• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.4 s.175
• /
• pp.982-990
• /
• 2000

The finite element alternating method is extended further for general three dimensional cracks in an isotropic body subjected to the mode I loading. The required analytical solution for a dime dimensional crack in an infinite isotropic body is obtained by solving the integral equations. In order to remove the high singularity in integration, the technique suggested by Keat et al. was used. With the proposed method several example problems are solved in order to check the accuracy and efficiency of the method.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.22 no.2
• /
• pp.365-371
• /
• 1998

In the present study, we attempted to add the incompatible functions as additional variable terms to the conventional u-p formulation. It is derived from the four-field generalized variational principle that encompasses velocity, pressure, velocity strains and stress fields as independent interpolated variables. As a severe test of the present formulation, we have investigated the driven cavity with the corner velocity singularity like leaky lid. Through the test, the present element performs very well without unstable oscillation of pressure distribution.

• Structural Engineering and Mechanics
• /
• v.26 no.5
• /
• pp.591-615
• /
• 2007

An improvement is introduced to solve the plane problems of linear elasticity by reciprocal theorem for orthotropic materials. This method gives an integral equation with complex kernels which will be solved numerically. An artificial boundary is defined to eliminate the singularities and also an algorithm is introduced to calculate multi-valued complex functions which belonged to the kernels of the integral equation. The chosen sample problem is a plate, having a circular or elliptical hole, stretched by the forces parallel to one of the principal directions of the material. Results are compatible with the solutions given by Lekhnitskii for an infinite plane. Five different orthotropic materials are considered. Stress distributions have been calculated inside and on the boundary. There is no boundary layer effect. For comparison, some sample problems are also solved by finite element method and to check the accuracy of the presented method, two sample problems are also solved for infinite plate.

• Proceedings of the KSME Conference
• /
• 2001.11a
• /
• pp.384-388
• /
• 2001

The higher order singularities[1] are systematically examined, and discussed are their complementarity relation with the nonsingular eigenfunctions and their relations to the configurational forces like J-integral and M-integral. By use of the so-called two state conservation laws(Im and Kim[2]) or interaction energy, originally proposed by Eshelby[3] and later treated by Chen and Shield[4], the intensities of the higher order singularities are calculated, and their roles in elasticplastic fracture are investigated. Numerical examples are presented for illustration.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.357-364
• /
• 2006

The meshfree method is extended by the local partition of unity method to model the cohesive cracks in two dimensional continuum The shape function of a particle whose domain of influence is completely cut by a crack is enriched by the step enrichment function. If the domain of influence contains a crack tip inside, it is enriched by the branch enrichment function without the stress singularity. It is found that this method is more accurate and converges faster than the meshless methods for LEFM cracks based on the visibility concept Several staic and dynamic examples are solved to verify the method.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.16 no.12S
• /
• pp.1165-1174
• /
• 2003

The responses of hypothetical silicon nanotubes under torsion have been investigated using an atomistic simulation based on the Tersoff potential. A torque, proportional to the deformation within Hooke's law, resulted in the ribbon-like flattened shapes and eventually led to a breaking of hypothetical silicon nanotubes. Each shape change of hypothetical silicon nanotubcs corresponded to an abrupt energy change and a singularity in the strain energy curve as a function of the external tangential force, torque, or twisted angle. The dynamics o silicon nanotubes under torsion can be modelled in the continuum elasticity theory.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.25 no.4
• /
• pp.39-46
• /
• 1988

The purpose of this paper is to apply the boundary element method to predict the crack growth path. The quarter point element with traction singularity at the crack tip is applied to compact tension type specimens and two inclined slit problems under compression load. The maximum stress criterion which was originally derived for the crack initiation is extended to the analysis of the crack propagation. The predicted crack paths with 1/4 crack growth increment of initial crack length agree quite well with experimental results. It is found that the computed crack path of the boundary element analysis is not mainly affected by the crack increment length.

• Computational Structural Engineering
• /
• v.2 no.4
• /
• pp.15-20
• /
• 1989

이글에서는 2가지 예제를 통해 h-version과 p-version의 비교를 살펴보면서 p-version 해석이 h-version에 비해 상대적으로 많은 장점들을 가지고 있으며, 신뢰도, 정확도, 효율성, 경제성, 용장성 등 측면에서 우월함을 증명해 보였다. 특히 응력집중(stress concentration)이 일어나는 crack-tips, cut-outs, reentrant corners, presence of stiffners, mixed boundary conditions 등 많은 특이성(singularity) 문제에 더욱 적합함을 본 예제 외의 발표된 많은 논문들을 통해 알 수 있으며, 모델링의 단순성에 기인하여 사용이 매우 쉽다는 것도 무엇보다 큰 이점이라 하겠다. p-version은 h-version의 비효율성을 차수 p를 1, 2 또는 3으로 줄인 후 이 값을 고정시키고 다시 요소분할을 통해 진해(true solution)에 접근시키는 방식을 위하면 다시 종래의 h-version으로 환원되는 호환성을 갖고 있다는 것이다. 고로 구조해석에서 h-p version이 가장 이상적인 유한요소해석 방법이라 할 수 있겠는데, 다시 말하면 균열문제의 경우 균열선단(crack-tip)에서는 p-level을 높이고 (p=8, 9 or 10) 비교적 응력집중이 낮은 영역에서는 p-level을 낮춤으로써 (p=3, 4 or 5) 그 효율성을 극대화할 수 있겠다.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.551-556
• /
• 2004

We propose a 2D 'crack' element for the simulation of propagating crack with minimal remeshing. A regular finite element containing the crack tip is replaced with this novel crack element, while the elements which the crack has passed are split into two transition elements. Singular elements can easily be implemented into this crack element to represent the crack-tip singularity without enrichment. Both crack element and transition element proposed in our formulation are mapped from corresponding master elements which are commonly built using the moving least-square (MLS) approximation only in the natural coordinate. In numerical examples, the accuracy of stress intensity factor $K_I$ is demonstrated and the crack propagation in a plate is simulated.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 1999.04a
• /
• pp.256-266
• /
• 1999

The angled crack which is the simplest and representative case in the mixed mode crack analysis has stimulated the interests of many investigators during past 20 years. In this study the conventional quadratic isoparametric elements were used in all regions except the crack tip zone where triangular singularity elements with 6 nodes were used. The stress intensity factor of K1 and KII were determined respectively by the displacement correlation method. The finite element analysis program in this paper based on maximum energy release rate criteria and the results obtaiend by this program were compared with those calculated from the maximum circumferential tensile criteria and those by Jenq and Shah's experiments of the same geometry and material properties