The Effect of Elliptic Holes on the Bending of Thick Plates

1955 ◽  
Vol 22 (1) ◽  
pp. 89-94
Author(s):  
P. M. Naghdi
Keyword(s):  
Stress Concentration ◽  
Elastic Plate ◽  
Elliptic Hole ◽  
Recent Theory ◽  
Mathieu Functions ◽  
Thick Plates ◽  
Transverse Normal Stress ◽  
Theory Of Plates ◽  
Concentration Factors ◽  
Stress Concentration Factors

Abstract The effects of an elliptic hole on both plain bending and pure twist of an elastic plate are investigated by application of the recent theory for bending of plates due to E. Reissner, where the influence of shear deformation and transverse-normal stress is taken into account. The stress-concentration factors are given for both cases mentioned. The solution, which is approximate in character, involves modified Mathieu functions of the second kind. In limiting cases, the results reduce exactly to the solution of corresponding problems with circular hole, as well as to the predictions of the classical theory of plates.

Stress Analysis of Holes in Thick Plates

2004 ◽  
Vol 1-2 ◽  
pp. 153-158 ◽  
Author(s):  
S. Quinn ◽  
Janice M. Dulieu-Barton
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Plate Surface ◽  
Flat Plates ◽  
Thick Plates ◽  
Concentration Factors ◽  
Stress Concentration Factors

A review of the Stress Concentration Factors (SCFs) obtained from normal and oblique holes in thick flat plates loaded in uniaxial tension has been conducted. The review focuses on values from the plate surface and discusses the ramifications of making a plane stress assumption.

Investigation of Pressure Stress Concentration Factors for Intersecting Elliptic Bores With Circular Bores in Blocks

2009 ◽  
Author(s):  
Elie A. Badr ◽  
Nataly Yousef
Keyword(s):  
Regression Analysis ◽  
Stress Concentration ◽  
Tilt Angle ◽  
Hoop Stress ◽  
Elliptic Hole ◽  
Lower Stress ◽  
Circular Holes ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Pressure Stress

Stress concentration factors due to intersecting elliptic bores as well as circular bores in blocks have been thoroughly investigated by Badr [1] and Sorem et al [2]. Results of these investigations indicated that intersecting elliptic crossbores generate lower stress concentration factors than those due to intersecting circular crossbores. In this study, we investigate stress concentration factors for crossbores in blocks (cubical and rectangular) emanating from intersecting elliptic with circular holes. Comparing these results with those generated by Badr [1] for elliptic hole intersections; it was found that crossbores due to intersecting elliptic with circular bores generate higher hoop stress concentration factors. A regression analysis was also performed to determine a relationship between the stress concentration factors, the bore ratio (a2/a1) and the tilt angle θ.

Dynamical Stress Concentration in an Elastic Plate

1962 ◽  
Vol 29 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Yih-Hsing Pao
Keyword(s):  
Stress Concentration ◽  
Elastic Plate ◽  
Wave Length ◽  
Thin Elastic Plate ◽  
Circular Cavity ◽  
Stress Concentrations ◽  
Compressional Waves ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Dynamical Stress

Stress concentrations around a circular cavity in an infinitely extended, thin elastic plate, during passage of plane compressional waves, are discussed. The dynamical stress concentration factors are found to be dependent on the incident wave length and Poisson’s ratio for the plate, and, at certain wave lengths, they are larger than those encountered under statical loading.

The Effect of a Rigid Elliptic Inclusion on the Bending of a Thick Elastic Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 379-382
Author(s):  
Fu Chow
Keyword(s):  
Stress Concentration ◽  
Elastic Plate ◽  
Plate Theory ◽  
Circular Inclusion ◽  
Elliptic Inclusion ◽  
Focal Distance ◽  
Classical Plate Theory ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Rigid Circular Inclusion

The effect of a rigid elliptic inclusion on both plain bending and pure twist of a thick elastic plate is investigated on the basis of Reissner’s plate theory [1, 2]. Comparison is made for the limiting cases of vanishing focal distance of the elliptic inclusion (a rigid circular inclusion), and vanishing thickness (Poisson-Kirchhoff plate theory), with the solutions of C. Pai [3], R. A. Hirsch [4], and M. Goland [5]. The stress-concentration factors are lower than those predicted by the classical plate theory.

scholarly journals Stress Concentration Factors for Welded Plate T-Joints Subjected to Tensile, Bending and Shearing Loads

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 546
Author(s):  
Krzysztof L. Molski ◽  
Piotr Tarasiuk
Keyword(s):  
Stress Concentration ◽  
Plate Thickness ◽  
Percentage Error ◽  
Geometrical Parameters ◽  
T Joints ◽  
Loading Mode ◽  
Weld Toe ◽  
Concentration Factors ◽  
Parametric Expression ◽  
Stress Concentration Factors

The paper deals with the problem of stress concentration at the weld toe of a plate T-joint subjected to axial, bending, and shearing loading modes. Theoretical stress concentration factors were obtained from numerical simulations using the finite element method for several thousand geometrical cases, where five of the most important geometrical parameters of the joint were considered to be independent variables. For each loading mode—axial, bending, and shearing—highly accurate closed form parametric expression has been derived with a maximum percentage error lower than 2% with respect to the numerical values. Validity of each approximating formula covers the range of dimensional proportions of welded plate T-joints used in engineering applications. Two limiting cases are also included in the solutions—when the weld toe radius tends to zero and the main plate thickness becomes infinite.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

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