Showing papers on "Half-space published in 2011"

Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method

Abstract: The propagation of plane waves in fibre-reinforced, rotating thermoelastic half-space proposed by Lord-Shulman is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the coupled theory and the theory of generalized thermoelasticity with one relaxation time in the presence and absence of rotation and reinforcement. It is found that the rotation has a significant effect and the reinforcement has great effect on the distribution of field quantities when the rotation is considered.

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space

Abstract: The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord–Shulman under the effect of a magnetic field is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of time. It is found that the reinforcement has a great effect on the distribution of field quantities.

A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation

Abstract: The theory of thermoelasticity with energy dissipation is employed to study plane waves in a fibre-reinforced anisotropic thermoelastic half-space. We apply a thermal shock on the surface of the half-space which is taken to be traction free. The problem is solved numerically using a finite element method. Moreover, the numerical solutions of the non-dimensional governing partial differential equations of the problem are shown graphically. Comparisons are made with the results predicted by Green–Naghdi theory of the two types (GNII without energy dissipation) and (GNIII with energy dissipation). We found that the reinforcement has great effect on the distribution of field quantities. Results carried out in this paper can be used to design various fibre-reinforced anisotropic thermoelastic elements under thermal load to meet special engineering requirements.

Reflection of magneto-thermo-elastic waves from a rotating elastic half-space in generalized thermoelasticity under three theories

Abstract: The model of the equations of generalized magneto{thermoelasticity based on Lord{ Shulman theory (LS) with one relaxation time, Green{Lindsay theory (GL) with two relaxation times, as well as the classical dynamical coupled theory (CD), is used to study the electro{magneto{thermoelastic interactions in a semi{inflnite perfectly conducting solid. The entire elastic medium is rotating with a uniform angular velocity. There an initial magnetic fleld acts parallel to the plane boundary of the half{space. Re∞ection of magneto{thermoelastic waves under generalized thermoelasticity theory is employed to study the re∞ection of plane harmonic waves from a semi{inflnite rotating elastic solid in a vacuum. The expressions for the re∞ection coe‐cients, which are the relations of the amplitudes of the re∞ected waves to the amplitude of the incident waves, are obtained. Similarly, the re∞ection coe‐cients ratios variation with the angle of incident under difierent conditions are shown graphically. Comparisons are made with the results predicted by the three theories in the presence and absence of rotation.

Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half-space

Abstract: The present paper is concerned with the study of propagation of torsional waves in an inhomogeneous isotropic layer whose material properties vary harmonically with a space variable, lying over a semi-infinite inhomogeneous isotropic half-space. The closed form solutions for the displacement in the layer and half-space are obtained separately. The dimensionless phase velocity has been plotted against dimensionless wave number and scaled wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves using 2D and 3D plot.

Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas

Abstract: We study the large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half space. We consider an inflow problem where the gas enter into the region through the boundary, and we show that a corresponding stationary solution is time-asymptotically stable in both the subsonic and transonic cases. The proof of asymptotic stability is based on a priori estimates of the perturbation from the stationary solution, which are derived by a standard energy method, provided the boundary strength and the initial perturbation in a certain Sobolev space are sufficiently small.

Rotation and magnetic field effects on P wave reflection from a stress-free surface of elastic half-space with voids under one thermal relaxation time

Abstract: The present paper is devoted to the investigation of the influence of the rotation, thermal field, magnetic field and voids on the reflection of a P wave with one relaxation time. The basic governing equations for isotropic and homogeneous generalized thermoelastic half-spaces with voids, rotation and Maxwell’s stress are formulated in the context of the Lord Shulman theory. The boundary conditions at the stress-free thermally insulated surface are satisfied to obtain an algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves: P1, P 2, P3 and P4. In addition, the reflection coefficients from insulated and stress-free surfaces for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, magnetic field, thermal relaxation time and void parameters.

A Problem on Elastic Half Space Under Fractional Order Theory of Thermoelasticity

Abstract: The present work is concerned with the solution of a problem on fractional order theory of thermoelasticity for an elastic medium We investigate the thermoelastic interactions inside the medium by employing the fractional order theory of thermoelasticity, recently advocated by Sherief et al (Int J Solids Struct, 47, 269–275, 2010) State space approach together with the Laplace transform technique is used to obtain the general solution of the problem The general solution is then applied to three specific problems on an elastic half space, whose boundary is subjected to (i) a thermal shock (ie, a step input in temperature and zero stress), (ii) a normal load (ie, a step input in stress and zero temperature change) and (iii) a ramp type increase in temperature and zero stress To observe the variations of displacement, temperature and stress inside the half-space we compute the numerical values of the field variables for a particular material by utilizing a numerical method of Laplace inversion T

Implementation of a second-order paraxial boundary condition for a water-saturated layered half-space in plane strain

Abstract: A half-space finite element and a transmitting boundary are developed for a water-saturated layered half-space using a paraxial boundary condition. The exact dynamic stiffness of a half-space in plane strain is derived and a second-order paraxial approximation of the stiffness is obtained. A half-space finite element and a transmitting boundary are then formulated. The development is verified by comparison of the dynamic stiffness of impermeable and permeable rigid strip foundations with other published results. The advantage of using the paraxial boundary condition in comparison with the rigid boundary condition is examined. It is shown that the paraxial boundary condition offers significant gain and the resulting half-space finite element and transmitting boundary can represent the effects of a water-saturated layered half-space with good accuracy and efficiency. In addition, the numerical method described herein maintains the strengths and advantages of the finite element method and can be easily applied to demanding problems of soil–structure interaction in a water-saturated layered half-space. Copyright © 2010 John Wiley & Sons, Ltd.

