Two-dimensional Stress Distribution Research Articles

Stress intensity factors for corner cracks at a hole under remote tension

The three-dimensional weight function method recently developed by the authors is used to determine stress intensity factors for two symmetric quarter-elliptical corner cracks at a hole in a wide finite-thickness plate subjected to remote tensile loading. The geometry parameters considered arer/t=0.5, 1, 2;a/c=0.2, 0.5, 1, 2;a/t=0.2, 0.5 withinc/r=2. The results are compared, where possible, with other solutions available in the literature. Generally good agreement is observed. The effect of an approximation of the two-dimensional unflawed stress distribution on the accuracy of stress intensity factors by the weight function method is discussed.

An analytical solution for anisotropic plates containing triangular holes

An analytical solution for the two-dimensional stress distribution around a triangular hole is investigated. The desired loading is a stress P in direction a from the x-axis of the plate. The solution presented here will account for anisotropic material and accept different length/height ratios of the triangular hole, different degrees of bluntness at the triangle vertex as well as different orientations of the load.

A method for the measurement of residual stresses using a fracture mechanics approach

A simple method for measuring residual stresses in a plate is described. In this method residual stresses are evaluated using a fracture mechanics approach, that is, the strains or displacements measured at a point on the edge of a plate as a crack is introduced and extended from the edge are used to deduce the state of stresses that existed in the uncracked plate. Through finite element analyses and experiments this method is shown to be valid and effective for measuring the two-dimensional residual stress distribution of a welded plate.

Two-dimensional Stress Distribution in a Compact Tension Specimen : Elastic Solution

The stress distribution in a compact specimen for fracture testing is numerically computed by the analytic method. The condition of free surface on the outer boundary in the state embedded in an infinite plate is expressed by a discrete arrangement of edge dislocations, and that on the crack plane is expressed by point forces acting on the plane of finite crack in an infinite plate. The dislocation distribution is obtained through a successive approximation developed empirically. The computed results are shown by contour maps of stresses, and by distributions of dislocations, surface stresses, and displacements on the external boundary. The stress intensity factor, the stress on the back face, and the displacement at the crack entrance are given as functions of crack length.

Two-Dimensional Stress Distribution in a Compact Tension Specimen : Elastic Solution

Two-Dimensional Stress Distribution in a Compact Tension Specimen : Elastic Solution

THERMOELASTIC ANALYSIS OF LAMINATED ORTHOTROPIC SLABS

Stationary two-dimensional temperature, stress, and displacement distributions are investigated for a simply supported slab consisting of bonded orthotropic layers. The top and bottom faces of the slab are subject to arbitrary variations of temperature, heat flux, or convection, and arbitrary distributions of tractions. Displacement potentials are used to obtain the exact thermo-elasticity solution. For purposes of comparison, a strength-of-materials approximation for the temperature-induced stresses and middle-surface displacements is presented. As an illustrative example, the thermoelastic response to a sinusoidal distribution of temperature rise over the top face of the slab is computed; numerical results are given for laminates of various geometric configurations.

Thermoelastic Analysis of a Finite Orthotropic Slab

Stationary two-dimensional temperature and stress distributions are examined for an orthotropic elastic body having a rectangular boundary. Temperature fields are determined for situations in which one edge of the rectangle experiences an arbitrary variation of temperature, heat flow or convection, while each of the remaining edges is either insulated or maintained at the initial temperature. Displacement potentials are then used to find the thermal stresses for those cases in which the temperature remains constant over two opposite ends of the rectangle. As an illustrative example, the temperature and stresses resulting from a uniform temperature rise over a portion of one edge of the rectangle are computed; numerical results are given for a fibre-reinforced composite material.

Two-Dimensional Interlaminar Stress Distribution within the Adhesive Layer of a Symmetrical Doubler Model

Abstract Two-dimensional stress distribution within the adhesive layer of a doubler model was derived by means of the finite element method. Results indicated significant variations in all stress components through the adhesive thickness in a region close to the adhesive edge, in contrast to the assumption of uniform stress distribution postulated by several authors. However, this assumption was found to be valid along most of the adhesive central length. The value, orientation and location of principal stresses, obtained by the analysis, may provide a guideline for the study of adhesive failure mechanism.

On the Analysis of Asymmetric Stress

An attempt has been made to analyze asymmetric stress. Bounds for the principal stresses have been established in terms of the principal stresses corresponding to the symmetric part of the stress tensor. Sufficient conditions for the existence of one or three principal stresses have been established. Bounds have also been established for the maximum shear stress. Detailed results have been given for the case of a quasi two-dimensional stress distribution.

