Biomedical subjects

WA Green

Publications and source records attributed to WA Green.

3 recordsLinked to original sources

PubMed2000

Elastic waves in fibre composite laminates

This paper considers the propagation of elastic waves in an eight-ply quasi-isotropic laminate arising from line sources of dislocation located at each of the seven interfaces in turn. The line source sets up a straight crested wave travelling along the laminate in a direction normal to the load line, and the elastodynamic equations within each layer are solved by taking the Laplace transform with respect to time and the Fourier transform with respect to the spatial coordinate in the direction of propagation. The resulting system of six first-order differential equations in each layer is solved to obtain the transforms of the displacement and stress components throughout the laminate. The time history of any displacement or stress component at any location may then be recovered by numerical inversion of the double transform. Examples are shown of the time history of the normal displacement of the top surface of the laminate at a distance of 20 plate thicknesses from the plane of action of the sources. The numerical inversion involves a summation over different modes of Rayleigh-Lamb waves in the laminate and contributions to the overall response from some of the individual modes are displayed.

Journal Article↗

PubMed2000

A computational method for wave propagation from a point load in an anisotropic material

One approach which is employed to solve dynamic point load problems in plates and laminates is to take integral transforms to reduce the governing equations to a system of ordinary differential equations with respect to the depth variable. The solution of this system leads to expressions for the transforms of the displacement and stress components at any level in the plate and the transient response at any location may then be recovered by inversion of the multiple transforms. The formal transform inversion involves a double infinite integral but by making a change of variable this may be replaced by an infinite integral associated with a line source and a finite integral with respect to the orientation of the line. A first attempt at applying this approach to obtain the point load response of quasi-isotropic fibre composite laminate led to a non-causal predicted signal. This paper deals with an investigation of this proposed method applied to the simpler model problem of wave propagation in a two-dimensional anisotropic medium. Results are obtained for two different time histories of point loads, namely: a delta function; and a single period of a sine function. In the case of the delta function source a comparison is made with the analytic solution and the errors arising from the numerical approach are discussed. Graphs are also presented showing the non-causal contributions to the overall response which arise at individual angles of orientation of the line source.

Journal Article↗

PubMed2000

Transient response of quasi-isotropic fiber composite laminates to internal line sources

This article considers the propagation of elastic waves in an eight-ply quasi-isotropic laminate arising from line sources of dislocation located at each of the seven interfaces in turn. The laminate is composed of identical layers of a fiber composite material which is modeled as a homogeneous transversely isotropic elastic continuum with the axis of transverse isotropy along the fiber direction. The line source sets up a straight crested wave traveling along the laminate in the direction normal to the load line and the elastodynamic equations within each layer are solved by taking the Laplace transform with respect to time and the Fourier transform with respect to the spatial coordinate in the direction of propagation. The resulting system of six first-order differential equations in each layer is solved to obtain the transforms of the displacement and stress components throughout the laminate. The time history of any displacement or stress component at any location may then be recovered by numerical inversion of the double transform. The graphs presented show the time history of the normal displacement of the top surface of the laminate at distances of 1 and 20 plate thicknesses from the plane of action of the sources. These graphs are for four different orientations of the line of action of the sources, namely, at angles 0, 30, 60, and 90 degrees to the fiber direction in the surface layer. The numerical inversion involves a summation over different modes of Rayleigh-Lamb waves in the laminate and results are also presented showing the contributions to the overall response from some of the individual modes.

Journal Article↗