Longitudinal elastic wave propagation in laminated composites with bonds

We extended the finite element displacement method to study the propagation of longitudinal elastic waves in laminated composite with bonds. The geometric arrangement of the composite model considered in this paper is treated as a special type of a trilaminated composite in which each of its major constituents is sandwiched between two bonding layers. The dispersion characteristics of this model are presented here and compared with some exact results. The exact dispersion relation for the trilaminated composite is formally obtained by solving the field equations subjected to continuity conditions at materials' interfaces. Also included in the comparisons are the results obtained with continuum theory with microstructure. It is found that numerical results of finite element analysis, continuum theory and exact analysis corelate well especially for the lower modes of wave propagation.     

Scattering of torsional waves by a spherical cavity in a long circular elastic cylinder

Summary. The axisymmetric wave equation is solved for the problem of torsional elastic waves scattered by a spherical cavity located symmetrically in an infinitely long circular cylinder. Using Fourier transforms, the problem is reduced to the solution of an infinite system of simultaneous equations, which is suitable for the numerical solution. The numerical results on the transmission and reflection coefficients are shown for various values of sphere radius and frequency. Equation of energy conservation is utilized to check the numerical procedure.     

Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stess intensity factors, far-field amplitudes and the scattering cross section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stress intensity factors, far-field amplitudes and the scattering cross-section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

A quasi-three-dimensional elastic wave propagation analysis for laminated composites

Localized impact problems for composite structures have recently become important. In this study, some elastic wave velocities in 7-ply GFRP laminate with [0₂/90₃/0₂] ply orientation after low speed impact was investigated by using both experimental methods and finite element methods. For the finite element simulation, the quasi-three-dimensional model was used. Comparing the results, the validity for the application of this model to the dynamic problem was estimated. Moreover the quasi-three-dimensional model is applied to the GFRP plates with interlaminar delamination. The relationship between the elastic wave velocities and delaminated states is discussed.     

Scattering of elastic waves by a crack with spring-mass contact

The scattering problem of elastic waves by a crack with spring-mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack-opening displacements and scattering cross-sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross-sections, even if the mass is small.     

Coupling of the BEM with the MFS for the numerical simulation of frequency domain 2-D elastic wave propagation in the presence of elastic inclusions and cracks

This paper proposes a coupling formulation between the boundary element method (BEM displacement and TBEM traction formulations) and the method of fundamental solutions (MFS) for the transient analysis of elastic wave propagation in the presence of multiple elastic inclusions to overcome the specific limitations of each of these methods. The full domain of the original problem is divided into sub-domains, which are handled separately by the BEM or the MFS. The coupling is enforced by imposing the required boundary conditions.The accuracy, efficiency and stability of the proposed algorithms, using different combinations of BEM and MFS, are verified by comparing the solutions against reference solutions. The computational efficiency of the proposed coupling formulation is illustrated by computing the CPU time and the error at high frequencies.The potential of the proposed procedures is illustrated by simulating the propagation of elastic waves in the vicinity of an empty crack, with null thickness placed close to an elastic inclusion.     

Stress wave propagation in elastic/viscoplastic cylindrical bodies containing a spherical cavity

Summary The effect of randomness of elastic parameters as well as the fulfilment of similarity laws in the statistical mean on the evaluation of prototype stresses within the framework of 3D-anisotropic photothermoelasticity is investigated. Stress differences due to the noncommutativity of the order of application of Hooke's law and model laws are determined, and the theory is applied to the determination of stress intensity factors.With 3 Figures     

Scattering of elastic waves by a diamond shaped inclusion with cracks

This paper studies the scattering of in-plane compressional and shear waves by a diamond shaped inclusion with cracks using the boundary element method. The special case that the shape of the diamond becomes square is also considered. Numerical calculations are carried out for the limited cases of diamond shaped hole and rigid inclusions, and the effects of frequency and inclusion shape on the scattering cross section and dynamic stress intensity factor are shown in graphical form. The results where the elastic properties of the inclusion are the same as those of the matrix are also discussed.     

3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions

In this paper, the traction boundary element method (TBEM) and the boundary element method (BEM), formulated in the frequency domain, are combined so as to evaluate the 3D scattered wave field generated by 2D fluid-filled thin inclusions. This model overcomes the thin-body difficulty posed when the classical BEM is applied. The inclusion may exhibit arbitrary geometry and orientation, and may have null thickness. The singular and hypersingular integrals that appear during the model's implementation are computed analytically, which overcomes one of the drawbacks of this formulation. Different source types such as plane, cylindrical and spherical sources, may excite the medium. The results provided by the proposed model are verified against responses provided by analytical models derived for a cylindrical circular fluid-filled borehole.The performance of the proposed model is illustrated by solving the cases of a flat fluid-filled fracture with small thickness and a fluid-filled S-shaped inclusion, modelled with both small and null thickness, all of which are buried in an unbounded elastic medium. Time and frequency responses are presented when spherical pulses with a Ricker wavelet time evolution strikes the cracked medium. To avoid the aliasing phenomena in the time domain, complex frequencies are used. The effect of these complex frequencies is removed by rescaling the time responses obtained by first applying an inverse Fourier transformation to the frequency domain computations. The numerical results are analysed and a selection of snapshots from different computer animations is given. This makes it possible to understand the time evolution of the wave propagation around and through the fluid-filled inclusion.     

