Effect of Surface Elasticity on the Interaction Between Steps

2006 ◽  
Vol 74 (4) ◽  
pp. 821-823 ◽  
Author(s):  
Gan-Yun Huang ◽  
Shou-Wen Yu
Keyword(s):  
Integral Transform ◽  
Surface Elasticity ◽  
Elastic Interaction ◽  
Fourier Integral ◽  
Shear Loads ◽  
Surface Steps ◽  
Fourier Integral Transform ◽  
Intrinsic Length ◽  
Force Components ◽  
Effect Of Surface

By taking into account the effect of surface elasticity, the problem of a half plane under concentrated normal or shear loads is first considered. The solutions for the displacements or alternatively named surface Green’s functions can be obtained by using the Fourier integral transform technique. Based on such solutions, the elastic interaction between two surface steps that are modeled as force dipoles is further investigated. The results show that the effect of surface elasticity on the interaction energy is significant when the distance between the two steps is in the range of several times the intrinsic length scale of the system. Further, surface elasticity seems to influence the interaction between steps with force components parallel to the surface more strongly than that when the steps exhibit force components only normal to the surface.

Effects of Interleaves on Fracture of Laminated Composites: Part I—Analysis

1990 ◽  
Vol 57 (1) ◽  
pp. 168-174 ◽  
Author(s):  
A. K. Kaw ◽  
J. G. Goree
Keyword(s):  
Composite Laminates ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Elastic Media ◽  
Two Dimensional ◽  
Shear Moduli ◽  
Fourier Integral Transform ◽  
Shaped Crack ◽  
Symmetric Crack

The influence of placing interleaves between fiber-reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as a two-dimensional, isotropic, linearly elastic media consisting of a damaged layer bonded between two half-planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. Fourier integral transform techniques are used to develop the solutions in terms of singular integral equations.

Transient Response of a Periodically Supported Cylindrical Shell Immersed in a Fluid Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 562-568 ◽  
Author(s):  
Harry Herman ◽  
J. M. Klosner
Keyword(s):  
Cylindrical Shell ◽  
Integral Transform ◽  
Circular Cylindrical Shell ◽  
Fourier Integral ◽  
Cylindrical Wave ◽  
Acoustic Medium ◽  
Steel Shell ◽  
Fluid Medium ◽  
Wave Approximation ◽  
Fourier Integral Transform

The dynamic response of a periodically simply supported, infinitely long, circular cylindrical shell to a pressure suddenly applied through the surrounding acoustic medium is investigated. The incident particle velocity is zero, and the pressure is assumed to have a harmonic spatial variation parallel to the shell axis. The exact solution is obtained by use of a Fourier integral transform, and the resulting inversion integral is evaluated by numerical and asymptotic integration. Two solutions to the same problem are obtained by using a plane and cylindrical wave approximation for the radiated field. The range of their applicability is investigated. For a steel shell in water ccs2=0.08815 it is found that, when the supports are placed three shell diameters apart, the use of the cylindrical wave approximation results in a 5-percent underestimation of the maximum deflection, while when the supports are placed one sixth of a shell diameter apart, the approximations are invalid.

On the theory of the diffraction of a plane wave by a large perfectly conducting circular cylinder

1961 ◽  
Vol 264 (1317) ◽  
pp. 235-245 ◽  
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Boundary Value Problem ◽  
Cross Section ◽  
Integral Transform ◽  
Forward Direction ◽  
Fourier Integral ◽  
Straightforward Application ◽  
Total Scattering Cross Section ◽  
Fourier Integral Transform

The solution is obtained by a method somewhat different from those previously given by other authors. The method is in principle a straightforward application of Fourier integral transform analysis to a boundary-value problem, and is shown to lead rather naturally to the various field representations suitable for different regions, including that at infinity in the forward direction which gives the total scattering cross-section. No new results are obtained in the present paper, but mention is made of other problems which have subsequently been successfully attacked on the basis of the method given.

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