Shape Of Inhomogeneity Research Articles

On the extremal value of the thermoelastic energy of a material with an inclusion subject to mechanical and thermal action

Under prescribed thermoelastic stresses and known properties of the matrix and the inclusion in an elastic medium with an inhomogeneity, we find the shape of inhomogeneity that leads to an extremal value of the thermoelastic energy. From the necessary conditions for an extremum of the thermoelastic energy functional we find a condition for seeking the interface. For the case of isotropic cornponents and under loads of stretching (compression) type and uniform heating of the medium the shape of the inclusion can be found explicitly within a certain range of initial parameter values. The results of numerical study are presented and analyzed. One table.

Fluid‐loaded plate coupled to a distributed inhomogeneity—Review.

The problem of scattering from a fluid‐loaded plate structure coupled to a distributed inhomogeneity is considered. Results have been presented which include the plate surface velocity Green’s function, the far‐field and near‐field scattered pressure, and the acoustic and structural intensity. The distributed inhomogeneities considered varied both in type (mass or stiffness) and shape. In all instances, the perturbation due to the inhomogeneity, relative to the elastic characteristics of the plate, is small. In the case of shape variations, the influence of ‘‘smoothness’’at the edges of the inhomogeneity, and of oscillations within the inhomogeneity distribution were also considered. In this presentation, the results that have been generated thus far, will be reviewed and general conclusions drawn from these results. It is shown that depending on the frequency range of interest, the results can be significantly influenced by the shape and type of inhomogeneity. Stiffness inhomogeneities, in general, are less significant compared to mass inhomogeneities. However, in relative terms, internal variations in the inhomogeneity shape are more significant for stiffness inhomogeneities than for mass inhomogeneities. Alternate forms of presenting the results will be explored. [Work sponsored by ONR.]

A new approach to find the stress distribution for an arbitrary shape of inhomogeneity

A new method for solving arbitrary-shaped inhomogeneity problems has been developed. The approach combines boundary integral equations, based on Betti's princple, with a sequence of cutting, straining, and welding procedures to numerically acquire stress and strain distributions at an inhomogencity with an arbitrary shape. Physically, the strain misfit is considered as the driving force to cause the stress concentration when a system comprised of an infinite domain and an inhomogeneity is subjected to a far-field stress. A general discussion of the effect of the inhomogeneity shape on fracture initiation has been included.

Three‐dimensional model results for an electrical hole‐to‐surface method: Application to the interpretation of a field survey

An important objective of borehole geophysics is to maximize information about inhomogeneities in the vicinity of existing boreholes. Three‐dimensional models (parallelepipedic inhomogeneities in a homogeneous half‐space) are used here to characterize the responses of an electrical hole‐to‐surface method ELECENT (ELECtrode ENTerrée) where conductive or resistive inhomogeneities (orebodies) occur in the vicinity of a borehole. Two types of surface measurements are carried out simultaneously at each station: electrical potential V (as in mise à la masse), and associated electrical field E. These two measured parameters give rise to three other parameters, two apparent resistivities (one for each V and E case) and another parameter quantifying the orientation of the E field. The influence of various geometrical and electrical parameters (such as the horizontal and vertical distances between the current source, the stations, and the inhomogeneity, and the size and resistivity of the inhomogeneity) on the five parameters above appears to be important. Values and positions of the extrema of these five parameters are characteristic of the geometrical and electrical parameters of the models. The orientation of the E field, for instance, is found to be critical to determining the shape of the inhomogeneity and its depth relative to the current source. The theoretical results obtained are used to interpret a field survey carried out around a borehole at the Beauvain prospect in France. Field maps of the five parameters show characteristics similar to the models described in the theoretical part of the study.

A three-dimensional inverse problem for inhomogeneities in elastic solids

The Newtonian potential is used to solve an inverse problem in which we seek the shape of an inhomogeneity in an infinite elastic matrix under uniform applied stresses at infinity such that certain stress components are uniform on the boundary of the inhomogeneity. It is shown that ellipsoids furnish the solution of this inverse problem. Exact and general expressions for the stress and displacement are given explicitly for points in the elastic matrix outside the inhomogeneity. The solution of the corresponding plane deformation problem is found as a limiting case. Several applications are presented, and results from the literature are confirmed as special cases.

Fundamental frequency of composite circular membranes with boundary disturbances

Abstract The title problem constitutes a basic mathematical model where the separate or combined effects of possible manufacturing flaws are taken into account. These flaws are (a) deviations with respect to the ideal circular shape and (b) presence of a central inhomogeneity. The effects of these complicating factors on the fundamental frequency of a membrane are calculated using two approximate analytical techniques and the finite element method. Excellent agreement is shown to exist between the results obtained by the three different approaches.