Influence of the viscoelastic properties of a composite on the stress distribution around an elliptic hole in a plate

The time variation in the stresses around an elliptic hole in a composite plate is studied. Solutions that characterize the effect of the time dependence of the relaxation moduli of the composite components on stresses are obtained. The solutions in the time domain are obtained from the elastic–viscoelastic analogy and the corresponding elastic solutions for the effective moduli of the composite and the stress field around an elliptic hole in an anisotropic plate. The inverse Laplace transformation is carried out by an effective numerical method     

Extension of a viscoplastic plate with a circular hole

International Applied Mechanics -     

Stress concentration around a hole in a radially inhomogeneous plate

The stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young’s modulus and Poisson’s ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson’s ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young’s modulus is obtained for the stress concentration factor in pure shear loading.     

Reinforcement of a plate with a circular hole by an eccentric circular patch

We study the reinforcement of an infinite elastic plate with a circular hole by a larger eccentric circular patch completely covering the hole and rigidly adjusted to the plate along the entire boundary of itself. We assume that the plate and the patch are in a generalized plane stress state generated by the action of some given loads applied to the plate at infinity and on the boundary of the hole. We use the power series method combined with the conformal mapping method to find the Muskhelishvili complex potentials and study the stress state on the hole boundary and on the adhesion line. We consider several examples, study how the stresses depend on the geometric and elastic parameters, and compare the problem under study with the case of a plate with a circular hole without a patch. In scientific literature, numerous methods for reinforcing plates with holes, in particular, with circular holes, have been studied. In the monographs [1, 2], the problem of reinforcing the hole edges by stiffening ribs is solved. Methods for reinforcing a circular hole by using two-dimensional patches pasted to the entire plate surface are studied in [3, 4]. The case of a plate with a circular cut reinforced by a concentric circular patch adjusted to the plate along the boundary of itself or along some other circle was studied in [5, 6]. The reinforcement of an elliptic hole by a confocal elliptic patch was considered in [7].     

Flexural vibrations of a semiinfinite plate with a circular hole

Khar'kov Aviation Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 3, pp. 69–73, March, 1990.     

Stress concentration around a circular hole in a transversely isotropic spherical shell

Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 99–106, December 2004.     

Stress distribution around a circular cylindrical cavity in a prestressed plate

A system of equilibrium equations for nonthin transversely isotropic plates with a uniform prestress field is derived by expanding the unknown functions into Fourier-Legendre series. A method of finding the general solution of this system is expounded and used to determine the stress state of a plate with a circular cylindrical cavity __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 28–39, January 2008.     

Elastoplastic analysis of a bent circular plate with a central hole

A circular aluminum plate with a small concentric hole (1/10 the plate thickness) and supported on its outer edge by a ring was subjected to a concentrated load at its center, applied through a rigid ball of radius equal to the plate thickness. Strains were determined using grids, moiré, and electrical strain gages on the top and bottom surfaces of the plate for loads up to and including the one associated with the appearance of the first crack in the plate. The investigation is related to the development of specimens to be used to determine fracture characteristics of materials used in lightweight construction.     

The turbulent flow field around a circular cylinder

The flow field around a circular cylinder mounted vertically on a flat bottom has been investigated experimentally. This type of flow occurs in several technical applications, e.g. local scouring around bridge piers. Hydrogen bubble flow visualization was carried out for Reynolds numbers ranging from 6,600 to 65,000. The main flow characteristic upstream of the cylinder is a system of horse-shoe vortices which are shed quasi-periodically. The number of vortices depends on Reynolds number. The vortex system was found to be independent of the vortices that are shed in the wake of the cylinder. The topology of the separated flow contains several separation and attachment lines which are Reynolds number dependent. In the wake region different flow patterns exist for each constant Reynolds number.     

Stress state around a circular hole in a prestressed transversely isotropic spherical shell

The stress state around a circular hole in a prestressed hollow spherical shell is found by expanding the unknown functions into Fourier-Legendre series __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 61–68, February 2008.     

The electric field in a circular semiconductor plate placed in a magnetic field

The current distribution in an isothermic isotropically conducting plate of circular form is investigated theoretically and experimentally, in the absence and in the presence of an external magnetic field that is perpendicular to the plate. The general solution of the Riemann-Hilbert boundary value problem has been obtained under these conditions. The analysis of this solution points to experimental possibilities of determining parameters of a crystal under consideration such as the specific electric conductivity (in the absence and in the presence of an external magnetic field), the mobility of current carriers in it, and others.All the basic results of the calculations undertaken were experimentally verified and quantitatively confirmed in a series of tests carried out on homogeneous monocrystalline n-germanium (with the specific resistivity of 1.1 ohm cm) at room temperature.It is known that investigations into the galvanomagnetic phenomena (longitudinal and transverse magneto-resistance, the usual, planar and longitudinal Hall effects and others) at the present time constitute not only a means of determining the characteristics of the parameters of the crystals in question (concentration of current carriers, their mobility, etc.) [1], but serve also as a proven and simple means of obtaining important information about the zone structure of crystals [2–5].Such broadening of the circle of problems affecting the sphere of galvanomagnetic investigations already begins not to correspond to the established traditions of carrying out these investigations on test pieces of rectangular shape (as a rule, in the form of parallelepipeds). This lack of correspondence is greater due to a number of completely logical causes, certain requirements as to the geometrical dimensions of such test pieces (the ratio of length to width) [6] can far from always be satisfied. We note in this connection that in the study of galvanomagnetic phenomena in impulsive magnetic fields, for example, the use of test pieces of circular form would simplify the use of working volumes of small diameter. This, in the final analysis, is equivalent to broadening the scale of magnetic fields that can be used. The replacement of a rectangular plate by a circular disc enables us also to simplify a measurement of the parameters of semiconductor crystals which usually are obtained in circular form.Below we present theoretical and experimental investigations into the problem of measuring the galvanomagnetic effects in conducting crystals having a circular form.The authors thank V. V. Gaiduchenko for his help in carrying out the tests.