively. The solutions are used to find closed form expressions for the echo width of the strip  

In this article we prove the stationarity of the solution of the H-valued integral equation, where H is a real separable Hilbert space. In this equation, U(t) is a semigroup generated by a strictly negative definite, self-adjoint unbounded operator A, such that A-1 is compact and f is of monotone type and is bounded by a polynomial and V (t) is a cadlag adapted stationary process  

The asymmetric problem of lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space is addressed. With the aid of appropriate Green's functions, the governing equations of the problem are written as a set of coupled integral equations. With further mathematical transformations, the system of dual integral equations is reduced to two coupled Fredholm integral equations of the second kind which are amenable to numerical treatments. The exact closed-form solutions corresponding to two limiting cases of a membrane resting on the surface of a half-space and embedded in a full-space are derived. The jump behavior of results at the edge of the membrane... 

The dynamic analysis of a surface rigid foundation in smooth contact with a transversely isotropic half-space under a buried inclined time-harmonic load is addressed. By virtue of the superposition technique, appropriate Green[U+05F3]s functions, and employing further mathematical techniques, solution of the mixed-boundary-value problem is expressed in terms of two well-known Fredholm integral equations. Two limiting cases of the problem corresponding to the static loading and isotropic medium are considered and the available results in the literature are fully recovered. For the static case, the results pertinent to both frictionless and bonded contacts are obtained and compared. With the... 

The aim of this paper is to approximate the solution of a class of integral equations of the third kind on an unbounded domain. For computing such approximation, the collocation method based on the generalized Laguerre abscissas is considered. In this method, the unknown function is interpolated at the nodal points {ti}i=1 n+1, where {t i } i=1 n are the zeros of generalized Laguerre polynomials and t n+1 =4. Then, the given equation is transformed to the Fredholm integral equation of the second kind. In the sequel, according to the integration interval, we apply the Gauss-Laguerre collocation method on the interval [0,∞) by using the given nodal points. Therefore, the solution of the third... 

A smooth rigid circular anchor disk encapsulated by a penny-shaped crack is embedded in and unbounded transversely isotropic medium. The lamellar rigid disk exerts a nonuniform axisymmetric loading to the upper face of the crack. With the aid of an appropriate stress function and Hankel transform, the governing equations are converted to a set of triple integral equations which in turn are reduced to a Fredholm integral equation of the second kind. For some transversely isotropic materials the normalized stiffness of the system falls well outside of the envelope pertinent to isotropic media. It is shown that mode I stress intensity factor is independent of the material properties and solely... 

In this study, the tractive rolling contact problem between a rigid cylinder and a graded coating is investigated. The main objective of this study is to investigate the effect of the stiffness ratio, the coefficient of friction and the coating thickness on the surface contact tractions, the surface in-plane stress, the stick zone length and the creep ratio parameter that may have a bearing on the fatigue life of the component. Assuming that the shear modulus varies exponentially through the thickness of the coating, the governing integral equations associated with the rolling contact problem are constructed. Furthermore, it is supposed that the contact patch is controlled by a central stick... 

We theoretically investigate the formation of hotspots at microwave frequencies in a partially filled, ferrite-loaded rectangular waveguide. When the unidirectional mode of this waveguide approaches an impenetrable conducting barrier, its magnetic field rises sharply due to the absence of reflection. To study this phenomenon, we use the magnetostatic approximation and derive a surface integral equation for the normal component of magnetic flux density on the surface of the ferrite layer. For a half-filled waveguide, an analytic solution is found, which shows the magnetic field to diverge near the barrier as | x | - q, where | x | is the distance from the barrier edge and q is slightly less... 

In this paper, the two-dimensional tractive rolling contact problem between a rigid cylinder and an orthotropic half plane is considered. A pair of singular integral equations is derived for the contact tractions using the Fourier transform technique. The governing integral equations are decoupled using the Goodman approximation and then solved numerically. Finally, the distribution of surface tractions is achieved in the contact region. This study emphasizes the significant effect of the orthotropic material parameters and the coefficient of friction on the contact tractions as well as the rolling contact characteristics for an orthotropic medium. © 2016, Springer-Verlag Wien  

Asymmetric contact problem of an elastic wedge and an elastic half-plane has been considered. Contact pressure distributions as well as the lengths of the contact zones are extracted analytically. The results have been compared with the results of the symmetric problem and also the FE modelling of the problem which show excellent agreement. The method of approach is a completely analytical method based on the singular integral equations. In this method, the boundary conditions of the problem are stated as some singular integrals and distribution of the contact pressure is determined. Then, with the aid of the equilibrium equations and the consistency conditions of the singular integral... 

New enrichment functions are proposed for crack modelling in orthotropic media using the extended finite element method (XFEM). In this method, Heaviside and near-tip functions are utilized in the framework of the partition of unity method for modelling discontinuities in the classical finite element method. In this procedure, by using meshless based ideas, elements containing a crack are not required to conform to crack edges. Therefore, mesh generation is directly performed ignoring the existence of any crack while the method remains capable of extending the crack without any remeshing requirement. Furthermore, the type of elements around the crack-tip remains the same as other parts of... 

With the aid of a complete representation using two displacement potentials, an efficient and accurate analytical derivation of the fundamental Green's functions for a transversely isotropic elastic half-space subjected to an arbitrary, time-harmonic, finite, buried source is presented. The formulation includes a complete set of transformed stress-potential and displacement-potential relations that can be useful in a variety of elastodynamic as well as elastostatic problems. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. For the numerical evaluation of the inversion integrals, a quadrature scheme... 

A new hybrid method based on multimode contour integral and mode matching techniques will be introduced. It is capable of analyzing any H-plane discontinuity in a rectangular waveguide. The process is based on segmentation and dividing the structure into key building blocks. We use the multimode contour integral method to analyze the blocks including irregular shape H-plane discontinuities. In opposite to traditional contour integral method, which considers only the effect of dominant mode (TE10) on wave ports, multimode contour integral considers the effect of higher order modes (TE n0) excited by discontinuities on these ports. The mode matching technique will be used to analyze the... 

In this article, we prove the existence, uniqueness, and measurability of the solution for the following stopped semimonotone nonlinear integral equation [image omitted] We also improve the previous results under weaker assumptions