Analytical Solution on the 3D Stress Concentration Problem of a Plate with a Circular Hole under Uniform Tension at Infinity

1986 ◽  
pp. 1021-1026 ◽  
Author(s):  
Tadahiko Kawai ◽  
Tetsuya Endoh
1948 ◽  
Vol 15 (2) ◽  
pp. 160-168
Author(s):  
Samuel Levy ◽  
A. E. McPherson ◽  
F. C. Smith

Abstract This paper presents a theoretical and experimental investigation of the effect of various reinforcements on the stresses and displacements near a small circular hole in a plane sheet under load in its plane. The first part of the paper gives a plane-stress analysis for a reinforcement of variable thickness when the load is a uniform tension in all directions. It is found that a reinforcement which crowds most of the material close to the edge of the hole is most effective in reducing the stress concentration at the hole. The next part presents the principal results of earlier plane-stress analyses for reinforcement by a “doubler plate” when the load is tension in one direction only. The last part describes tests in the elastic range of riveted doubler-plate reinforcements of several sizes and with several rivet arrangements. Details of a test to failure of one reinforcement riveted to one side of the sheet only are given. The tests indicate that the plane-stress theory gives a good estimate of the state of stress outside the reinforcement, and that it may be used for computing median-surface stresses and average elongations of the hole in the specimen, provided that the reinforcement is attached to the sheet by more than one row of rivets.


2011 ◽  
Vol 239-242 ◽  
pp. 558-562
Author(s):  
Bu Xi Bian ◽  
Yi Hua Liu

Coating craft process is often used on the hole surface, thus it must affect the degree of the stress concentration near the hole edge. Airy stress function methodology is used to obtain the analytical stress solution for a plate with a small coating circular hole in the center and subjected to the uniaxial uniform tension in this paper. With the help of the finite element software MSC.Patran & Nastran, the K3alloy plate is numerically analyzed, and its coating material is a ZrO2, and with the comparison of the acquired analytical solutions, it can be found that the numerical results coincide with the analytical ones very well. The results show that coating affects greatly the stress distribution near the hole edge, and the stress concentration factor in the coating increases with the coating thickness but decreases in the plate, and it increases with the shear modular ratio of the coating to the plate but decreases in the plate. The effect of the coating on the stress distribution near the hole and the stress concentration cannot be neglected.


Author(s):  
Qiang Luo ◽  
Ming Wei ◽  
Qingyuan Lu ◽  
Tengfei Wang

AbstractPiled embankments have been extensively used for high-speed rail over soft soils because of their effectiveness in minimizing differential settlement and shortening the construction period. Stress concentration ratio, defined as the ratio of vertical stress carried by pile heads (or pile caps if applicable) to that by adjacent soils, is a fundamental parameter in the design of piled embankments. In view of the complicated load transfer mechanism in the framework of embankment system, this paper presents a simplified analytical solution for the stress concentration ratio of rigid pile-supported embankments. In the derivation, the effects of cushion stiffness, pile–soil interaction, and pile penetration behavior are considered and examined. A modified linearly elastic-perfectly plastic model was used to analyze the mechanical response of a rigid pile–soil system. The analytical model was verified against field data and the results of numerical simulations from the literature. According to the proposed method, the skin friction distribution, pile–soil relative displacement, location of neural point, and differential settlement between the pile head (or cap) and adjacent soils can be determined. This work serves as a fast algorithm for initial and reasonable approximation of stress concentration ratio on the design aspects of piled embankments.


2002 ◽  
Vol 37 (3) ◽  
pp. 259-264 ◽  
Author(s):  
Q. Z Wang

First, based on an approximate analysis, simple closed-form expressions of the stress concentration factor (SCF) for two- or three-dimensional models with a circular hole or a spherical cavity in a finite domain are derived. Then, an asymptotic method is adopted to improve the accuracy of the derived solutions for an extremely large circular hole or spherical cavity, when the remaining ligament approaches zero. Exact limit SCF values for these two kinds of models were given by Koiter; these values are used for the adjustment of the coefficients in the SCF expressions. Finally, simple SCF formulae for these finite domain problems are obtained, their accuracy is demonstrated to be very good by comparison with the available data from the literature, and the asymptotic validity is guaranteed.


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