Thermal stresses in heat-generating multi-bore square or circular region

A general solving method is given for problems of the steady state two-dimensional thermal stress distributions in a heat-generating square or circular cylinder which contains many circular holes symmetrically placed around its center with uniform heat generation having thermally insulated outer boundary. The graphical illustrations of the thermal stress distributions are given for the problems of heat-generating square cylinder with four circular holes, and of heat-generating circular cylinder with three or four circular holes.

Observation of Crystal Defects by Pseudo-Kossel Lines on X-Ray Projection Micrograph

When divergent X-rays from the source of size below 1 µ are diffracted from Fe-Si (Si 3%) single crystals of about 0.05 mm thickness, a pseudo-Kossel pattern superimposed with the X-ray projection micrograph is obtained. Distortion of absorption lines in the pseudo-Kossel pattern shows the change in orientation or spacing of the crystal planes at their locations on the X-ray projection micrograph. By traversing the X-ray source on a target film, pseudo-Kossel lines change their locations on the X-ray projection micrograph. Thus, two-dimensional stress distribution in the neighborhood of the crystal defect can be revealed. The detectable limit of distortion is about 10-4 in order and the resolution of the X-ray projection micrograph is about 1 µ.

A new interferomemtric method of two-dimensional stress analysis

An interformetric method of obtaining the two principal stresses separately in two-dimensional stress distribution is described. An analytical interpretation is given of the relation between the stress-strain state of a transparent elastic plate and the light intensity of the plate observed through the Mach-Zehnder interferometer. The isopachic fringes which give the distribution of the sum of the principal stressesσ1 +σ2 are modulated by simultaneous appearance of the isochromatic fringes which related to the distribution of the difference of principal stressesσ1 -σ2. Accordingly, a single pattern obtained by this method provides sufficient information for evaluating the two principal stresses separately.

On the Plane Stress Problem in a Ring of Orthotropic Material

In the present paper, the two-dimensional stress distribution in an orthogonally aeolotropic plate, bounded by two concentric circular contours, is treated by the perturbation method using the orthogonal co-ordinates, similar to that of the previous papers. Numerical examples are worked out for three kinds of material, oak, plywood and isotropic plate. The results show that considerably large stress concentration may occur in some aeolotropic plates even in the case of uniform inner pressure.

On the Plane Stress Problem in a Ring of Orthogonally Aeolotropic Material

In the present paper, the two-dimensional stress distribution in an orthogonally aeolotropic plate, bounded by two concentric circular contours, is treated. The same problems, in the case of isotropic material, have been solved easily by the use of the polar co-ordinates. In the case of aeolotropic plate, however, the solutions are rather complicated because of the directionality of its elastic properties, and the author treats it by the perturbation method using the orthogonal co-ordinates, similar to that of th previous papers. Numerical examples are worked out for three kinds of material, showing that considerably large stress concentration may occur in some aeolotropic plate even in the case of uniform inner pressure.

Relaxation Methods Applied to Two Problems of Two-Dimensional Stress Distribution Involving Mixed Boundary Conditions

Relaxation methods have been used to determine the stress distributions in both a rectangular and a highly tapered plate under tension when the load is applied through absolutely rigid clamps. Both problems require the treatment of boundary conditions involving the values of both stresses and displacements. The solutions were obtained in terms of displacements and the stresses were subsequently determined from them.

Two-Dimensional Stress-Distributions in Long Beams

両端が支持されて任意1箇所で荷重を受ける梁及び2箇所で支持されて適宜2箇所で荷重を受ける梁の應力分布を二次元的に取扱ひ、その正解と普通の工学的実用解とを比較論及したものである。

XLVI.A general property of two-dimensional thermal stress distribution

(1935). XLVI. A general property of two-dimensional thermal stress distribution. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 19, No. 127, pp. 540-549.

A graphical representation of two-dimensional stress distributions

A graphical representation of two-dimensional stress distributions

Compression of Rectangular Blocks, and the Bending of Beams by Non-Linear Distributions of Bending Forces

Abstract An existing method for the approximate analysis of two-dimensional stress distributions is extended in scope and applied to two examples of some practical interest. The first is a rectangular plate or block compressed by forces applied centrally to two opposite sides, as by knife edges. Tensions of considerable magnitude are developed across the middle plane through the knife edges. These tensions are determined, and illustration given of their dependence on the extent of spreading of the load over the bearing area. The second is intended as quantitative example of Saint-Venant’s principle in the bending of beams. The stresses due to a non-linear distribution of bending forces on the ends are investigated in order to estimate how far from the end one must go to find the linear distribution assumed in the elementary theory of flexure. Conclusions are given in the paper proper and the mathematical analyses from which they are drawn are given in appendices.