Charles Sve

On the bending of cracked plates

Abstract An analysis is presented for the investigation of the effects of crack geometry in finite rectangular plates. Three cases are considered: (1) crack at opposite edges,(2) crack in center, and (3) crack on one side only. Each problem is formulated in terms of dual series equations and reduced by standard techniques to a Fredholm integral equation, which is solved numerically. Numerical results are included for the strain energy and the moment stress intensity factor. Comparison of the various cases demonstrates the possible effects of geometry on the propagation of cracks in finite plates.

Stress Wave Attenuation in Composite Materials.

Abstract : An analysis is presented for one-dimensional wave propagation in composite materials. The effects of geometric dispersion and spatial attenuation are included through the introduction of a complex wave number. This type of problem arises when the constituents of the composite are viscoelastic or when heat is generated due to thermoelastic coupling or scattering from inclusions occurs. The analysis is restricted to the low-frequency portion of the response and is therefore valid only in the far field. (Author-PL)

Thermally Induced Stress Waves in an Elastic Layer.

Abstract : A solution is presented for the stress wave response of a partially transparent elastic layer subjected to electromagnetic radiation. The radiation is assumed to be deposited with a Gaussian spatial distribution in a time short compared with thermal diffusion times. The development is based on the equations of uncoupled dynamic thermoelasticity with heat conduction neglected. Laplace and Hankel transform techniques provide the formal solution and numerical integration of the resulting expressions yields the time-dependent stress distributions in the layer. Several examples are included that illustrate the significance of the dynamic effects and their dependence on the radial coordinate and heating time. (Author)

Moving Load on a Laminated Composite

A solution is presented for the dynamic response of a periodically laminated half plane that consists of alternating layers of two different materials and is subjected to a moving load. The laminations are parallel to the surface of the half plane, and the velocity of the load is steady and supersonic. An effective stiffness theory developed by Sun, Achenbach, and Herrmann is used to model the layered material, and the formal solution is obtained with the aid of Laplace transforms. A far-field solution is constructed with the head-of-the-pulse procedure, and several numerical examples are presented.

Elastic wave propagation in a porous laminated composite

Abstract An analysis is presented for linear elastic wave propagation normal to the laminations of a periodically laminated porous composite. The porosity is randomly distributed throughout one constituent and is composed of small spherical voids. This type of porosity is called randomly periodic and produces Rayleigh scattering where the wavelength of the incident wave is much larger than the void diameter. Porosity also reduces the wave speed in a constituent and thereby affects geometric dispersion. A dissipative equation of motion is developed for porous material that includes a porosity-dependent wave speed and a scattering term that provides spatial attenuation. This equation is then used for a constituent of a composite, and a dispersion relation and pulse solution are obtained to determine the significance of porosity in a laminated composite. It is concluded that Rayleigh scattering produces a small damping effect in far-field pulse shapes and small-void porosity can be adequately simulated with an effective wave speed.

Thermoelastic waves in a periodically laminated medium

Abstract The oblique propagation of time-harmonic waves in a periodically laminated composite is studied. Governing equations are those of the coupled thermoelasticity theory for plane strain. The exact dispersion relation in the form of a determinant of order twelve is presented, and several numerical cases are included. Results indicating differing amounts of dispersion and attenuation for various angles of propagation are compared with results from an isothermal analysis.

Indentations of an elastic layer by moving punches

Abstract A layer in plane strain (or stress) is indented by two frictionless punches of a given profile moving at a uniform velocity along its surfaces. Symmetry about the midsurface of the layer is preserved and Fourier transforms are utilized to reduce the problem to the solution of a set of dual integral equations. Standard techniques yield a Fredholm integral equation that is solved numerically for parabolic and wedge punches. Results for the static case are compared with a photoelastic experiment. An analysis including the effects of prestress is briefly presented.

ONE-DIMENSIONAL PULSE PROPAGATION IN AN OBLIQUELY LAMINATED HALF-SPACE.

Abstract : A solution is presented for the response of a periodically laminated half-space to a suddenly applied surface pressure. The lamination angle is arbitrary. Dispersion due to the structure of the composite is included by using a continuum theory that approximately models such behavior. The predominant long-time far-field solution is obtained using the head-of-the-pulse technique. This solution is contrasted with the first-order approximation obtained when the composite is represented by an equivalent homogeneous anisotropic elastic medium. Both theories yield a response to the step load consisting of two pulses, each traveling with a separate velocity. For the anisotropic elasticity theory, the pulses are simple steps, while for the dispersive theory, oscillations are superposed on the steps. The character of these oscillations is highly dependent on the lamination angle and other properties of the composite, particularly for the slower pulse. Representative numerical examples are presented. (Author)

Experiments on Pulse Propagation in an Obliquely Laminated Composite

Abstract : Experimental results are presented for the linear elastic dynamic response of periodically laminated composites. A shock tube-capacitive transducer technique is used to determine the rear surface velocity history of three laminated samples that have different lamination angles and are subjected to a step pressure loading. Viscosity effects are discussed, and comparisons are made with predictions based on previous theoretical work. (Author-PL)

Indentation of an Elastic Layer by an Array of Punches Moving With Steady Velocity

Abstract : A solution is presented for the problem of an elastic layer that is indented by an infinite array of punches moving with a steady velocity below the Rayleigh wave speed. The layer is assumed to be loaded symmetrically about its midplane. The equations of plane elasticity are used to develop dual series equations which are reduced to a single Fredholm integral equation. An asymptotic solution to the integral equation is developed for the case when the ratio of contact length to punch spacing is small, and it is compared with a numerical solution. Numerical calculations for the effective stiffness of the layer and the stresses along the midplane are included. (Author)