Plane Solutions for Traction Problems on Orthotropic Unsymmetrical Wedges and Symmetrically Twinned Wedges

1974 ◽  
Vol 41 (1) ◽  
pp. 203-208 ◽  
Author(s):  
M. C. Kuo ◽  
D. B. Bogy
Keyword(s):  
Stress Concentration ◽  
Mellin Transform ◽  
Wedge Angle ◽  
Complex Function ◽  
Anisotropic Materials ◽  
Function Representation ◽  
Material Constants ◽  
Plane Solution ◽  
Composite Wedge

The plane traction problem for a composite wedge formed from two identical orthotropic wedges is solved by use of the complex function representation of the plane solution for anisotropic materials in conjunction with the Mellin transform. As a preliminary to this solution the traction problem for a single unsymmetrical orthotropic wedge is also studied. For both problems the stress concentration at the wedge apex is examined and the dependence of the order of the singularity on the wedge angle and material constants is exhibited graphically.

Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges

1974 ◽  
Vol 41 (1) ◽  
pp. 197-202 ◽  
Author(s):  
M. C. Kuo ◽  
D. B. Bogy
Keyword(s):  
Mellin Transform ◽  
Symmetry Axis ◽  
Wedge Angle ◽  
Complex Function ◽  
Material Symmetry ◽  
Stress Singularities ◽  
Material Parameters ◽  
Plane Solution ◽  
Anisotropic Elastic ◽  
Plane Displacement

The plane displacement and traction-displacement problems for anisotropic elastic wedges are solved by use of the complex function representation of the plane solution in conjunction with the Mellin transform. The special forms of the solutions pertinent to orthotropic wedges with a material symmetry axis along the wedge bisector is also presented and the dependence of the order of the stress singularities at the apex on the wedge angle and material parameters is shown graphically for this case.

Dynamic Response of Shallow Buried Tunnel Subjected to SH Wave

2010 ◽  
Vol 163-167 ◽  
pp. 4265-4268
Author(s):  
Zhi Gang Chen
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Dynamic Stress ◽  
Complex Function ◽  
Least Square ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Scattering Wave

The dynamic stress concentration on quadratic and U-shaped cavities in half space, which are similar to the cross-section of the tunnels, is solved in this paper impacted by SH-wave. The analytical solution for the cavity in elastic half space is gained by the complex function method. In the complex plane, the scattering wave which satisfies the zero-stress condition at the horizontal surface can be constructed, the problem can be inverted into a set of algebraic equations to solve coefficients of the constructed scattering wave by least square method. For the earthquake-resistance researches, the numerical examples of the dynamic stress concentration around the quadratic and U-shaped cavities impacted by SH-wave are given. The influences of the dynamic stress concentration by the incident wave number and angle, the depth and shape of the cavity are discussed. It is showed that the interaction among the wave, the surface and the shallow buried tunnels should be cared in half space. In this situation, the dynamic stress concentration around the tunnel is greater obvious than the whole space.

The Numerical Simulation of Microstress for Hypereutectic Al-Si Alloys

2011 ◽  
Vol 211-212 ◽  
pp. 1133-1136 ◽  
Author(s):  
Ai Qin Wang ◽  
Jing Pei Xie ◽  
Wen Yan Wang ◽  
Ji Wen Li
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Stress Concentration ◽  
Mechanical Model ◽  
Wedge Angle ◽  
Spherical Particles ◽  
Matrix Interface ◽  
Ansys Software ◽  
The Matrix ◽  
Mechanics Characteristic

The elastic-plastic finite element mechanical model of hypereutectic Al-Si alloy was established based on ANSYS software. When the Si particles were circle, trapezium, rectangle or triangle, the microstress of Al-Si alloy under the external load were simulated. When the size of Si particles changed from 25μm to 45μm, the stress of Si particles and matrix interface was calculated. The effects of morphology and size of Si particles and loads on micro-mechanics characteristic of alloy were analyzed. The results showed that: under the same load, triangle or wedge angle Si particles make the biggest stress in the matrix, trapezoidal particles make the second and the spherical particles make the smallest. With the increase of the load, the stress and the stress concentration of Si particles in the matrix was increased, the stress of wedge angle particle increases remarkably, but the stress of spherical particles increases slowly. With the increase of the size of Si particles, the stress and the stress concentration of Si particles in matrix are increased.

On the generating function e xt+yϕ(t) and its fractional calculus

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Alireza Ansari ◽  
Amirhossein Sheikhani ◽  
Sohrab Kordrostami
Keyword(s):  
Fractional Calculus ◽  
Laplace Transform ◽  
Generating Function ◽  
Mellin Transform ◽  
Complex Function ◽  
Inverse Laplace Transform ◽  
Explicit Solutions ◽  
Associated Functions ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

AbstractIn this article, we derive the coefficient set {H m(x,y)}m=1∞ using the generating function ext+yϕ(t). When the complex function ϕ(t) is entire, using the inverse Mellin transform, and when ϕ(t) has singular points, using the inverse Laplace transform, the coefficient set is obtained. Also, bi-orthogonality of this set with its associated functions and its applications in the explicit solutions of partial fractional differential equations is discussed.

scholarly journals Scattering of SH Waves by a Partially Debonded Cylindrical Inclusion in the Covering Layer

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hui Qi ◽  
Yang Zhang ◽  
Fuqing Chu ◽  
Jing Guo
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Complex Function ◽  
Surface Displacement ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Sh Waves ◽  
Covering Layer ◽  
The Impact

This article presents analytical solutions to the problem of dynamic stress concentration and the surface displacement of a partially debonded cylindrical inclusion in the covering layer under the action of a steady-state horizontally polarized shear wave (SH wave); these solutions are using the complex function method and wave function expansion method. By applying the large-arc assumption method, the straight line boundary of the half-space covering layer is transformed into a curved boundary. The wave field of the debonded inclusion is constructed utilizing a Fourier series and boundary conditions of continuity. The impact of debonding upon the dynamic stress concentration and surface displacement around the cylindrical concrete or steel inclusion is analyzed through numerical examples of the SH waves that are incident at normal angles, from a harder medium to a softer medium and from a softer medium to a harder medium. The examples show that various factors (including the medium parameters of the soil layers and the inclusion, the frequency of the incident waves, and the debonding situations) jointly affect the dynamic stress concentration factor and the surface displacement around the structure.

A Note on Interface Cracks With and Without Friction in Contact Zone

1994 ◽  
Vol 61 (4) ◽  
pp. 994-995 ◽  
Author(s):  
X. Deng
Keyword(s):  
Contact Zone ◽  
Crack Surface ◽  
Complex Function ◽  
Crack Tip ◽  
The Body ◽  
Bimaterial Interface ◽  
Crack Tip Field ◽  
Function Representation ◽  
Complete Set ◽  
Bimaterial Interface Crack

A complete set of Comninou’s bimaterial interface crack-tip fields with and without friction in the contact zone (Comninou, 1977a,b) is given in terms of several arbitrary analytic functions. When the bimaterial becomes homogeneous, the complex function representation fully describes the crack-tip field for a cracked body under conditions of crack surface contact and slip, which can occur when the body is subjected to combined compression and shear loadings.

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