Bending of a plate with a thin-walled elastic inclusion along a circular arc

1984 ◽  
Vol 20 (8) ◽  
pp. 730-737
Author(s):  
I. I. Bernar ◽  
V. K. Opanasovich
Keyword(s):  
Elastic Inclusion ◽  
Circular Arc ◽  
Thin Walled

Cross-Section Deformation Effects in the Vibration of Thin-Walled Beams of Arc Section

1965 ◽  
Vol 7 (3) ◽  
pp. 292-299 ◽  
Author(s):  
S. A. Hasan ◽  
A. D. S. Barr
Keyword(s):  
Cross Section ◽  
Reasonable Agreement ◽  
Natural Frequencies ◽  
Characteristic Functions ◽  
Curved Beam ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Circular Arc ◽  
Beam Geometry ◽  
Thin Walled

Differential equations describing the coupling of ordinary bending motion with cross-sectional distortion are obtained for thin-walled beams of circular-arc cross-section using Hamilton's principle. In deriving the theory the cross-sectional deformation is assumed to take the form of the characteristic functions of a curved beam of the shape of the section. The variation with wavelength of the frequency spectra which result from the coupling is obtained. Experimental results showing the effects of the variation of the parameters of the beam geometry on the natural frequencies are in reasonable agreement with the theory.

Distortion of U-Channel Sections in Plastic Bending

1999 ◽  
Vol 121 (2) ◽  
pp. 208-213 ◽  
Author(s):  
K. A. Stelson ◽  
A. Kramer
Keyword(s):  
Material Properties ◽  
Energy Minimization ◽  
Plastic Bending ◽  
Circular Arc ◽  
Channel Section ◽  
Analytical Expression ◽  
Flat Base ◽  
Thin Walled ◽  
Good Agreement

When a thin-walled U-channel section is plastically bent, considerable in-plane distortion occurs. The initially flat base of the U is deformed into a circular arc. The sides remain perpendicular to the base so that an angle between the sides develops. In this paper, an analytical expression for the amount of distortion is derived based on energy minimization. The expression is purely geometrical indicating that distortion should not depend on material properties. The theory is compared with fourpoint bending experiments of thin-walled channels, with good agreement found.

Welding Defect Analysis in Thin-Walled Steel Tube under Bending Moment

2011 ◽  
Vol 94-96 ◽  
pp. 1711-1714
Author(s):  
Jin Feng Geng ◽  
Hong Sheng Cai ◽  
Xing Pei Liang ◽  
Hui Wang ◽  
Yu Jie Wang ◽  
...  
Keyword(s):  
Stress Intensity ◽  
Bending Moment ◽  
Steel Tube ◽  
Circular Arc ◽  
Linear Elastic ◽  
Weld Defect ◽  
Bending Load ◽  
Thin Walled ◽  
Welding Defect ◽  
Circular Arc Crack

The linear elastic problem for two welded thin-walled steel tubes containing circular arc weld defect subjected to bending load is analyzed in the present paper. The welding defect is firstly simplified as a circular arc crack and then the finite element based technique is used to calculate the corresponding energy release rate (J-integral), which is related to stress intensity factor directly. Finally, the arc length of welding defect is changed to investigate the variation of stress intensity factors.

The limiting load for a brittle body with a thin-walled elastic inclusion

1987 ◽  
Vol 23 (2) ◽  
pp. 219-222 ◽  
Author(s):  
S. Yu. Popina ◽  
G. T. Sulim
Keyword(s):  
Elastic Inclusion ◽  
Brittle Body ◽  
Limiting Load ◽  
Thin Walled

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

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