scholarly journals The Green's Function BEM for Bimaterial Solids Applied to Edge Stress Concentration Problems

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Denda
Keyword(s):  
Stress Concentration ◽  
Green’S Function ◽  
Green's Function ◽  
Free Edge ◽  
Fundamental Solutions ◽  
Singular Stress ◽  
Thin Coatings ◽  
Edge Stress ◽  
Line Force ◽  
Isotropic Solids

A boundary element method (BEM) for bimaterial domains consisting of two isotropic solids bonded perfectly along the straight interface will be developed. We follow the physical interpretation of Somigliana’s identity to represent the displacement in the bimaterial domain by the continuous distributions of the line forces and dislocation dipoles over its boundary. The fundamental solutions used are the Green’s functions for the line force and the dislocation dipole that satisfy the traction and displacement continuity across the interface of two domains. There is no need to model the interface because the required continuity conditions there are automatically satisfied by the Green’s functions. The BEM will be applied to study the edge stress concentration of the bimaterial solids. We calculate the singular stress distribution at the free edge of the interface for various bimaterial configurations and loadings, in particular, for the domain consisting of thin coating over the substratum. Since the Green's function BEM does not require the boundary elements on the interface, it can handle the edge singularity on the interface accurately even for extremely thin coatings. The BEM developed here is not limited to the edge stress concentration problems and can be applied to a broad range of the bimaterial domain problems effectively.

Free-Edge Effects in Composite Laminates

2007 ◽  
Vol 60 (5) ◽  
pp. 217-245 ◽  
Author(s):  
Christian Mittelstedt ◽  
Wilfried Becker
Keyword(s):  
Stress Concentration ◽  
Edge Effect ◽  
Edge Effects ◽  
Composite Laminates ◽  
Relevant Literature ◽  
Free Edge ◽  
Experimental Investigations ◽  
Singular Stress ◽  
Concentration Problem ◽  
Concentration Phenomena

There are many technical applications in the field of lightweight construction as, for example, in aerospace engineering, where stress concentration phenomena play an important role in the design of layered structural elements (so-called laminates) consisting of plies of fiber reinforced plastics or other materials. A well known stress concentration problem rich in research tradition is the so-called free-edge effect. Mainly explained by the mismatch of the elastic material properties between two adjacent dissimilar laminate layers, the free-edge effect is characterized by the concentrated occurrence of three-dimensional and singular stress fields at the free edges in the interfaces between two layers of composite laminates. In the present contribution, a survey on relevant literature from more than three decades of scientific research on free-edge effects is given. The cited references date back to 1967 and deal with approximate closed-form analyses, as well as numerical investigations by the finite element method, the finite difference method, and several other numerical techniques. The progress in research on the stress singularities which arise is also reviewed, and references on experimental investigations are cited. Related problems are also briefly addressed. The paper closes with concluding remarks and an outlook on future investigations. In all, 292 references are included.

Interaction of Circular Lining and Interior Linear Crack by Incident SH-Wave

2007 ◽  
Vol 348-349 ◽  
pp. 521-524 ◽  
Author(s):  
Hong Liang Li ◽  
Guang Cai Han ◽  
Hong Li
Keyword(s):  
Stress Concentration ◽  
Fundamental Solution ◽  
Green’S Function ◽  
Green's Function ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Elastic Space ◽  
Sh Wave ◽  
Out Of Plane ◽  
Train Of Thought

In this paper, the method of Green’s function is used to investigate the problem of dynamic stress concentration of circular lining and interior linear crack impacted by incident SH-wave. The train of thought for this problem is that: Firstly, a Green’s function is constructed for the problem, which is a fundamental solution of displacement field for an elastic space possessing a circular lining while bearing out-of-plane harmonic line source force at any point in the lining. In terms of the solution of SH-wave’s scattering by an elastic space with a circular lining, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the crack existent actually, we called this process “crack-division”. Finally, the expressions of the displacement and stress are given when the lining and the crack exist at the same time. Then, by using the expressions, some example is provided to show the effect of crack on the dynamic stress concentration around circular lining.

scholarly journals Numerical Green's Functions for Line Force and Dislocation around Multiple Cracks

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
M Denda ◽  
P Quick
Keyword(s):  
Error Analysis ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Crack Opening ◽  
Crack Tip ◽  
Function Technique ◽  
Multiple Cracks ◽  
Line Force

The numerical Green's function technique for an in¯nite isotropic domain with multiple cracks is developed. The singularities considered are the line force and dislocation. The Green's function is decomposed into the singular and the image terms. To obtain the image term we represent the crack opening displacement (COD) by the dislocation dipole distribution, embed the pr crack tip behavior, and integrate the resulting singular/hyper-singular integrals analytically. The re- sulting whole crack singular element (WCSE) consists of multiple independent crack opening modes and is strictly algebraic with the correct crack tip singular behavior but the magnitude for each mode is unknown. They are determined to give the negative of the crack surface traction induced by the singular term. Ex- tensive error analysis is performed for the line force and dislocation in an in¯nite domain with a single crack to identify the region where, when these singularities are placed, the solution achieves high accuracy. Following the guideline set by the error analysis, numerical Green's functions for a few multiple crack con¯gurations are obtained for the line force and dislocation.

