Optimization of inner and outer boundaries of beams and plates with holes

1981 ◽  
Vol 16 (4) ◽  
pp. 211-216 ◽  
Author(s):  
A J Durelli ◽  
K Rajaiah
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Small Area ◽  
Outer Boundary ◽  
Central Hole ◽  
Uniform Pressure ◽  
Two Dimensional ◽  
Photoelastic Method ◽  
Simply Supported ◽  
Square Plate

This paper presents optimized shapes of inner and outer boundaries for three specific problems: a long rectangular plate with a central hole subjected to uniaxial tension, a simply-supported slotted beam subjected to a load uniformly distributed over a small area at the centre, and a square plate with a central hole under uniaxial uniform pressure. The two-dimensional photoelastic method is used for optimization. The results indicate a significant reduction in stress concentration factor or in weight, or in both. The examples presented also include cases where the inner and outer boundary stresses are mutually dependent.

The Flow and Fracture of a Brittle Material

1950 ◽  
Vol 17 (3) ◽  
pp. 233-248
Author(s):  
L. F. Coffin
Keyword(s):  
Cast Iron ◽  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Gray Cast Iron ◽  
Gray Cast ◽  
Residual Tensile Stress ◽  
Two Dimensional ◽  
Combined Stress ◽  
Plastic Stress

Abstract The mechanism of flow and fracture of a gray cast iron can be understood if one considers the microstructure to consist of a ductile structure with a random dispersion of cracks due to the graphite flakes following the concept of Fisher. A notch effective stress can be calculated for a critically situated crack by a knowledge of the external stresses, a plastic stress-concentration factor of 3, and a residual tensile stress at the sharp edge of the crack, based upon either the “maximum-shear” theory or the “distortion-energy” theory. This allows the formulation of generalized plastic stress-strain relationships and renders gray cast iron applicable to the many known solutions for plastic flow of ductile metals. Fracture in the region of tension-tension and tension-compression can be evaluated by a similar analysis, using the same stress-concentration factor and the same residual stress. A combined stress-testing program is described wherein thin-walled cast-iron tubes are subjected to two-dimensional states of combined stress covering the complete two-dimensional field.

The Interaction of Holes on Stress and Strain Concentrations in Uniaxially Loaded Tensile Plates

2012 ◽  
Vol 268-270 ◽  
pp. 767-771
Author(s):  
Zheng Yang
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Thickness Effect ◽  
Central Hole ◽  
Stress And Strain ◽  
Strain Concentration ◽  
Minimum Value ◽  
R Ratio ◽  
Stress Concentration Region

Abstract. The elastic stress and strain fields of plates containing one central hole and two auxiliary holes subjected to uniaxial tension are examined using finite element method. The interaction between holes and the thickness effect on stress and strain concentration factors are investigated. It is shown that the distributions of strain concentration factor and stress concentration factor are different near central hole and auxiliary hole, and both of them depend on the hole radii and the distance between central hole and auxiliary hole. There is a minimum value of Kε/Kσ in stress concentration region and the quantity and location of this minimum value in plane stress state depend on the r/R ratio and d/R ratio of the plate. There are some specific distances between central hole and auxiliary hole corresponding to the radii of auxiliary hole to make the stress concentration factor in the plate minimum.

On the Stress Concentration in Multiple Notches

1962 ◽  
Vol 29 (3) ◽  
pp. 575-577 ◽  
Author(s):  
Kunio Nishioka ◽  
Nobuyoshi Hisamitsu
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Two Dimensional ◽  
Notch Depth ◽  
Pure Bending ◽  
Finite Plate ◽  
Photoelastic Investigation ◽  
Plate Width

The two-dimensional photoelastic investigation has been made on the effect of plate width, pitch, and depth of notch on the stress-concentration factor in a finite plate, which is for the single and multiple notches of any depth, under pure bending. Thus the stress-concentration factor, the effective notch depth, and the reduction of stress concentration caused by multiple notches were clarified.

A Design Equation for the Stress Concentration Factor of an Oblate Ellipsoidal Cavity

2011 ◽  
Vol 46 (2) ◽  
pp. 87-94 ◽  
Author(s):  
C-R Chiang
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Isotropic Material ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Ellipsoidal Cavity ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Correction Terms

The stress concentration factor (SCF) of an oblate ellipsoidal cavity in an isotropic material subjected to a uniform normal stress at infinity perpendicular to the equator of the cavity is determined by the equivalent inclusion method. Numerical results are obtained for general cases; particularly, explicit and exact results are obtained for cases of strongly oblate cavities. To extend the range of validity for these cases, a two-dimensional model is developed for finding the correction terms and a simple equation for the SCF of an oblate ellipsoidal cavity is thus obtained. The accuracy of the equation is probed and it is shown that the proposed formula is sufficiently accurate for design purposes.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

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