Reflection of disturbances produced by a three-dimensional heat source from a plane shock wave

The flow in the shock layer between a plane wedge and a plane attached shock is considered. The flow two-dimensionality is violated by the presence of a weak heat source in the shock layer. The relation between the mechanical actions of the disturbances singly reflected from the shock and those proceeding from the source and directly incident on the wedge surface is analyzed. The three-dimensional features of the field of the disturbances reflected from the shock are illustrated with reference to several examples.     

Stress and electric fields in an infinite electrostrictive plate with an elliptic inhomogeneity

The stress and electric fields in electrostrictive materials under general electric loading at infinity are obtained in this paper. It is shown that the pseudo total stresses are continuous in the whole body. The elliptic inhomogeneity problem is first discussed in this paper and its solution is also given. The results show that the stress in the inhomogeneity is not uniform which is different from the solution of Eshelby theory for elastic materials. When the inhomogeneity and matrix have the same dielectric permittivity or the matrix is a non-electrostrictive material, the stress field is uniform in the inhomogeneity. The form of stress function is simple when the inhomogeneity degenerates to a circle.     

Stress and electric displacement analyses in piezoelectric media with an elliptic hole and a small crack

In this paper, the interactions between an elliptic hole and an arbitrary distributed small crack in plane piezoelectric medium, which are often happened in engineering problems, are discussed. The Green’s functions in a piezoelectric plate with an elliptic hole for a generalized line dislocation and a generalized line force are presented. The small crack is represented by unknown continuous distributed dislocations. By considering traction free conditions on the surface of the small crack, the problem is then reduced to a group of singular integral equations which are solved by using a special numerical technique. Accuracy of the present method is confirmed by comparing the numerical results with those in literatures for PZT-4 when the elliptic hole is degenerated into a crack. The generalized stress intensity factors of cracks and the generalized stress on the edge of the elliptic hole are shown graphically. It is shown that the small crack may have shielding or amplifying effects on the main elliptic hole or crack, which depends on the location and orientation of the small crack. The hole near a crack can significantly reduce the stress intensity factor of the crack. The direction of the electric field is important to shielding effect.     

Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow

The two-dimensional problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates. When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The effect of the heat flow direction and the dielectric constant of air inside the crack on the thermal electroelastic fields are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results are valid.     

The fundamental solutions for the plane problem in piezoelectric media with an elliptic hole or a crack

1.IntroductionItiswell-knownthatthefundame,ltalsolutionsorGreen'sfunctionsplayanimportantroleilllinearelasticity.Forexample,theycanbeusedtoconstructmanyanalyticalsolutionsofpracticalproblems.Itismoreimportantthattheyareusedasthefundamentalsolutionsintheboundaryelementmethod(BEM)tosolvesomecomplicatedproblem.Withthewidely-increasingapplicationofpiezoelectricmaterialsinengineeringproblems,thestudyregardingtheGreen'sfLlnctionsinpiezoelectricsolidshasreceivedmuchinterest.The3DGreen'sfunctionsi…     

Stress concentration in a uniformly rotating circular plate weakened by an elliptic hole and two rectilinear cuts

We consider a uniformly rotating isotropic plate whose cross-section is a two-connected domain bounded from the outside by a circle of radius R and from inside by an ellipse with semiaxes a and b. The rectilinear cuts coming to the ellipse are located symmetrically on the real axis OX. On the imaginary axis OY, two point masses m are located at the distances ±id from the center of the plate. Such a plate can be considered as a plate under the action of bulk forces (forces of inertia), X, Y, and under the action of two lumped tensile forces P = mdw ² applied at the points ±id.     

Stress concentration at an elliptic hole in transversely isotropic piezoelectric solids

Two-dimensional electroelastic analyses have been performed theoretically on a transversely isotropic piezoelectric material containing an elliptic hole, subjected to a uniform stress field and a uniform electric displacement field at infinity while the surface of the hole is free of traction and electrically open. Solutions are obtained by using the exact electric boundary condition based on the complex variation method. Explicit solutions for the distributions of the mechanical and electrical components on the rim of the elliptic hole are obtained. An interesting relationship between the stress concentration factor of an elliptic hole (K_t) and that of a circular hole (K_t∣_t=1), $K_t=1+\frac{K_t{\mid }_{t=1}-1}{t}$, is found in both elastic and piezoelectric materials. It is shown that the electromechanical coupling effect is helpful to reduce the stress concentration. And the influence of the dielectric parameter of the medium inside the hole on the stresses and the concerned stress concentration factor at the surface of the hole is weak in a wide range of the dielectric parameter. Comparisons with available results show good coincidence.     

Far fields of the surface disturbances produced by a pulsating source in an infinite-depth fluid

The problem of constructing uniform asymptotics for the far fields of surface disturbances produced by a localized pulsating source in a heavy homogeneous infinite-depth fluid is considered. The wave pattern of the excited fields is the sum of waves of two types, namely, annular and wedgeshaped. The solutions obtained describe the wave disturbances far from the pulsating source both inside and outside the Kelvin wave wedges.     

Stress distribution in a transversally isotropic piezoceramic body with an elliptic crack in a uniform heat flow

An explicit solution is constructed for the static problem of thermoelectroelasticity for an infinite transversally isotropic body with a heat-insulated elliptic crack located in the isotropy plane. It is assumed that at a large distance from the crack the body is affected by a uniform heat flow perpendicular to the crack plane. Formulas are derived for the stress intensity factors at the crack end, which depend on the value of the heat flow, crack geometry, and the thermoelectroelastic properties of the piezoceramic body. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 72–82, February, 2000.     

Natural convection from a buried elliptic heat source

Numerical solutions are presented for the natural convection heat transfer from an elliptic heat source buried beneath a semi-infinite, saturated, porous medium. The surface of the medium is assumed to be permeable. The governing equations for Darcy flow are solved using finite differences. The complicated geometry is handled through the use of a body-fitted curvilinear coordinate system. Results are presented for Ra values ranging from 10 to 200 and ellipse aspect ratio values from 1.0 (circular cylinder) to 0.167. Two body orientations have been considered. The slender orientation yields much higher hear transfer rates (especially at low ellipse aspect ratio values) than the blunt orientation. The numerical simulations indicate that the boundary-layer approximations cannot be employed for low ellipse aspect ratios. In addition, the heat loss does not depend on the burial depth.     

The moving, plane heat source in an elastic medium

Summary This note presents an exact solution for the stress and displacement field in an unbounded and transversely constrained elastic medium resulting from the motion of a plane heat source travelling through the medium at constant speed in the direction normal to the source plane.Nomenclature mass density - diffusivity - thermal conductivity - Q heat emitted by plane heat source per unit time per unit area - speed of propagation of plane heat source - shear modulus - Poisson's ratio - T temperature - _x, _y, _z normal stress components - u _x, u_y, u_z displacement components - c speed of irrotational waves - t time - x, y, z Cartesian coordinates - =x–vt moving coordinate     

Stress measurements in an infinite plate with a hole reinforced by different materials

Stress distributions are measured around the reinforced circular hole in an infinite plate subjected to uniaxial tension. Test plates are made of aluminum and reinforcing rings are of aluminum, brass, copper and mild steel. The relationships between stress-concentration factors, the ratio of Young's moduli of a plate and rings and dimensions of rings are studied. Results are compared with those obtained by the other authors and Gurney's theoretical results.