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Showing papers by "Subhendu K. Datta published in 1991"


Journal ArticleDOI
TL;DR: In this paper, a hybrid method for analyzing the scattering of time-harmonic plane strain waves by cracks in an infinite laminated composite plate is presented by dividing the domain into two regions: an interior region that consists of cracks and a finite region of the plate around the cracks; and an unbounded exterior region.
Abstract: A hybrid method is presented for analyzing scattering of time-harmonic plane strain waves by cracks in an infinite laminated composite plate. The modeling is achieved by dividing the domain into two regions: an interior region that consists of the cracks and a finite region of the plate around the cracks; and an unbounded exterior region. The hybrid method combines a finite element formulation in the interior region with a wave-function expansion representation in the exterior region. The method is illustrated through solving the problem of scattering by a symmetric normal-edge crack. Numerical results for the reflection coefficients are presented for an isotropic plate, a homogeneous fiber-reinforced plate, and a laminated fiber-reinforced plate. The validity and accuracy of the results are checked by satisfaction of the reciprocity relations and the principle of energy conservation. The technique presented can be used to characterize cracks in laminated composite plates.

45 citations


Journal ArticleDOI
TL;DR: In this article, the dispersion of a cross-ply laminated plate has been studied using a stiffness method and an exact method, and it was shown that the number of laminae strongly influences the dispersive behavior.
Abstract: Dispersion of guided waves in a cross-ply laminated plate has been studied here using a stiffness method and an exact method It is shown that the number of laminae strongly influences the dispersion behavior Further, it is found that when the number of laminae is sufficiently large, then the dispersion behavior can be predicted by treating the plate as homogeneous with six stiffness constants obtained by using an effective modulus method

38 citations


Journal ArticleDOI
TL;DR: In this article, a cylindrical alluvial valley embedded in a layered half-space is investigated by using the combination of the boundary integral representation and the finite element method.
Abstract: Three-dimensional scattering of seismic waves by a cylindrical alluvial valley embedded in a layered half-space is investigated by using the combination of the boundary integral representation and the finite element method. The surface displacements due to incident plane harmonic body waves (P, SV and SH) propagating at an arbitrary angle to the axis of the cylindrical valley are evaluated numerically for two semi-elliptical alluvial valleys. The presence of the layer is found to have a strong effect on the amplification of the surface displacements in some cases. The three-dimensional motion seems to be quite critical and may cause large amplification. The surface ground motion becomes significant when compared with corresponding free-field motion as the wavelengths become comparable to the characteristic length of the valley. The maximum amplification always occurs atop the valley. Numerical results show that the amplitude and the amplification pattern of the surface displacement strongly depend upon the frequency, the angle and the type of the incident waves.

31 citations


Journal ArticleDOI
TL;DR: In this paper, a wave function expansion method was used to solve the problem of reflection of time-harmonic plane strain waves normally incident upon the free edge of a semi-infinite, laminated ortholropic plate of linearly elastic materials.

22 citations




Book ChapterDOI
01 Jan 1991
TL;DR: In this article, a surface-breaking crack is characterized by ultrasonic techniques using Lamb wave modes, and the model of the scattered wave in terms of the Lamb wave mode is studied.
Abstract: Recent investigations of space construction techniques have explored the use of composite materials in the construction of space stations and platforms These composites offer superior strength to weight ratio and are thermally stable Examples of these materials are laminates of graphite fibers in an epoxy or a metal (Al, Mg) matrix and boron fibers in an aluminum matrix The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in [1] and [2] The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques In particular, the use of Lamb waves for this purpose is studied here The Lamb waves travel through the plate, encountering a crack, and scatter Of interest is the modeling of the scattered wave in terms of the Lamb wave modes The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction The top and bottom surfaces are traction free Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation This equation yields the guided modes in the homogeneous plate The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements A finite region containing the defects is discretized by finite elements Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements This method was used for out-of-plane (SH) wave scattering in an isotropic plate[3] A combined analytical and finite element formulation for a single layered isotropic plate in the state of plane strain was investigated in [4] In this study the authors considered only the lowest symmetric mode and geometrically symmetric cracks In [5] a variational approach was used to investigate scattering by a symmetric pair of surface breaking thin slots Employing standard elastostatic crack solutions as trial functions the authors examined the scattering by the first symmetric mode A finite difference method was used in [6] to calculate the scattering of Lamb and shear waves from surface breaking cracks In [7] a modified Wiener-Hopf technique was used to analyze scattering of Lamb waves by a crack Applying this technique, the authors in [8] studied quantitative sizing of spot welds in joined sheets Besides the finite difference and finite element techniques, the analytical approaches are not suitable for analyzing arbitrarily shaped defects and anistropic media In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different material Recently, using the hybrid method, the scattering by surface-breaking cracks in isotropic homogeneous and welded plates has been examined in [9]

7 citations


Journal ArticleDOI
TL;DR: In this paper, the scattering of elastic waves by interfacial cracks in a layered medium is investigated, and a hybrid numerical method is employed to obtain the solution, combining the finite element equations and the Green's function boundary integral representation.

2 citations


Book ChapterDOI
01 Jan 1991
TL;DR: In this paper, the authors present a systematic study of the influence of layering on the dispersion behavior of free Lamb waves in a cross-ply laminated plate, which can also be used to ultrasonically characterize the mechanical properties of the laminate plate.
Abstract: Although propagation of guided (Lamb) waves in a homogeneous isotropic plate has been studied extensively in the past, relatively few studies have been reported that deal with homogeneous anisotropic plate. In a recent paper Nayfeh and Chimenti [1] have reviewed the literature and they have presented results for dispersion of free Lamb waves in a homogeneous anisotropic plate. The present study is concerned with dispersion of free guided waves in a cross-ply laminated plate. Since laminated composite plates are finding usage in a variety of applications, there is a need to understand their response under dynamic loading. Of particular interest for this purpose is the characteristic dispersion of modes of propagation in a multi-layered laminated plate. This dispersion behavior influences the dynamic response and it can also be used to ultrasonically characterize the mechanical properties of the laminated plate. The motivation is to present a systematic study of the influence of layering on the dispersion behavior.

2 citations



Journal ArticleDOI
TL;DR: In this paper, the dynamic response of pipelines buried in a back-filled rectangular trench in a semi-infinite medium has been investigated, where the pipelines are modeled as long cylindrical shells of small thickness.
Abstract: Dynamic response of pipelines buried in a back-filled rectangular trench in a semi-infinite medium has been investigated. The pipelines are modeled as long cylindrical shells of small thickness. By using the boundary integral representation and finite element method, we have studied the three-dimensional response to account for either pane P or SV wave incident at an arbitrary angle to the pipe-axis. In this paper numerical results are presented for the normal displacements, displacements along pipe-axis, and the hoop stresses in the pipe wall. It is shown that the response depends critically on the back-filled material as well as on the directions of propagation of the incident waves.