• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.1
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• pp.206-214
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• 1998

When a crack meets bimaterial interface stress singularity depends on the elastic constants of the adjacent materials. In the present study we are going to describe the finite element formulation for problems with a crack to be embedded in the stiffer material$({\mu}_2/{\mu}_1)$. The cubic isoparametric singular element, represented by adequately shifting the mid-side nodes adjacent to the crack tip is constructed to enclose the crack tip. An alternative method to obtain the optimal position of the mid-side nodes of cubic isoparametric elements is presented. In addition, a proper definition for the stress intensity factors of a crack normal to bimaterial interface is provided. It is based upon near a tip displacement solutions. Models for numerical analysis are two dimensional elastic bodies with a through crack under plain strain. The results obtained are compared with the previous solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2398-2406
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• 1993

Abdi's numerical method(ref.13) for representing a stress singularity by shifting the mid-side nodes of isoparametric elements is reviewed. A simple technique to obtain the optimal position of the mid-side nodes in quadratic isoparametric finite element is presented. From this technique we can directly obtain the position of the side-nodes adjacent to the crack tip. It is also observed that the present technique provides good accuracy for the expression of the opening displacement and the determination of the mid-side nodes for more wide range of material properties than that obtained by Abdicant the finite element method is applied to determine stress intensity factors for pressurized crack perpendicular to and terminating at the interface of two bonded dissimilar materials. A proper definition for stress intensity factors of a crack perpendicular to bimaterial interface is provided. It is based upon a near-tip displacement solutions on the crack surface for interface crack between two dissimilar materials. Numerical testing is carried out with the eight-node and six-node elements. The results obtained are compared with the previous solutions.

• Structural Engineering and Mechanics
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• v.43 no.3
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• pp.321-336
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• 2012

As an improvement on the isoparametric element method, the derivation presented in this paper is close to that done by Wang (1990) for the 2-D finite element. We extend this idea to solve 3-D crack problems in this paper. A new displacement modelling is constructed with local solutions of three-dimensional cracks and a quasi-compatible isoparametric element for three-dimensional fracture mechanics analysis is presented. The stress intensity factors can be solved directly by means of the present method without any post-processing. A new method for calculating the stress intensity factors of three-dimensional cracks with complex geometries and loads is obtained. Numerical examples are given to demonstrate the validity of the present method. The accuracy of the results obtained by the proposed element is demonstrated by solving several crack problems. The results illustrate that this method not only saves much calculating time but also increases the accuracy of solutions. Because this quasi-compatible finite element of 3-D cracks contains any singularities and easily meets the requirement of compatibility, it can be easily implemented and incorporated into existing finite element codes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.5
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• pp.904-913
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• 2002

In this paper, the dynamic stress intensity factors of fracture mechanics are numerically computed in time domain using the FEM. For which the finite element formulations are derived applying the Galerkin method to the equations of motion in convolution integral as has been presented in the previous paper. To assure the strain fields of r$^{-1}$ 2/ singularity near the crack tip, the triangular quarter-point singular elements are imbedded in the finite element mesh discretized by the isoparametric quadratic quadrilateral elements. Two-dimensional problems of the elastodynamic fracture mechanics under the impact load are solved and compared with the existing numerical and analytical solutions, being shown that numerical results of good accuracy are obtained by the presented method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.59-65
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• 2004

The stress intensity factors have been widely used in numerical studies of crack growth direction. However in many cases, omissive terms of the series expansion are quantitatively significant, so we consider the computation of such terms. For this purpose, we used the finite element method with isoparametric quadratic quarter-point elements. For examples, infinite square plate with a slant crack subjected to a uniaxial load is analyzed. The numerical analysis were performed for the wide range of crack tip element lengths and inclined angles. The numerical results obtained are compared with the theoretical solutions. Also they were accurate and efficient.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.234-239
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• 2001

The stress intensity factors have been widely used in numerical studies of crack growth direction. However in many cases, omissive terms of the series expansion are quantitatively significant, so we consider the computation of such terms. For this purpose, we used the finite element method with isometric quadratic quarter-point elements. For examples, infinite square plate with a slant crack subjected to a uniaxial load is analyzed. The numerical analysis were performed for the wide range of crack tip element lengths and inclined angles. The numerical results obtained are compared with the theoretical solutions. Also they were accurate and efficient.

• Structural Engineering and Mechanics
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• v.2 no.3
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• pp.227-244
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• 1994

The purpose of this investigation is to propose a numerical simulation method of the crack propagation behavior in 3-dimensionl elastic body. The simulation method is based on the displacement-type finite element method, and the linear fracture theory is introduced. The results from the proposed method are compared with those from the structural experiments, and the good coincidences between them are shown in this paper. At the same time, 2-dimensional analysis is also done, and the results are compared with those obtained from 3-dimensional analysis and the structural experiments.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.787-797
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• 1986

An implicit approach is employed to obtain a general boundary integral formulation of axisymmetric elastic problems in terms of a pair of singular integral equations. The corresponding kernel functions from the solutions of Navier's equation are derived by applying a three dimensional integral and a direct axisymmetrical approach. A numerical discretization schem including the evaluation of Cauchy principal values of the singular integral is described. Finally the typical axisymmetric elastic models are analyzed, i.e. the hollow sphere, the constant thickness and the V-notched round bar.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.529-534
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• 1998

To find out an adequate failure criterion in two-dimensional linear elastic crack problems, finite element programs, SED, which determine stress intensity factors $K_I, K_{II}$, crack angle and peak load by the minimum strain energy density failure criterion were developed. In this program, the conventional quadratic isoparametric elements were used in all regions except the crack tip zone where triangular singular elements with 6 nodes were used. The results of SED were compared with the results of those which followed by the maximum circumferential tensile stress criteria and those by the maximum energy release rate criteria and those by Jenq and Shah`s experiments of the same geometry and material properties. The maximum energy release rate criteria were better close to those of the Jenq and Shah`s experiments than the maximum circumferential tensile stress criteria and the minimum strain energy density criteria.