Stress Concentration In Plate Research Articles

Evaluation of the effects of stress concentrations on plates using granular micromechanics

This work is dedicated to the study of the effect of stress concentrations in plates induced by notches and holes using a Granular Micromechanics (GM) model. To this end, three structural configurations were analyzed: an intact plate, a plate with a central circular hole, and a plate with two notches. For comparison of the mechanical response of these plates, the radii of the hole and the notches are taken the same. The material behavior of the plates is described through the multiscale GM constitutive law. The equations of this model are formulated based on the mechanical properties of the grains, the grain-pair interactions and the relative movement of the grains. So the identification of the material parameters needs only the determination of the grains’ properties and grain-pair interactions. This micromechanics-based model has been implemented into the finite element code Abaqus/Explicit through a Vectorized User MATerial (VUMAT) subroutine. The model is applied to study the plates under uniaxial and biaxial loadings. This study aims to assess the pertinence of applying the GM model to structural analysis and show the influence of the two geometrical imperfections on the overall behavior of the structure. It has been found that the model can describe the behavior of plates under tension and compression loadings. Moreover, the effects of a hole and notches on the behavior and failure of the granular-made plates are captured.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

Stress concentration around an elliptical hole in a large rectangular plate subjected to linearly varying in-plane loading on two opposite edges

Stress concentration in plates due to geometric irregularities such as holes and cracks is a crucial factor in design. The main objective of this paper is to derive the formula for tangential stress concentration factor around an elliptical hole in a large rectangular plate subjected to linearly varying in-plane loading on two opposite edges. The problem is investigated by the two-dimensional theory of elasticity using Muskhelishvili’s complex variable method. The stress functions are evaluated using the conformal mapping method and Cauchy’s integral formula. The stress functions thus obtained are coded to compute the non-dimensional stress components in the plate. The stress concentration factors at the edge of the elliptical hole are compared for different aspect ratios under various in-plane loading conditions. The results indicate that the formula obtained for tangential stress matches to the Kang’s [1] formula when elliptical hole is reduced to a circular hole, by taking its aspect ratio equal to 1. Furthermore, the classical solutions proposed by Inglis and Kirsch are easily obtained as special cases of the problem presented in this work, which confirms the efficacy of the solution. A plane stress finite element model is prepared in ABAQUS and results are compared with present method for a particular case of linearly varying in-plane loading.

Stress Analysis for an infinite plate with circular holes

Isotropic plate with central circular hole under different loading, have found widespread applications in various fields of engineering such as aerospace, marine, automobile and mechanical. For design of plates with holes accurate knowledge of deflection, stresses and stress concentration are required. Stress concentration arises from any abrupt change in geometry of plate under loading. As a result, stress distribution is not uniform throughout the cross section. Failures such as fatigue cracking and plastic deformation frequently occur at points of stress concentration. Hence, it is very important in any engineering structures to know about the stress concentration in plates with holes. In the present study stress concentration in an infinite isotropic plate around circular hole subjected to transverse, longitudinal and biaxial loading is calculated using analytical approach. For calculating stress concentration around two holes complex variable and bipolar coordinate method are used. The results obtained from this approach shows good agreement with result given in literatures.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scattering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonal function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concentration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

Thermal Stress Concentration in Plates from Different Materials

DOI: 10.2514/1.C031661 Manufacturing of welded plates with different materials are widely employed in industrial application that is exposed to mechanical and temperature loads. In this study, thermal stress distribution in plates from different materials containing a defect, a rectangular hole with semicircular caps, near a joining line is numerically investigated under the homogeneous change of temperature. Investigations are carried out for the cases of butt and bevel-jointweldsfordifferentlocationsof thehole.Maximumofstress concentrationfactorisencountered whenthe longitudinal-axis of the hole is at an angle of 45 deg to the joining line in the case of butt-joint weld. Variation of the tangentialstresscomponentofthehole-tiphasajumpwhenitcrossesoverthejoiningline.Thestressintensityfactors in considered structures are determined using the obtained results of stress concentration factors for variations of radius of hole-caps. An expression is proposed to obtain the stress in the bevel-joint using values in the butt-joint plate. For a comparison, thermal stresses are also investigated in a model made from an optical sensitive material using the method of mechanical modeling of photothermoelasticity for a butt-joint plate. The comparison shows the agreement between numerical and experimental solutions.