Polynomials With Linear Structure and Maiorana–McFarland Construction

Abstract: In this paper, we study permutation polynomials over the finite fields that have linear structures. We present some results on such a permutation which transforms a hyperplane to another hyperplane. We fully characterize the bilinear polynomial with linear structure. The most important result of this paper is to show the relation between a Maiorana-McFarland function with an affine derivative and a polynomial with a linear structure. Moreover, we highlight this result in the context of resilient functions which are based on Maiorana-McFarland construction.

Indentation of an Elastic Half-space by a Rigid Flat Punch as a Model Problem for Analysing Contact Problems with Coulomb Friction

Abstract: One important problem which still remains to be solved today is the uniqueness of the solution of contact problems in linearized elastostatics with small Coulomb friction. This difficult question is addressed here in the case of the indentation of a two-dimensional elastic half-space by a rigid flat punch of finite width, which has been previously studied by Spence in Proc. Camb. Philos. Soc. 73, 249–268 (1973). It is proved that all the solutions have the same simple structure, involving active contact everywhere below the punch and a sticking interval surrounded by two inward slipping intervals. All these solutions show the same local asymptotics for surface traction and displacement at a border between a sticking and a slipping zone. These asymptotics describe (soft) singularities, which are universal (they hold with any geometry) and are explicitly given. It is also proved that in cases where the friction coefficient is small enough, the sticking intervals present in two distinct solutions, if two distinct solutions exist, cannot overlap.

Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave

Abstract: In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density The dispersion equation of the phase velocity has been derived It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs

Influence of porosity on characteristics of rayleigh-type waves in multilayered half-space

Abstract: Poroelastic fluidsaturated multilayered halfspace is considered; particle motion in this half� space is described by Biot-Frenkel equations for twophase media. A brief description of the derivation of integral and asymptotic representations for wave fields excited by a given surface load is presented; the influ� ence of the porous microstructure on the form of dispersion curves and amplitude characteristics of excited traveling waves is analyzed. It is demonstrated using numerical examples that the amplitude of additional modes occurring due to the presence of a microstructure can be essentially larger than the amplitudes of prin� cipal modes present in the waveguide with purely elastic layers.

Complements and Higher Resonance Varieties of Hyperplane Arrangements

Abstract: Hyperplane arrangements form the geometric counterpart of combinatorial objects such as matroids. The shape of the sequence of Betti numbers of the complement of a hyperplane arrangement is of particular interest in combinatorics, where they are known, up to a sign, as Whitney numbers of the first kind, and appear as the coefficients of chromatic, or characteristic, polynomials. We show that certain combinations, some nonlinear, of these Betti numbers satisfy Schur positivity. At the same time, we study the higher degree resonance varieties of the arrangement. We draw some consequences, using homological algebra results and vector bundles techniques, of the fact that all resonance varieties are determinantal.

Application of generalized images method to contact problems for a transversely isotropic elastic layer on a smooth half-space

Abstract: The idea, first used by the author for the case of crack problems, is applied here to solve a contact problem for a transversely isotropic elastic layer resting on a smooth elastic half-space, made of a different transversely isotropic material. A rigid punch of arbitrary shape is pressed against the layer’s free surface. The governing integral equation is derived; it is mathematically equivalent to that of an electrostatic problem of an infinite row of coaxial charged disks in the shape of the domain of contact. The case of circular domain of contact is considered in detail. As a comparison, the method of integral transforms is also used to solve the problem. The main difference of our integral transform approach with the existing ones is in separating of our half-space solution from the integral transform terms. It is shown that both methods lead to the same results, thus giving a new interpretation to the integral transform as a sum of an infinite series of generalized images.

Faces with given directions in anisotropic Poisson hyperplane mosaics

Abstract: For stationary Poisson hyperplane tessellations in d-dimensional Euclidean space and for a dimension k ∈ {1, . . . , d}, we investigate the typical k-face and the weighted typical k-face (weighted by k-dimensional volume), without isotropy assumptions on the tessellation. The case k = d concerns the previously studied typical cell and zero cell, respectively. For k < d, we first find the conditional distribution of the typical k-face or weighted typical k-face, given its direction. Then we investigate how the shapes of the faces are influenced by assumptions of different types: either via containment of convex bodies of given volume (including a new result for k = d), or, for weighted typical k-faces, in the spirit of D.G. Kendall’s asymptotic problem, suitably generalized. In all these results on typical or weighted typical k-faces with given direction space L, the Blaschke body of the section process of the underlying hyperplane process with L plays a crucial role.

Contact problems for several transversely isotropic elastic layers on a smooth elastic half-space

Abstract: The idea of generalized images, first used by the author for the case of crack problems, is applied here to solve a contact problem for n transversely isotropic elastic layers, with smooth interfaces, resting on a smooth elastic half-space, made of a different transversely isotropic material. A rigid punch of arbitrary shape is pressed against the top layer’s free surface. The governing integral equation is derived for the case of two layers; it is mathematically equivalent to that of an electrostatic problem of an infinite row of coaxial charged disks in the shape of the domain of contact. This result is then generalized for an arbitrary number of layers. As a comparison, the method of integral transforms is also used to solve the problem. The main difference of our integral transform approach with the existing ones is in separating of our half-space solution from the integral transform terms. It is shown that both methods lead to the same results, thus giving a new interpretation to the integral transform as a sum of an infinite series of generalized images.