Stress Distribution In Plane Research Articles

Changes of EPR Spectra by Inhomogeneous Plane Stress Distributions in a Two‐Layer System

AbstractThe influence of plane stress distributions on lineshapes and line positions of EPR transitions in a two‐layer system (film‐substrat) is investigated. Basing on previous calculations explicit expressions for the lineshape of EPR transitions are derived also for the case of an inhomogeneous stress distribution. The effects of homogeneous and inhomogeneous stress distributions on the EPR spectra of paramagnetic systems with S = 1 are represented. The possibility to confuse stressinduced changes of the lineshape with hyperfine and superhyperfine structures is demonstrated.

多点スポット溶接継手の応力分布と疲労強度 Ｉ 応力分布について

As a part of investigation on the fatigue strength of multi-spot welded joints arranged in perpendicular to load direction, plane stress distributions of single- and multi-spot welded joints were studied. The purposes are to make clear effects of specimen width and/or lap length on stress distribution of single-spot welded joint and of spot space and/or lap length on that of multi-spot welded joint. Moreover, it was intended to find out a relationship between plane stress distributions of single- and multi-spot welded joints.First, qualitative studies of stress distribution on line (the X-axis in Fig. 1) including nugget front where fatigue crack may generate were carried out. Second, based on the above qualitative studies, quantitative studies of stress distribution by means of finite element method were carried out. Main conclusions obtained in this investigation are as follows:(1) Effects of specimen width and/or lap length on stress distribution of single-spot welded joint were made clear.(2) Effects of spot space and/or lap length on stress distribution of multi-spot welded joint were made clear.(3) Effects of specimen width on stress distribution of single-spot welded joint and of spot space of the same length on that of multi-spot welded joint are equivalent, as long as ratio of specimen width of single-spot welded joint or of spot space of multi-spot welded joint to nugget diameter is not extremely small.(4) If the stress distribution (σy on the X-axis) of single-spot welded joint with sufficiently large specimen width is known, it is possible to estimate. approximately stress distributions of single- and multi-spot welded joints with different specimen widths or spot spaces but with the same lap length.(5) Moreover, if an applied load that either maximum stress of single-spot welded joint with some specimen width and lap length or of multi-spot welded joint with some spot space and lap length becomes a specific stress value is known, it is possible to estimate, by using the graph shown in Fig.12 (This figure shows the relationships between specimen width or spot space and load ratios, using lap length as parameter), a similar load for single-spot welded joint with any specimen width and lap length or for multi-spot welded joint with any spot space and lap length.

A three-dimensional study of nuclear fuel rod behavior during startup

A three-dimensional finite element study is made of the behavior of cylindrical uranium dioxide fuel pellets during startup. The finite element code uses an eight-noded box element of arbitrary shape to build up the stiffness and stress characteristics by Gaussian integration. Each box has 33 degrees of freedom: 24 corresponding to the three motions at each of the eight nodes; and nine internally eliminated to minimize strain energy. The nine internal degrees of freedom are highly effective in eliminating shear error, and thus permitting far fewer elements than are required when tetrahedron elements are used. The element uses an isoparametric approach, so that the box can have eight arbitrarily positioned nodes. So long as the thermal expansions of the fuel rod can be described by a linear variation in the element, the code takes highly accurate account of it. Plasticity is accounted for by the secant modulus approach. Friction between the pellet and the cladding can be introduced by springs between the relevant finite elements in each area. A feature of the analysis allows cracks to appear in the uranium dioxide fuel as it is heated and the growth of the cracks can be traced as a function of linear power generated in the rod. The code can predict such things as pellet deformations and the stress and strain distributions within the pellets and the cladding. The three-dimensionality of the analysis allows a detailed view of these stresses and strains, and the interaction between the axial and plane stress distributions.

Stress Distribution of Single Spot Welded Lap Joint under Tension-Shear Load

The state of stress under tension-shear load was investigated experimentally and analytically on the single spot welded lap joint of single shear splice.Specimens were made from mild steel sheet of 1.0mm thickness. The stress distributions on the surfaces of the specimen were examined experimentally by the brittle coating and strain gage methods.According to the experimental results, the state of stress in the joint under tension-shear load appeared to be determined by the following factors.(i) Plane stress distribution near the weld nugget caused by the local transmission of load.(ii) Bending in the longitudinal direction resulted from the offset of lapped plates.(iii) Bending in the transverse direction, occured secondarily by the superposed effect of factors (i) and (ii).To clarify the state of stress owing to factor (i), the plane stress distribution was examined by the experiments on the middle plate of single spot welded double shear lap joint in tension, which was not affected by bending. Two-dimensional analysis by the finite element method was also made of the assumption of the idealized“Plane Model”.In connection with the state of stress due to longitudinal bending (factor (ii)), two-dimensional finite element analysis was employed on the“Section Model”of single spot welded single shear lap joint.Finally, the experimental stresses on the single spot welded single shear lap joint were compared with the analytical values, which were obtained by superposition of the stresses computed by Plane and Section Models.The results obtained are as follows:(1) In the stress measurement on the single spot welded single shear lap joint, the peak stress at 3mm distant above the nugget edge attained the value 3.9 or -1.3 times of the nominal tensile stress on the inner or outer surface of lapped plate, respectively.(2) The plane stress distribution computed by Plane Model agreed fairly well with the experimental result observed on the middle plate of double shear lap joint. In the finite element analysis by Plane Model, the lapped plates of the joint were doubly defined in the same plane.(3) The stress concentration factor deduced from the plane stress distribution was 2.2∼2.3 at the nugget edge of the joint, where the width of joint was 25mm and the nugget diameter was 5φ.(4) At the representative positions on the inner and outer surfaces of single shear lap joint, the superposed values of the stresses computed on the factors (i) and (ii) corresponded well with the axial stresses obtained from the experiments.