Scattering of acoustic waves by movable lightweight elastic screens

This paper computes the insertion loss provided by movable lightweight elastic screens, placed over an elastic half-space, when subjected to spatially sinusoidal harmonic line pressure sources. A gap between the acoustic screen and the elastic floor is allowed. The problem is formulated in the frequency domain via the boundary element method (BEM). The Green's functions used in the BEM formulation permit the solution to be obtained without the discretization of the flat solid–ground interface. Thus, only the boundary of the elastic screen is modeled, which allows the BEM to be efficient even for high frequencies of excitation. The formulation of the problem takes into account the full interaction between the fluid (air) and the solid elastic interfaces.The validation of the algorithm uses a BEM model, which incorporates the Green's functions for a full space, requiring the full discretization of the ground. The model developed is then used to simulate the wave propagation in the vicinity of lightweight elastic screens with different dimensions and geometries. Both frequency and insertion loss results are computed over a grid of receivers. These results are also compared with those obtained with a rigid barrier and an infinite elastic panel.     

Scattering of SH waves by a spherical layer

In the frame work of the theory of classical elasticity we study the interaction of spherical elastic SH waves of harmonic type with a spherical layer when the source is placed outside the layer. The exact solution of this scattering problem is investigated in detail after a generalized Debye's expansion is established. The presence of the spherical layer is evident from the second term of this development. The interpretations obtained for a one-sphere model remain valid. However, among the differences we note that the surface waves created on the outer face of the layer rise or die out according to an angle which depends on the mechanical and geometrical features of the layer.     

A note on the low frequency diffraction of elastic waves by a Griffith crack

The two dimensional problem of the diffraction of normally incident compressional and antiplane shear waves by a Griffith crack in an infinite isotropic elastic medium is considered. For wavelengths long compared to the crack length, the stress intensity factors as well as the maximum crack openings are expressed in series of ascending powers of the normalized wave number. The approximate solutions are compared with exact solutions obtained in a previous paper[1], for a Poisson's solid. The results indicate that a five term expansion of each of the series solutions is sufficiently accurate for most problems of practical interest.     

Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers

Elastic waves are scattered by an elastic inclusion. The interface between the inclusion and the surrounding material is imperfect: the displacement and traction vectors on one side of the interface are assumed to be linearly related to both the displacement vector and the traction vector on the other side of the interface. The literature on such inclusion problems is reviewed, with special emphasis on the development of interface conditions modeling different types of interface layer. Inclusion problems are formulated mathematically, and uniqueness theorems are proved. Finally, various systems of boundary integral equations over the interface are derived.     

Interaction of plane harmonic waves with inclusions in the elastic space

We solve the problem of interaction of harmonic elastic waves with a thin elastic inclusion in the form of a strip in an unbounded body (matrix) under the conditions of plane deformation. In view of the small thickness of the inclusion, it is assumed that its bending and shear displacements coincide with the displacements of the corresponding points of its median plane. The displacements of the medium plane are found from the corresponding equations of the theory of plates. The method of solution is based on the representation of displacements in the form of singular solutions of the Lamé equations with subsequent determination of the unknown jumps from singular integral equations. The indicated integral equations are solved numerically (by the collocation method). The relations for the approximate evaluation of the stress intensity factors at the ends of the inclusion are obtained. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 3, pp. 58–64, May–June, 2007.     

On the micromechanics of composites containing spherical inclusions

Exact solutions for the stress distribution inside a spherical inclusion embedded in an other-wise homogeneous matrix are obtained. Such expressions provide a framework for discussing the load carrying capacity of rubber inclusions and the effect of interfacial bonding on the toughness of such filled systems. Parametric studies of the influence of constituent stiffness ratios on the resultant stress patterns in the inclusion and matrix have been conducted. Results indicate that chemical bonding between the particle and matrix is not necessary for soft inclusions, but is essential for rigid inclusions.     

Scattering of electromagnetic spherical waves by a buried spheroidal perfect conductor

We examine the electromagnetic scattering of spherical waves by a buried spheroidal perfect conductor. The proposed analysis is based on the integral equation formalism of the problem and focuses on the establishment of a multiparametric model describing analytically the scattering process under consideration. Both the theoretical and the numerical treatment are presented. The outcome of the analysis is the determination of the scattered field in the observation environment along with its multivariable on several physical and geometric parameters of the system.