Tensile stress concentration in plates with double countersunk rivet holes

The present study investigates the in-plane stresses generated around two adjacent countersunk holes in isotropic plates subjected to uniaxial tension perpendicular to the line of centres of the two holes. Finite element analysis (FEA) is used to build the geometric model and to perform the analysis under various combinations of plate and hole geometric parameters, namely, the defining dimensions of the plate and the holes and the distance between the two holes. Results obtained from the study illustrate an increase in stress concentration as the width of the plate or the distance between holes decrease. Moreover, an increase in the countersink depth, the thickness of the plate or the countersink angle increases stress concentration.

Stress concentration in a spherical shell with two neighboring circular holes

UDC 539.3 We have solved analytically the problem of the stressed state in an isotropic shallow spherical shell with two circular holes. The cases of the close location of holes of both equal and unequal radii in the shell under the action of internal pressure have been investigated numerically. We have detected a considerable increase in stresses on the bulkhead between the holes at their approach. Stress concentration in plates and shells with several holes has been investigated since long ago [2], but, nevertheless, these data remain important for engineering practice [3–8], especially in the case of close location of the holes between themselves [7]. Numerical results for an isotropic shallow spherical shell with two equal circular holes under the action of internal pressure are described in [1, 2]. Here, the minimal bulkhead width constituted 0.7 of the hole radius. As shown in [7] for a stretched plate with two holes, a significant increase in stress concentration takes place if the holes are located closely. Therefore, in the present work, we study the cases of close location of two circular holes (including unequal) in a spherical shell.

Effect of Cutout Orientation on Stress Concentration of Perforated Plates with Various Cutouts and Bluntness

Perforated plates with cutouts (or holes) are widely used in structural members. These cutouts provide stress concentration in plates. Extensive studies have been carried out on stress concentration in perforated plates, which consider cutout shapes, boundary conditions, bluntness of cutouts, and more. This study presents stress concentration analyses of perforated plates with not only various cutouts and bluntness but also different cutout orientations. Especially, the effect of cutout orientation on stress concentration is emphasized since structural members have become more complicated recently. To obtain stress concentration patterns, a finite element program, ANSYS, is used. For the designated goal, three parameters are considered as follows: the shapes of polygonal cutouts (circle, triangle, and square), bluntness (a counter measure of radius ratio, r/R), and rotation of cutouts (<TEX>${\theta}$</TEX>). From the analyses, it is shown that, in general, as bluntness increases, the stress concentration increases, regardless of the shape and rotation. A more important finding is that the stress concentration increases as the cutouts become more oriented from the baseline, which is the positive horizontal axis (+x). This fact demonstrates that the orientation is also a relatively significant design factor to reduce stress concentration. In detail, in the case of the triangle cutout, orienting one side of the triangle cutout to be perpendicular to the applied tensile forces is preferable. Similarly, in the case of the square cutout, it is more advantageous to orient two sides of square cutout to be perpendicular to the applied tensile force. Therefore, at the design stage, determining the direction of a major tensile force is required. Then, by aligning those polygon cutouts properly, we can reduce stress concentration.

Analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping – Finite element approach

Plates with rectangular openings develop stress concentrations under bending. While these stresses can be determined using finite elements, in many problems this would be difficult because a high density mesh would be needed in the neighborhood of every opening corner. In this paper, it is shown how a complex-variable conformal mapping approach can be numerically coupled with the finite element method to analyze these corner stresses. This approach can be used even with relatively coarse meshes where the finite element results, by themselves, do not resolve the stress concentrations. In essence, the method relies on finite element analysis to obtain information on the stress field in a region surrounding the plate opening; this information is subsequently used to set up the parameters of the conformal mapping approach to obtain the near field stresses at the opening corners.

Acoustical wave propagator for time-domain dynamic stress concentration in a plate with a sharp change of section

The acoustical wave propagator technique is applied to study the time-domain dynamic stress concentration in a two-dimensional flexible plate with a sharp change of section. As a wave packet approaches the plate discontinuity where the sharp change of thickness is introduced, the spatial interference patterns in the displacement of the plate and internal stresses vary with time. The constructive interference of stresses is referred to as time-domain stress concentration. The superposition of wave fronts of incident and reflected wave packets is used to explain the spatial distribution of the interference patterns. The increase of dynamic stress near the vicinity of the discontinuity boundary of the plate is studied as a function of time and the thickness ratio of the plates.

