scholarly journals Analysis of Elliptical Ring by Using Laurent Series Expansion of Complex Stress Functions.

1997 ◽  
Vol 46 (9) ◽  
pp. 1011-1016 ◽  
Author(s):  
Shohei KAWAKUBO ◽  
Ken-ichi HIRASHIMA
Keyword(s):  
Series Expansion ◽  
Laurent Series ◽  
Complex Stress ◽  
Elliptical Ring ◽  
Stress Functions

Forces on a Circular Hole Located in Functionally Graded Material

2011 ◽  
Vol 704-705 ◽  
pp. 631-635
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Circular Hole ◽  
Constant Term ◽  
Complex Stress ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Dimensional Problem ◽  
Stress Components ◽  
Graded Material ◽  
Stress Functions ◽  
Stress Function Method

The complex stress function method is used in this study to formulate the 2-dimensional problem for nonhomogeneous materials. The Young’s modulus E varies linearly with the coordinate x and the Poisson’s ratio of the material is assumed constant and. The stress components and the boundary conditions are expressed in terms of two complex stress functions in explicit forms. It is noted that the constant term in stress functions has an influence on the stress components, which is different from the homogeneous material case. Subsequently, the problem of a nonhomogeneous plane containing a circular hole subjected to a uniform internal pressure is studied.

Compressibility of Two-Dimensional Cavities of Various Shapes

1986 ◽  
Vol 53 (3) ◽  
pp. 500-504 ◽  
Author(s):  
R. W. Zimmerman
Keyword(s):  
Closed Form Solution ◽  
Mapping Function ◽  
Complex Stress ◽  
Form Solution ◽  
Hydrostatic Compression ◽  
Biaxial Compression ◽  
Cavity Surface ◽  
Uniform Pressure ◽  
Two Dimensional ◽  
Stress Functions

Muskhelishvili-Kolosov complex stress functions are used to find the stresses and displacements around two-dimensional cavities under plane strain or plane stress. The boundary conditions considered are either uniform pressure at the cavity surface with vanishing stresses at infinity, or a traction-free cavity surface with uniform biaxial compression at infinity. A closed-form solution is obtained for the case where the mapping function from the interior of the unit circle to the region outside of the cavity has a finite number of terms. The area change of the cavity due to hydrostatic compression at infinity is examined for a variety of shapes, and is found to correlate closely with the square of the perimeter of the hole.

scholarly journals Integrand reduction of one-loop scattering amplitudes through Laurent series expansion

2012 ◽  
Vol 2012 (6) ◽  
Author(s):  
Pierpaolo Mastrolia ◽  
Edoardo Mirabella ◽  
Tiziano Peraro
Keyword(s):  
Scattering Amplitudes ◽  
Series Expansion ◽  
Laurent Series

Contact Stress Analysis Around Elliptic Pin-Loaded Holes in Orthotropic Plates

2010 ◽  
Author(s):  
O. Aluko ◽  
H. A. Whitworth
Keyword(s):  
Coulomb Friction ◽  
Complex Stress ◽  
Stress Distributions ◽  
Orthotropic Plates ◽  
Carbon Fiber Reinforced Plastics ◽  
Reinforced Plastics ◽  
Method Of Solution ◽  
Stress Functions ◽  
Fiber Reinforced Plastics ◽  
Lower Magnitude

This analysis utilizes the complex stress function approach to obtain the stress distribution in pin loaded composite joints with elliptic openings. The stress functions were derived from assumed displacement expressions that satisfy the boundary conditions around the hole. In the method of solution Coulomb friction was used to determine the prescribed displacements at the boundary. The material properties of graphite/epoxy and carbon fiber reinforced plastics laminates were used in this investigation and the results also compared with available data for joints with circular openings. It was revealed that the stress distributions followed the same pattern in both geometries but with lower magnitude in elliptical shape and the reduction in stress distributions caused by changing the pin/hole shape from circular to elliptic depend on friction.

In-Plane Bending Fracture of a Large Beam Containing a Circular-Arc Crack

2002 ◽  
Vol 18 (3) ◽  
pp. 145-151
Author(s):  
Y. C. Shiah ◽  
Jiunn Fang ◽  
Chin-Yi Wei ◽  
Y.C. Liang
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Stress ◽  
Bending Moments ◽  
Intensity Factors ◽  
Boundary Equation ◽  
Circular Arc ◽  
Stress Functions ◽  
Arc Crack ◽  
Circular Arc Crack

AbstractIn this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.

Sign in / Sign up

Export Citation Format

Share Document