• 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.22 no.2
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• pp.189-196
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• 2009

This paper presents the subparametric finite element model formulated by partial-linear layerwise theory for the analysis of laminate composites. The proposed model is based on refined approximations of two dimensional plane for orthotropic thick laminate plate as well as thin case. Three dimensional problem can be reduced to two dimensional case by assuming piecewise linear variation of in-plane displacement and a constant value of out-of-plane displacement across the thickness. The integrals of Legendre polynomials are chosen to define displacement fields and Gauss-Lobatto numerical integration is implemented in order to directly obtain maximum values occurred at the nodal points of each layer without other extrapolation techniques. The validity and characteristics of the proposed model have been tested by using orthotropic multilayered plate problem as compared to the values available in the published references. In this study, the convergence test has been carried out to determine the optimal layer model in terms of central deflection and stresses. Also, the distribution of displacements and stresses across the thickness has been investigated as the number of layer is increased.

• Journal of Power System Engineering
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• v.4 no.1
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• pp.68-73
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• 2000

A mixed degree finite element solutions using hierarchical elements are investigated for convergences on a 2-D simple cases. Elements are generated block by block and each block is assigned an arbitrary solution degree. The numerical study showed that a well constructed blocks can increase the convergence and accuracy of finite element solutions. Also, it has been found that for higher order elements, the convergence trends can be deteriorated for smaller mesh sizes. A procedure for a variable fixed boundary condition has been included.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.422-429
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• 2001

A two dimensional hierarchical elements are investigated for a use on the incompressible flow computation. The construction of hierarchical elements are explained through the tensor product of 1-D hierarchical functions, and a systematic treatment of essential boundary values has been developed for the degrees of freedom corresponding to higher order terms. The numerical study for the poisson problem showed that the present scheme can increase the convergence and accuracy of finite element solutions, and can be more efficient than the standard first order with many elements. Also, for Stokes and cavity flow cases, solutions from hierarchical elements showed better resolutions and future promises for higher order solutions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.9
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• pp.1209-1217
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• 2002

The use of a two dimensional hierarchical elements are investigated for the incompressible flow computation. The construction of hierarchical elements are explained by both a geometric configuration and a determination of degrees of freedom. Also a systematic treatment of essential boundary values has been developed for the degrees of freedom corresponding to higher order terms. The numerical study for the poisson problem shows that the computation with hierarchical higher order elements can increase the convergence rate and accuracy of finite element solutions in more efficient manner than the use of standard first order element. for Stokes and Cavity flow cases, a mixed version of penalty function approach has been introduced in connection with the hierarchical elements. Solutions from hierarchical elements showed better resolutions with consistent trends in both mesh shapes and the order of elements.

• Journal of Ocean Engineering and Technology
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• v.13 no.4 s.35
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• pp.1-9
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• 1999

일차원 및 이차원의 단순한 문제에 대하여 계층 요소를 사용한 혼합 차수 유한 요소해의 정확성 및 수렴성을 조사하였다. 이러한 작업은 임의의 차수를 가진 블록들을 조합하여 요소를 구성함으로서 이루어질 수 있다. 블록간의 연결성이 유지될 수 있는 블록의 구성과 요소 생성에 대하여는 코드개발과 관련하여 설명하고 있으며, 서로 다른 차수를 가진 인접 블록간의 해의 연속성에 대하여는 계층 요소의 구성과 관련하여 서술되었다. 수치적 결과는 블록의 차수를 잘 선택함으로서 유한 요소해의 수렴성과 정확성을 증가시킬 수 있음을 보여주고 있으며, 고차 요소 영역을 너무 많이 할당하여 선형 요소의 영역이 너무 적을 경우에는 경계 조건에 따라 오차가 내부로 전파됨을 보여준다. 또한 세분화된 요소에 대한 고차 보간의 경우, 해의 수렴성이 저해될 수 있음이 발견되었다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.1A
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• pp.11-18
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• 2012

This paper deals with the numerical determination of the stress intensity factors of cracked aluminum plates under the mixed mode of $K_I$ and $K_{II}$ in glass-epoxy fiber reinforced composites. For the stress intensity factors, two different models are reviewed such as VCCT and two-step extension method. The p-convergent partial layerwise model is adopted to determine the fracture parameters in terms of energy release rates and stress intensity factors. The p-convergent approach is based on the concept of subparametric element. In assumed displacement field, strain-displacement relations and 3-D constitutive equations of a layer are obtained by combination of 2-D and 1-D higher-order shape functions. In the elements, Lobatto shape functions and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature. Using the models and techniques considered, effects of composite laminate configuration according to inclined angles and adhesive properties on the performance of bonded composite patch are investigated. In addition to these, the out-of-plane bending effect has been investigated across the thickness of patch repaired laminate plates due to the change of neutral axis. The present model provides accuracy and simplicity in terms of stress intensity factors, stress distribution, number of degrees of freedom, and energy release rates as compared with previous works in literatures.