An elastic-plastic plane stress solution using the incremental theory

A numerical procedure is presented to determine the elastic-plastic plane stress distribution for a rectangular plate acting under any type of partial edge loading. The incremental theory of Prandtl-Reuss is used in conjunction with a Ramberg-Osgood stress-strain relationship. A linear partial differential equation is arrived at through the required load-history dependent constitutive equations. The necessity of incompressible material throughout both the initial and subsequent stress range is eliminated. Finally, because of the assumed Ramberg-Osgood equation, a solution in plasticity can be carried out without any fixed yield point.A finite difference scheme is incorporated to solve the partial differential equation and application is made considering a highly concentrated boundary loading. Comparison between the plastic and elastic solution shows that for increasing load situations, the plastic effective stress is larger than an elastic equivalent effective stress in the so-called plastic region.

Thickness-variation analog for nonhomogeneous plane-elasticity problems

This investigation was undertaken to show that the experimental study of the stress distribution in plane nonhomogeneous bodies may be accomplished by using models of varying thickness. Fabrication of models makes the experimental analysis of heterogeneous plane bodies difficult. Equations of elasticity are given which show that models with thickness variation should give the same results as those with a comparable variation in Young's modulus. Experimental results are given for the thickness-variation analog of the classical inclusion problem of varying modulus. These results are compared with the known theoretical results of the classical problem.

Rotationally Symmetric Plane Stress Distributions

Rotationally Symmetric Plane Stress Distributions

On the Stresses in Statical and Rotating Circular Plates Having Symmetrically Placed Noncentral Holes

In this paper a solution is given for problems of generalized plane stress distributions in a circular plate of radius α, containing k holes of same radius, the centres of which are arranged symmetrically on the circle of radius b. Using a stress function in polar coordinates, the boundary conditions are satisfled. As a particular case of this solution, the problem of the stress distributions in a rotating circular plate containing k holes (their radii bλ) is discussed under the conditions that the periphery of the plate and the edges of holes are free from external forces. Calculations have been carried out for the case b/α=3/7 and tangential stresses along holes are obtained for λ=1/5, 1/3 when two holes, λ=1/5 when 4 and 6 holes.

Bending Problem for an Infinite Plate containing Three Circular Holes in a Row

In this paper, as a paticular case of the present writer's general solution for a problem of generalized plane stress distributions in an infinite plate containing circular holes of varing sizes in any positions under the action of bending moment, a solution for the same problem but containing three circular holes in a row is obtained and discussed in detail using the method of Green's general bi-harmonic analysis and some numerical results respectively. Comparing these results with those obtained for the similar problems for an infinite plate containing (1) a singular hole treated by Dr. Tsuzi and (2) an infinite row of holes reported by the present writer, somewhat clear knowledge with respect to the influence of the presence of holes upon the stresses in a stressed plate etc. are obtained.

General bi-harmonic analysis for a plate containing circular holes

A general solution is given for problems of generalized plane stress distributions in an infinite plate which contains circular holes of varying sizes in any positions, subject only to certain conditions of convergence of the solution. The method for extending the results to allow for the effect of one or two straight boundaries is indicated. As a particular case of the general solution the problem of the stress distribution in an infinite plate under tension containing three holes in a row, is discussed, and a few numerical results are given. These results are compared with experiments which were carried out by Mr P. L. Capper. The comparison is incomplete as the experiments were done for a finite plate and the influence of the edges of the plate on the numerical values of the stresses is considerable. Agreement, however, is found for the general character of some of the stresses.

On an experimental method for the solution of plane stress problems

1—Many cases of plane stress distribution which are of importance to the engineer, present problems of mathematical analysis which are intractable and it becomes necessary to rely for a solution either on approximations, which are often crude, or on experimental methods. Perhaps the best known of these experimental methods is that of photoelastic analysis developed by Coker and Filon ; but this requires a wellequipped laboratory and considerable experience in technique if reliable results are to be obtained.

The Stresses in Fusion Joints

Modern use of fusion joints instead of riveted or bolted connexions has produced a variety of new forms which offer numerous fields of inquiry covering a great range of problems. One set of problems relates to stress distribution directed more especially to the determination of the maximum stresses in fusion joints. This is almost entirely an experimental matter, since nearly all such joints have discontinuities imposed by practical necessities which render them insoluble by theoretical analysis, while little or no help can be gained from our existing knowledge and long experience of riveted and bolted joints on account of their essentially different nature. The present inquiry deals with problems of plane stress distribution in which models are used for measuring the stress at any point required by photo-elastic means, and in the first instance some typical butt welds of an unsymmetrical type are analysed experimentally. Other ways of connecting plates in line are then considered in which a joint is made by a lenticular section of weld metal on one side and a cover plate on the other, the ends of the latter being joined to the main plates by triangular sections of fusion metal. When the gap between the two main plates is sufficient the lenticular section of metal may be replaced by a pair of triangular fillets binding the inner ends of the plates to the cover strap, and this form is also dealt with. The effects of triangular fillets of lesser height than the butt straps and of corresponding fillets of curved quadrantal form are also examined with reference to a double butt strap joint. The paper concludes with a brief summary of the main results afforded by the experimental analysis.