Central Circular Hole Research Articles

Estimates of the creep rupture lifetime of structures using the finite element method

Multi-axial creep constitutive laws are presented and discussed for materials which obey different rupture criteria. The finite element method is formulated and used to investigate the creep rupture behaviour of uni-axially loaded tension-plates containing central circular holes. Experimental values of rupture lifetimes and plate displacements for copper and aluminium plates are shown to be closely predicted by the calculated ones. The calculated shapes of zones of material deterioration or rupture are shown to be in close agreement with the results of metallographic examinations of copper and aluminium plates.

Elasto-dynamic analysis of rectangular plates with circular holes

The problem of the free vibrations of a rectangular elastic plate, either clamped or simply supported, with a central circular hole has been investigated by a least-squares point-matching method. The results are given in the form of curves relating the natural frequency of the plate to the hole size for a variety of Poisson's ratios. The curves do not behave monotonically, and the hole size at which the frequency is a minimum is seen to be dependent not only on the boundary conditions but also on Poisson's ratio. A two-fold mechanism of strain relief and mass reduction is proposed to explain these results as well as the results of previous studies on the vibrations of plates with discontinuities.

Investigation of stress-concentration factors in tensile strips

A photoelastic and a numerical investigation has been carried out to determine the stress-concentration factors at the edge of a central circular hole in a tensile strip for different ratios of hole diameter to width of the strip. The photoelastic data and the numerical results indicate that the stress-concentration factor at the minimum cross-sectional area tends to a value of two if the ratio of the hole diameter to the strip-width approaches a value of one.

Unsteady thermal stresses in fuel elements under heat generation

In designing some types of fuel elements, it is necessary to find the thermal stresses in a continuous medium performated by cylindrical channels of circular cross-section. In order to set up the problem, assume that the strength and heat transfer calculation are based on the phenomena that occur in a typical unit lattice cell, and that the heat generation is uniform over the whole section: Therefore, the problems reduce to solve the temperature and thermal stresees in a polygonal prism with a central circular hole under uniform heat generation and for insulated outer boundary. In out previous papers we obtained the steady thermal stress distribution in such formed regions by use of the five elementary functions method.In starting up or shutting down of the reactor, however, the problem becomes one of the unsteady state. It is felt that no analysis has been given to the transient thermoelastic problem of the multiply-connected region. The problems considered here are concerned with unsteady thermal stresses in a polygonal prism with a circular hole under a uniform heat generation. The solving process is divided into two basic steps. First, the heat conduction equation is solved by the technique of Laplace transform. Secondly, the plane thermoelastic problem is solved by use of the five elementary functions method. Throughout the treatment of both problems, in order to satisfy the boundary conditions, we use the point-matching technique in conjunction with the least square method.

Thermal stresses and couple-stresses in square cylinder with a circular hole

This article deals with the effect of couple-stresses on thermal stress distribution in a square cylinder with a central circular hole under steady state temperature distribution. The analysis is developed by the point-matching technique. From our calculation, it may be concluded that stress concentration around a circular hole, taking couple-stress into account, results in lower values than those accepted heretofore.

Approximate Fundamental Frequency of Noncircular Ring Membranes

An exact solution for the frequency of a ring membrane can be obtained when the inner and outer boundaries are concentric circles or confocal ellipses. If either boundary has some other shape, approximate methods must be used. This paper presents a simplified approximate method for determining the fundamental frequency of ring membranes whose boundaries deviate only slightly from circular. This method was initially used by Rayleigh in his investigation of simply connected membranes. The radii of both bounding curves are approximated by a truncated Fourier series. The membrane transverse motion, which is written as a superposition of the modes of a circular ring membrane, is forced to vanish on the approximated boundaries. A characteristic equation is obtained from which the approximate frequencies may be found. This technique is used to determine the fundamental frequency of the following: (1) Elliptical ring membrane with the inner and outer ellipses being confocal; (2) square membrane with a centered circular hole; (3) square ring membrane; and (4) an eccentric annulus. Comparisons with exact solutions, when known, are given.

Effects of Couple-stresses on Stress Concentration in Square Prism with Hydrostatically Loaded Central Circular Hole

Effects of Couple-stresses on Stress Concentration in Square Prism with Hydrostatically Loaded Central Circular Hole

Bending of a Simply Supported Plate Clamped about a Central Circular Hole

Bending of a Simply Supported Plate Clamped about a Central Circular Hole

Creep of large thin plates with central circular holes subjected to biaxial edge tractions

Using the C.E.G.B. TESS Program, the creep behaviour in the vicinity of a circular hole in a thin plate has been investigated for a time-hardening material law. The results show how stress concentration factors vary with time for various combinations of loading and stress index.

Steady-state thermoelastic problem for a triangular prism with a circular hole under non-uniform heat generation

This paper is concerned with a treatment of thermal stresses in an equilateral triangular prism with a central circular hole under steady state of temperature distribution with a non-uniform heat generation which is represented by a linear function of the radius. This problem is an applicable problem in the structure of a moderator as a triangular cell. Moreover, in this paper, a new treatment of solving is presented for the thermoelastic problems of the multiply connected region under non-uniform heat generation.

Approximate formulae for temperature distribution in a heat-generating polygonal cylinder with a central circular hole

Derivation of approximate formulae for temperature distribution in heat-generating polygonal cylinders with a central circular hole and thermally insulated outer boundary using the point matching method is being discussed.