Stress concentration in plates under tension with local thinnings in elastoplastic deformations and creep

The results are given of a calculation-experimental investigation of the stress concentration in the zone of two-sided and one-sided craters in the form of spherical segments. The elastoplastic problem was solved by the method of variable parameters of elasticity with use of the finite element method. The experiments were made on plates of AL2 alloy with the use of short-base strain gauges. The relationship was obtained of the stress concentration factors to the parameters of thinning and loading at characteristic points. The picture is given of the successive transition of the elements into the plastic state. The simulation of creep based on the method of isochronous curves made it possible to obtain curves of the change in stress concentration factors with time for the characteristic points applicable to the steels used in turbine production from the data of experimental investigation of aluminum elastoplastic models.

Stress concentration in plates with thin regions

Stress concentration in plates with thin regions

Approximate methods for the solution of problems of stress concentration near holes in orthotropic plates made out of composite materials. 4. Stress concentration in plates made out of directionally reinforced fiber composites

Approximate methods for the solution of problems of stress concentration near holes in orthotropic plates made out of composite materials. 4. Stress concentration in plates made out of directionally reinforced fiber composites

A fringe-compensation technique for stress analysis by reflection holographic interferometry

The use of holographic interferometry for stress analysis of nontransparent objects is limited by rigid-body displacements of the object. These displacements can alter the fringe patterns and often cause the fringes to disappear completely. A technique of compensation for this deterioration of the fringe pattern forreal-time holographic interferometry is described in this paper. It is especially designed to permit the accurate measurement of the out-of-plane component of strain near regions of stress concentration in plates that are subjected to in-plane loading. It is first shown that the fringes caused by a pure rigid-body displacement can be eliminated almost completely by translations of the hologram and rotation of the illumination wave. This procedure is first described when the displacement is known; then when it is unknown. A method to estimate the error made in the correction is presented.

Stress concentration in plates with holes having large curvatures at corner points

Stress concentration in plates with holes having large curvatures at corner points

Stress concentration in plates and shells with polygonal apertures

Stress concentration in plates and shells with polygonal apertures

On the Stiffening of the Edge of the Hole in Orthogonally Aeolotropic Plate with a Circular Hole : stiffened with the coaming plate

As a means of reducing the circumferential stress concentration in plate, the coaming plate is usually introduced around the edge of the hole to supplement the doubling plate. This paper deals with the effect of the coaming plate on the stress distribution in orthogonally aeolotropic plate under uniform tension. That is, we assume the coaming plate is a circular ring and by using the following formula for the edge stress of the plate, namely, [numerical formula] the problem can be solved theoretically and simply. In conclusion, the larger the Young's modulus of the coaming plate is, and the greater its height is, and the greater its thickness is, the more the circumferential stress is reduced.

On the Stiffening of the Edge of the Hole in Orthogonally Aeolotropic Plate with a Circular Hole : 2nd Retport, stiffened with the coamins plate

As a means of reducing the circumferential stress concentration in plates, the coaming plate around the edge of the hole to supplement the doubling plate is usually introduced. This paper deals with the effect of the coaming plate on the stress distribution in orthogonally aeolotropic plate under uniform tension. That is, we assume the coaming plate is a circular ring and by putting the edge stress of the plate [numerical formula], the problem can be solved theoretically and simply. In conclusion, the larger Yong's modulus of the coaming plate is, and the higher its height is, and the thicker its thickness is the more the circumferential stress is reduced.

Stress Concentrations in Plates Loaded Over Small Areas

If a considerable pressure is applied within a small area as a transverse load on a plate or slab, a concentration of stress will occur within and around that area. This stress concentration differs in type from that observed at fillets, re-entrant corners, or holes in solids; it is caused by concentration of the load. If the load on the plate or slab is not too close to any lines or points of concentrated support or to any edge and is neither too concentrated nor too dispersed, and if the material of the plate or slab is homogeneous, isotropic, and elastic, the important features of the stress concentration produced by the load can be expressed conveniently and with good approximation by means of six coefficients, all of which are pure numbers. Three of these-B, C, and D-are called “place coefficients”; they depend on the place of the load, but not on its manner of distribution over the small loaded area. The remaining three-K, S, and Tare called “area coefficients”; they depend on the size and shape of the loaded area and on the manner of distribution of the load over that area, but are independent of the place of the load. When the place coefficients have been determined in m cases and the area coefficients in n cases, solutions are thereby made available in m times n combined cases.