Reduction of Free-Edge Stress Concentration

1985 ◽  
Author(s):  
P. R. Heyliger ◽  
J. N. Reddy
Keyword(s):  
Stress Concentration ◽  
Free Edge ◽  
Edge Stress

Green’s Functions for a Half-Space and Two Half-Spaces Bonded to a Thin Anisotropic Elastic Layer

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Thin Layer ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Elastic Material ◽  
The Body ◽  
Reference Length ◽  
Line Force ◽  
Line Dislocation ◽  
Anisotropic Elastic

The Green’s function for an anisotropic elastic half-space that is bonded to a thin elastic material of different anisotropy subject to a line force and a line dislocation is presented. Also presented is the Green’s function for two different anisotropic elastic half-spaces that are bonded to a thin elastic material of different anisotropy subject to a line force and a line dislocation in one of the half-spaces. The thickness h of the thin layer is assumed to be small compared with a reference length. Thus, instead of finding the solution in the thin layer and imposing the continuity conditions at the interface(s), we derive and apply effective boundary conditions for the interface between the layer and the body that take into account the existence of the layer.

Interaction of Multiple Circular Inclusions and a Linear Crack by SH-Wave

2010 ◽  
Vol 452-453 ◽  
pp. 677-680
Author(s):  
Hong Liang Li ◽  
Hong Li
Keyword(s):  
Stress Concentration ◽  
Green’S Function ◽  
Green's Function ◽  
Dynamic Stress ◽  
Analytic Solutions ◽  
Dynamic Stress Concentration ◽  
Elastic Space ◽  
Sh Wave ◽  
Sh Waves ◽  
Out Of Plane

Multiple circular inclusions exists widely in natural media, engineering materials and modern municipal construction, and defects are usually found around the inclusions. When composite material with multiple circular inclusions and a crack is impacted by dynamic load, the scattering field will be produced. The problem of scattering of SH waves by multiple circular inclusions and a linear crack is one of the important and interesting questions in mechanical engineering and civil engineering for the latest decade. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the method of Green’s function is used to investigate the problem of dynamic stress concentration of multiple circular inclusions and a linear crack for incident SH wave. The train of thoughts for this problem is that: Firstly, a Green’s function is constructed for the problem, which is a fundamental solution of displacement field for an elastic space possessing multiple circular inclusions while bearing out-of-plane harmonic line source force at any point: Secondly, in terms of the solution of SH-wave’s scattering by an elastic space with multiple circular inclusions, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the crack is in existent actually; Finally, the expressions of the displacement and stress are given when multiple circular inclusions and a linear crack exist at the same time. Then, by using the expression, an example is provided to show the effect of multiple circular inclusions and crack on the dynamic stress concentration.

An Improved Technique for Elastodynamic Green's Function Computation for Transversely Isotropic Solids

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Samaneh Fooladi ◽  
Tribikram Kundu
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Composite Structures ◽  
Transversely Isotropic ◽  
Computational Effort ◽  
Computational Time ◽  
Function Computation ◽  
Time Harmonic ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

Elastodynamic Green's function for anisotropic solids is required for wave propagation modeling in composites. Such modeling is needed for the interpretation of experimental results generated by ultrasonic excitation or mechanical vibration-based nondestructive evaluation tests of composite structures. For isotropic materials, the elastodynamic Green’s function can be obtained analytically. However, for anisotropic solids, numerical integration is required for the elastodynamic Green's function computation. It can be expressed as a summation of two integrals—a singular integral and a nonsingular (or regular) integral. The regular integral over the surface of a unit hemisphere needs to be evaluated numerically and is responsible for the majority of the computational time for the elastodynamic Green's function calculation. In this paper, it is shown that for transversely isotropic solids, which form a major portion of anisotropic materials, the integration domain of the regular part of the elastodynamic time-harmonic Green's function can be reduced from a hemisphere to a quarter-sphere. The analysis is performed in the frequency domain by considering time-harmonic Green's function. This improvement is then applied to a numerical example where it is shown that it nearly halves the computational time. This reduction in computational effort is important for a boundary element method and a distributed point source method whose computational efficiencies heavily depend on Green's function computational time.

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