Local stress measurement using the thermoelastic effect

A technique for measuring local stresses in metallic specimens is proposed and tested. The technique depends on the experimental measurement of temperature changes in stressed members due to adiabatic elastic deformation. At a free boundary in a body under plane stress, these temperature changes are directly related to the value of the tangential principal stress. The technique is suited for measurement of stress-concentration effects, since the temperature changes can be measured with thermocouples featuring extremely small junctions.A simple stress-concentration geometry, the finitewidth strip with a central circular hole, is chosen as a model system for this study. Heat transfer in this geometry due to the temperature gradients produced by elastic deformation is analyzed. It is shown that the ratio of the temperature change at a reference section to the change at the locale of the stress concentration can be used to determine the stress-concentration factor, allowing for heat-transfer effects. An experimental measurement system capable of obtaining reproducible results with the thermal-measurement technique is described, and experimental results are given for the model geometry which agree favorably with theoretical predictions. Application of the technique to other problems is discussed.

On the application of the energy method to the stress concentration problem of a rectangular plate with a central circular hole

The stress concentration problem of thin elastic plates is one of the classical problems in the theory of elasticity, and since E. Goursat's work on the complex variable representation of stress functions in plane elasticity problems, much work has been done all over the world, and Muskhelishvili and others have established the unified theory on the two-dimensional elasticity problems. Unfortunately, however, the existing theoretical solutions obtained along this line are quite limited for the practical purpose and the development of a more practical method of analysis is definitely required. It seems that the energy methods will provide the alternative procedure powerful enough to treat the more practical problems although actually not attempt along this line has been made. In this paper, a first effort is made in the application of energy methods to the stress analysis of a perforated rectangular plate, the result of which is found consistent with the famous Howland's solution on the perforated plate strip problem and some test results.

Thermal stresses in a polygonal cylinder with a circular hole under internal heat generation

AbstractThis paper is concerned with a treatment of thermoelastic problems for a multiply connected cross section in polygonal cylinder under uniform internal heat generation. In the first part of this paper a general theory is presented for thermal stress analysis in multiply connected region which has been subjected different temperature distribution of unsteady or steady state. As examples of the above theory, in the second part, approximate numerical solutions are obtained by the point‐matching method for the thermal stress distribution of the polygonal cylinder with a central circular hole having the thermally insulated outer boundary under uniform heat generation.

Stress Concentration in a Rubber Sheet Under Axially Symmetric Stretching

A class of axially symmetric problems, concerning a highly elastic, circular rubber sheet with (a) a centered circular hole, (b) a rigid circular inclusion under outward radial loading at outer boundary, and (c) a rigid outer boundary and a concentric hole under inward radial loading around the hole, is solved. The solution of (a) has been obtained by Rivlin and Thomas [1] by solving simultaneously a set of differential equations numerically. In this paper, their equations are reduced to a single second-order differential equation governing the deformation function ρ(r). This is further reduced to two decoupled first-order equations after introducing the phase plane (λ1 – λ2 plane). The solutions are obtained conveniently in the phase plane by Picard’s method and by straightforward numerical integration.

Note on stresses and displacements in square plates and cylinders with pressurized central circular holes

Accurate elastic solutions for perforated squares subjected to internal pressure are reported for hole diameter to plate width ratios of 0.5, 0.6, 0.7, 0.8, 0.85 and 0.9. A point-matching procedure is used to generate solutions that satisfy the internal boundary conditions exactly and the external boundary conditions approximately. The degree of approximation is examined by inspection of residual tractions along the outer boundary. Plane-stress and plane-strain conditions are considered, and the superposition by which the solutions for external pressure can be obtained from the solutions for internal pressure is indicated.

Stresses in a Square Plate Having a Central Circular Hole

An established method is used to find the stresses in a square plate pierced by a central circular hole. Although the method is not new, the problem is a practical one which has attracted some interest and for which some excellent experimental results are available.The general problem of a finite plate containing a circular hole was examined by Sekiya who selected various combinations of the general solutions of the biharmonic equation in polar co-ordinates such that the boundary conditions on the hole were satisfied exactly. The boundary conditions on the sides of the plate were satisfied approximately by collocation. The same approach has recently been suggested by Waters for the particular case of a stress-free hole.

Thermal stresses in a thick-walled tube: An experimental study by electrical analogy

Experiments are described in which pure resistance networks were used to determine, by analogy, the temperature and stress distributions in a long tube whose cross-section had a rectangular outer boundary and a central circular hole. It is shown that the electrical analogy method is valuable for the solution of thermal stress problems and requires only a moderate amount of work.

Dynamic stress-concentration factors

The problem of the response of structural discontinuities to short-duration stress pulses is studied experimentally. Employing explosively induced stress pulses in thin plastic plates containing central circular holes, a dynamic stress-concentration factor is determined as a function of pulse frequency. It is concluded, for the loading case, that the dynamic stress concentration is significantly lower than the static value.

Bending of a rectilinear regular polygonal plate with a circular hole by concentrated edge couples

This paper presents a solution for the deflection, moments and shearing forces in a rectilinear regular polygonal plate, with even number of sides having a central circular hole, subjected to concentrated edge couples at two opposite points of the outer boundary. Complex variable technique has been employed to find the solution of the problem. The solution involves an infinite system of linear algebraic equations and a method of solving them is provided. The solution for a corresponding plane stress (strain) problem has been derived. Numerical results are presented in the form of tables and graphs.