Analysis of Planar Crack Coalescence by Mesh-Free Body Force Method

2017 ◽  
Vol 754 ◽  
pp. 161-164
Author(s):  
Yohei Sonobe ◽  
Takuichiro Ino ◽  
Akihide Saimoto ◽  
Md. Abdul Hasib ◽  
Atsuhiro Koyama ◽  
...  
Keyword(s):  
Weight Function ◽  
Crack Front ◽  
Body Force ◽  
Nodal Point ◽  
Crack Face ◽  
Moving Least Square ◽  
Force Method ◽  
Body Force Method ◽  
Nodal Points ◽  
Crack Problems

In a standard body force method analysis, a mesh division is required to define the boundary of a problem and to solve a governing equation using discretization procedure. However, in the present study, a moving least square strategy is introduced to define a weight function for the density of body force doublet and therefore a crack analysis is carried out without providing a standard mesh-division. Hence, the standard crack face elements are not required at all. A variety of 3D crack problems can be analyzed simply by providing a data that only de nes a crack front. Besides the nodal points for crack front, several internal nodes are generated on the crack face to represent a distribution of unknown function. At the internal nodes, an unknown variable is assigned which uniquely de ne a distribution of the relative crack face displacement. In the present approach, a crack problem is formulated as a singular integral equation whose unknown is a value of the weight function at the internal nodal points. A crack growth can be simulated directly by changing the shape of crack front, by means of adding a new nodal point in the vicinity of the current crack front. In the present paper, the proposed method is used to simulate a coalescence of interacting planar cracks.

Influence of Small Cavity Existing in the Vicinity of 3D Crack Front

2015 ◽  
Vol 665 ◽  
pp. 5-8
Author(s):  
Md. Abdul Hasib ◽  
Akihide Saimoto
Keyword(s):  
Weight Function ◽  
Crack Front ◽  
Body Force ◽  
Numerical Results ◽  
Current Analysis ◽  
Force Method ◽  
Body Force Method ◽  
Planar Crack ◽  
Triangular Elements ◽  
Good Agreement

In this paper, the interference between arbitrary shaped 3D planar crack and cavity existing in the vicinity of the crack front is evaluated. It is assumed that the treated region is unbounded and subjected to uniaxial tension at infinity. The interaction between crack and cavity is treated by body force method. The surface of the crack and cavity is modeled by number of small triangular elements and the density of body force and weight function of the force doublet is assumed at a constant on each triangle. Numerical stress analyses are examined by changing the radius of cavity and the distance between the cavity and crack front systematically. Numerical results are presented for the stresses along the centerline between cavity and crack. To validate the current analysis, numerical results are compared with the results in the literature and found good agreement.

D-24 Analysis of two-dimensional crack problems by mesh-free Body Force Method

2016 ◽  
Vol 2016.69 (0) ◽  
pp. 171-172
Author(s):  
Ryosuke HONDA ◽  
Akihide SAIMOTO ◽  
Yohei SONOBE ◽  
Konatsu TOMINAGA
Keyword(s):  
Body Force ◽  
Two Dimensional ◽  
Force Method ◽  
Body Force Method ◽  
Mesh Free ◽  
Crack Problems ◽  
Free Body

scholarly journals Analysis of 3D Planar Crack Problems by Body Force Method

2014 ◽  
Vol 627 ◽  
pp. 5-8
Author(s):  
A. Hasib ◽  
Akihide Saimoto
Keyword(s):  
Integral Equation ◽  
Body Force ◽  
Crack Problem ◽  
Boundary Integral ◽  
Simultaneous Equations ◽  
Force Method ◽  
Body Force Method ◽  
Crack Problems ◽  
Planar Crack ◽  
Triangular Elements

Derivation of the integral equation for general 3D crack problems was examined based on the theory of body force method. In the present analysis, stress intensity factors (SIFs) along a front of arbitrary shaped 3D planar crack are obtained directly only by solving simultaneous equations expressing a boundary condition. The crack surface is discretized using number of triangular elements and the variation of the force doublet embedded in each triangle is assumed at constant. The derived boundary integral equation was transformed into a set of simultaneous equations and was solved computationally. In order to improve the accuracy of the numerically examined boundary integral, a polar transformation scheme combined with Tayler expansion of the fundamental solutions is introduced. Not only a single crack problem but also an interference among coplanar cracks can be calculated using the unique program developed in this research. It was verified that as the number of triangular elements increases, the evaluated SIF converges to the reference solution.

An Iterative Algorithm of Hypersingular Integral Equations for Crack Problems

2008 ◽  
Vol 385-387 ◽  
pp. 793-796
Author(s):  
Kazuhiro Oda ◽  
Naoaki Noda
Keyword(s):  
Integral Equations ◽  
Body Force ◽  
The Body ◽  
Algebraic Equations ◽  
Hypersingular Integral ◽  
Force Method ◽  
Hypersingular Integral Equations ◽  
Body Force Method ◽  
Linear Algebraic Equations ◽  
Crack Problems

Crack problems are reducible to singular integral equations with strongly singular kernels by means of the body force method. In the ordinary method, the integral equations are reduced to a system of linear algebraic equations. In this paper, an iterative method for the numerical solution of the hypersingular integral equations of the body force method is proposed. This method is based on the Gauss- Chebyshev numerical integration rule and is very simple to program. The solution is achieved without solving the system of linear algebraic equations. The proposed method is applied to some plane elasticity crack problems and is seen to give convergent results.

The solution of the dynamic field of the Haskell fault model reconsidered

1982 ◽  
Vol 72 (4) ◽  
pp. 1069-1083
Author(s):  
R. D. List
Keyword(s):  
Half Space ◽  
Displacement Field ◽  
Body Force ◽  
Fault Model ◽  
Earthquake Source ◽  
Infinite Space ◽  
Force Method ◽  
Body Force Method ◽  
Rupture Speed ◽  
Seismic Dislocations

abstract A method of obtaining the displacement field of the Haskell model of an earthquake source, based on the well-known equivalence of seismic dislocations and body force, is described. It is shown that the solution of Madariaga (1978) can be generalized and that the two methods are equivalent for the problem of a rectangular dislocation expanding on a plane in an infinite space with a variable rupture speed and variable slip in the direction of rupture. One of the advantages of the equivalent body force method is that it can be used to readily obtain the transformed solution to the Haskell model in a half-space for a rectangular dislocation, expanding with variable rupture speed and variable slip.

scholarly journals Accurate Solutions of Stress Intensity Factors of Standard Fracture Test Specimens

2010 ◽  
Vol 452-453 ◽  
pp. 405-408 ◽  
Author(s):  
Akihide Saimoto ◽  
Fumitaka Motomura ◽  
Hironobu Nisitani
Keyword(s):  
Stress Intensity ◽  
Body Force ◽  
General Purpose ◽  
Two Dimensional ◽  
Fracture Test ◽  
Intensity Factors ◽  
Force Method ◽  
Body Force Method ◽  
Standard Specimens ◽  
Significant Figures

Practically exact solutions of stress intensity factor for several two-dimensional standard specimens were calculated and shown in numeric tables. The solutions were confirmed to converge until 6 significant figures through a systematical computation of discretization analysis. The convergence analyses were carried out by using a general purpose program based on a body force method.

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