Creep stress concentration during loading and unloading processes in a strip with semi circular notches

The stress concentration during the loading and unloading processes of transient creep is investigated for a strip with semi circular notches by means of the photo-viscoplasticity, using specimens of celluloid at 65C. The relations between the stress concentration factor, the geometries of strips, and time during the loading and unloading processes are derived from the time dependent variations of isochromatic fringe orders. Such trends cannot be analysed by the ordinary photoplasticity in which the time effect is not taken into account.     

The effect of couple-stresses on stress concentrations around a circular hole in a strip under tension

The stress concentrations in a strip containing a circular hole is considered within the linearized theory of couple-stress elasticity. The resulting stress distributions are determined for variations in the couple-stress material moduli and cavity radius. Significant differences are found when compared with those based on classical theory of elasticity.     

On the elasto-plastic stress concentration at a circular hole in an anisotropic sheet

Summary The classical problem of determining the stress concentration factor at a circular hole embedded in an infinite sheet subjected to remote uniform tension is investigated. A finite strain elasto-plastic deformation theory based on Hill's new anisotropic flow theory [7] is used. It is shown that the governing field equations can be reduced to a single first order differential equation from which the stress concentration factor is obtained by a standard numerical method. The solution covers the entire elasto-plastic range and is valid for any strain hardening function. Comparison with experimental results, for a few materials, shows good agreement.With a pure power hardening law and within the framework of small strain plasticity, our results agree with those obtained from a more general solution discovered by Budiansky [8].With 3 Figures     

孔口缝合补强对含孔层板应变集中影响的实验研究

对复合材料开口缝合补强结构进行了实验研究。测试了不同缝合参数(针距、行距、边距、单重和双重缝合) 补强的含孔复合材料层板的拉伸强度, 研究了孔边应力集中、应变集中对强度、刚度等力学性能参数的影响, 分析讨论了孔边及邻近区域应变集中及应变分布的规律, 得到不同缝合参数、孔边不同位置以及不同载荷条件下的应变集中系数。结合实验结果和分析讨论, 给出了含孔复合材料层板缝合补强的缝合设计参数。      

Axisymmetric stress distribution in a transversely isotropic thick plate with a circular hole

Summary An exact solution for the stresses in a transversely isotropic infinite thick plate having a circular hole and subjected to axisymmetric uniformly distributed load on the plane surfaces has been given. The solution is in the form of Fourier-Bessel series and integrals. Numerical results for the stresses are given using the elastic constants for magnesium, and are compared with the isotropic case.

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Achsensymmetrische Spannungsverteilung in einer transversal isotropen, dicken Platte mit einem kreisförmigen Loch

Zusammenfassung Eine exakte Lösung für die Spannungen in einer transversal isotropen, unendlich ausgedehnten, dicken Platte mit einem kreisförmigen Loch, belastet durch eine achsensymmetrische, gleichmäßig verteilte Last an der ebenen Oberfläche, wird angegeben. Die Lösung ist in Form von Fourier-Bessel Reihen und Integralen dargestellt. Numerische Ergebnisse für die Spannungen werden unter Verwendung der elastischen Konstanten für Magnesium angegeben und mit dem isotropen Fall verglichen.

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With 4 Figures     

The problem of internal cracks in an infinite strip having a circular hole

Summary. The elastostatic plane problem of an infinite strip having a circular hole and containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of triply coupled integral equations. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. Quantities of physical interest are displayed in graphical forms.     

Dynamic stress concentration around a hole in a viscoelastic plate

Summary The transient hoop stresses which are generated at the circumference of a circular hole in a large viscoelastic plate when a radial pressure pulse acts on the hole boundary, are determined. An analytical/numerical approach is employed which is based on the use of Laplace transform and Hankel functions, and the Dubner-Abate-Crump technique for inverting the Laplace-transformed solution. In our formulation of the problem, a general linear-viscoelastic material for the plate is considered, but numerical results are extracted only for a three-parameter model (standard linear solid). The present work accompanies recent efforts by Georgiadis on analogous transient viscoelastodynamic problems involving finite-length cracks in a stress-wave environment. The mathematically simpler problem considered here demonstrates the influence of viscoelastic effects on the dynamic-stress-concentration in marked similarity with the dynamic-stress-intensity behavior of crack-tip viscoelastic stress fields. Besides that, the present problem generalizes the classical Kromm-Selberg-Miklowitz problem in the sense that it considers viscoelastic response. The latter solutions were not utilized here through the usual elastic/viscoelastic correspondence principle but, instead, an independent solution was derived by simple means.     

On stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole

Scale factors (SFs) are widely used in engineering applications to describe the stress concentration factor (SCF) of a finite width isotropic plate with a circular hole and under uniaxial loading. In this paper, these SFs were also found to be valid in an isotropic plate with biaxial loading and an isotropic cylinder with uniaxial loading or internal pressure, if a suitable hole to structure dimension ratio was chosen. The study was further expanded to consider orthotropic plates and cylinders with a center hole and under uniaxial loading. The applicable range of the SFs was given based on the orthotropic material parameters. The influence of the structural dimension on the SCF was also studied. An empirical calculation method for the stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole was proposed and the results agreed well with the FEM simulations. This research work may provide structure engineers a simple and efficient way to estimate the hole effect on plate structures or pressure vessels made of isotropic or orthotropic materials.     

Bending of piezoelectric plates with a circular hole

Departing from the refined theory of transversely isotropic piezoelectric plates, an analytical solution for the bending of an infinite piezoelectric plate with a circular hole is obtained. Expressions of moment, stress and electric displacement concentration factors are presented in closed form. When the piezoelectric coupling is absent, the results reduce to the corresponding solutions for the transversely isotropic elastic plates. Some numerical results for PZT-6B piezoelectric ceramics are obtained and illustrated by figures. These results show that the effect of piezoelectric coupling on the concentration factors is not negligible.     

On the three-dimensional stress field around a circular hole in a plate of arbitrary thickness

An analytical solution for the three-dimensional stress field in a plate of an arbitrary thickness, 2h, and weakened by a cylindrical hole of radius a is presented. Far away from the hole, the plate is subjected to a uniform tensile load, ₀, in a direction parallel to the plane of the plate. The solution is shown to be derivable from a general 3D solution, which the first author constructed in a previous paper. The analysis shows the stress concentration factor to vary across the thickness and to be sensitive to the value of the radius to thickness ratio, a/h. Furthermore, it is shown that for ratios of (a/h)4, the results predicted by plane stress theory are more than adequate for engineering applications. Finally, the transition between plane stress and plane strain appears to occur at a/h=0.5.Comment refers to an in-plane tensile load     

Loaded loose-fitted rough circular rigid pin in a circular hole

Summary This paper is concerned with an infinite plate of homogeneous elastic material in a state of generalized plane stress and having a circular hole. A rough loose-fitted rigid pin is pressed against one portion of the boundary of the hole, thus giving a specified displacement on the contact area while the rest of the boundary is stress free. The problem has been solved after converting it into aHilbert's Problem. Values of stresses at different points of the boundary have been calculated.

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Zusammenfassung Die Arbeit beschäftigt sich mit dem verallgemeinerten ebenen Spannungszustand in einer unbegrenzten, homogenen elastischen Platte mit kreisförmigem Loch. Ein rauher, lose passender starrer Bolzen wird seitlich gegen den Lochrand gedrückt. Damit ist im Berührungsgebiet die Verschiebung vorgeschrieben, während der übridge Teil der Berandung spannungsfrei bleibt. Nach Umformung in einHilbert-Problem wird die Aufgabe gelöst. Die Spannungen an verschiedenen Stellen des Lochrandes werden angegeben.

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With 2 Figures     

Finite shearing of a FRR block with a circular hole

Summary By using the idealized theory of fiber-reinforced materials, an exact equilibrium solution is obtained for the finite shearing of a rubber block reinforced by fibers in the shearing direction and weakened by a circular hole. Deformed configurations of the hole and block ends are obtained in explicit forms. It is found that the infinite normal stress occurs along the fiber lines tangent to the hole while the infinite hydrostatic pressure along the normal lines tangent to the hole. The edge stress around the hole obtained in an explicit form can be reduced to that given by the infinitesimal theory of anisotropic elasticity for the infinite ratio of elastic moduli when the block is infinite in length. These results are also presented in the figures.     

Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer

This work aims at understanding the effect of a radially heterogeneous layer around the hole in a homogeneous plate on the stress concentration factor. The problem concerns a single hole in a plate under different far-field in-plane loading conditions. By assuming a radial power law variation of Young’s modulus and constant value for Poisson’s ratio, the governing differential equations for plane stress conditions, and general in-plane loading conditions are studied. The elastic solutions are obtained in closed form and, in order to describe localized interface damage between the ring and the plate, two different interface conditions (perfectly bonded and frictionless contact) are studied. The formulae for the stress concentration factors are explicitly given for uniaxial, biaxial and shear in-plane loading conditions and comparisons with interface hoop stress values are performed. The solutions are investigated to understand the role played by the geometric and graded constitutive parameters. The results are validated with numerical finite element simulations in which some simplified hypotheses assumed in the analytical model, are relaxed to explore the range of validity of the elastic solution presented. In this way the results obtained are useful in tailoring the parameters for specific applications.