The Saint-Venant principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains

1979 ◽  
Vol 19 (5) ◽  
pp. 813-822 ◽  
Author(s):  
O. A. Oleinik ◽  
G. A. Iosif'yan
Keyword(s):  
Biharmonic Equation ◽  
Unbounded Domains ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Boundary Problems

Stress Analysis and the Characteristics of T-Shape Bolted Joints Under Tensile Loadings

2005 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Seiichi Hamamoto
Keyword(s):  
Bending Moment ◽  
Theory Of Elasticity ◽  
Bolted Joints ◽  
Load Factor ◽  
Two Dimensional ◽  
Bolted Joint ◽  
Dimensional Theory ◽  
Matching Method ◽  
Point Matching ◽  
Bolt Stress

In designing a bolted joint, it is important to examine the interface stress distribution (clamping effect) and to estimate the load factor, that is the ratio of an additional axial bolt force to a load. In order to improve the clamping effect raised faces of the interface have been used. But these interfaces in bolted joints have been designed empirically and the theoretical grounds are not made clear. In the present paper, in the case of T-shaped flanges with raised faces the clamping effect is analyzed by a two-dimensional theory of elasticity and the point matching method. Then, the load factor is analyzed. Moreover, with the application of the load a bending moment is occurred in bolts and the stress is added due to this bending moment. The bending moment in the bolt is also analyzed. In order to verify these analyses experiments to measure the load factor and the maximum bolt stress were carried out. The values of the load factor and the load when interface start to separate are compared with those of the joints with flat-faces. The analytical results are in fairly good agreements with the experimental ones.

Exact Stress Distribution in Standard Gear Teeth and Geometry Factors

1973 ◽  
Vol 95 (4) ◽  
pp. 1159-1163 ◽  
Author(s):  
C. N. Baronet ◽  
G. V. Tordion
Keyword(s):  
Stress Distribution ◽  
Gear Tooth ◽  
Theory Of Elasticity ◽  
Tooth Profile ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Concentrated Load ◽  
Gear Teeth ◽  
Pressure Angle ◽  
Surface Stresses

Using the two-dimensional theory of elasticity and an appropriate transform function, the stress distribution in a gear tooth acted on by a concentrated load has been obtained. Computations were carried out for the 20 and 25-deg pressure angle, standard full-depth system, for numbers of teeth ranging from 20 to 150. The intensities of the maximum static surface stresses along the root fillets are given for different loading positions on the tooth profile. Some of the results are compared with others found in the literature.

Integral characteristics of elastic inclusions and cavities in the two-dimensional theory of elasticity

1992 ◽  
Vol 3 (1) ◽  
pp. 21-30 ◽  
Author(s):  
A. B. Movchan
Keyword(s):  
Conformal Mapping ◽  
Unit Disk ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
The Matrix ◽  
Integral Characteristics ◽  
Elastic Inclusions

Integral characteristics, such as elastic polarization matrices of elastic inclusions and cavities, are described. The matrix of elastic polarization of a finite cavity is constructed in the case of the two-dimensional Lamé operator under the assumption that the geometry of the domain occupied by the cavity is defined by a conformal mapping from the unit disk. Examples and applications of these integral characteristics in the theory of cracks are considered.

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