• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.3
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• pp.331-340
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• 2010

The basic theory and application of new adaptive finite element algorithm have been proposed in this study including the adaptive hp-refinement strategy, and the effective method for constructing hp-approximation. The hp-adaptive finite element concept needs the integrals of Legendre shape function, nonuniform p-distribution, and suitable constraint of continuity in conjunction with irregular node connection. The continuity of hp-adaptive mesh is an important problem at the common boundary of element interface. To solve this problem, the constraint of continuity has been enforced at the common boundary using the connectivity mapping matrix. The effective method for constructing of the proposed algorithm has been developed by using hierarchical nature of the integrals of Legendre shape function. To verify the proposed algorithm, the problem of simple cantilever beam has been solved by the conventional h-refinement and p-refinement as well as the proposed hp-refinement. The result obtained by hp-refinement approach shows more rapid convergence rate than those by h-refinement and p-refinement schemes. It it noted that the proposed algorithm may be implemented efficiently in practice.

• Journal of Korea Foundry Society
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• v.24 no.2
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• pp.85-93
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• 2004

Mechanical property of hypereutectic Al-Si alloy is changed according to size and distribution of primary Si. Consequently, the study on the refinement for primary Si is progressed for a long time. But such effect of refinement comes out fading phenomena with the lapse of time. Therefore, this study investigated the optimum condition of primary Si refinement for hypereutectic Al-Si alloy. And we observed various primary Si size with P's fading phenomena. The experiment results were as follows. For experiment of primary Si refinement, we made hypereutectic Al-Si alloy with various amounts of P addition. As a result of experiment, we obtained the fine microstructure at 0.01wt.%P. And the optimum condition of P addition, for preventing from growth of primary Si by P fading, is estimated 0.1wt.%P.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.481-486
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• 2007

The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.1
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• pp.55-60
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• 2011

In the present work, isogeometric analysis in linear elasticity problem is conducted using the basis functions from NURBS. The objectives of isogeometric analysis introduced is to integrate both geometric modeling(CAD) and computational analysis(CAE), and this can be accomplished from direct usage of geometric modeling by NURBS as the computational mesh. The merit of the isogeometry analysis is that NURBS surface are able to represent exact geometry from the control points and knot vectors, and also subsequent refinement is relatively simple relatively. In order to verify the computer codes developed in this study, it has been applied to two structural models of which geometry are simple ; 1) circular cylinder subjected to the constant internal pressure loading, 2) square plate with circular hole at center subjected to uniform tension. The exact solutions of these two models are available. Convergence of the approximate solutions by the present code for the isogeometry analysis are investigated by mesh refinement with inserting knots (h-refinement) and by mesh refinement with order elevation of the basis functions (p-refinement).

• Journal of Korean Port Research
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• v.10 no.2
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• pp.61-68
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• 1996

The main problems in structural analysis by Finite Eelement Method are difficulty in making data file and error estimation. For decreasing these problems' pays. have been suggesting the adaptive mesh refinement and error estimation method. Posteriory error estimation methods suggested by Jang[1], Babuska[2,3], Ohtsubo[8,9], and this paper. Comparing these methods and examine their properties. According this paper, In the problem supposed having singularity, the method suggested by this paper is good, But the problem supposed having no singularity, the method suggested by Jang[1] is good. For decreasing the effect of initial mesh in p-refinement, make application h-refinement at first and apply p-refinement, and confine polynomial's degree to two, for making program simply by plural mesh models are not needed.

• Journal of Korea Foundry Society
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• v.17 no.4
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• pp.347-355
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• 1997

It is well known that the coarse primary Si in hypereutectic Al-Si alloys deteriorate castability, machinability, and mechanical properties. So, many treatment has been tried to refine the primary Si increasing cooling rate and adding refinement agent. Therefore. the purpose of our work was the observation of the effect on the refinement of primary Si and the analysis of the trend to apply to the casting process by changing the amount of P addition and the cooling rate while fixing the temperature at $750^{\circ}C$ of P addition and the type of AlCuP. In the condition of amount of P addition was fixed, primary Si was finer as cooling rate increased but in case of cooling rate was fixed, the effect of refinement was resisted as incersed the amount of P addition. At a relatively slow cooling rate of $22^{\circ}C/sec$, refinement was governed by the amount of P addition rather than cooling rate. At elevated cooling rate of $51^{\circ}C/sec$ and $99^{\circ}C/sec$, the undercooling due to faster cooling rate promoted nucleation of primary Si rather than P addition more significantly.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.495-502
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• 2013

Let $\mathcal{T}^{(p)}_n$ be the set of p-ary labeled trees on $\{1,2,{\ldots},n\}$. A maximal decreasing subtree of an p-ary labeled tree is defined by the maximal p-ary subtree from the root with all edges being decreasing. In this paper, we study a new refinement $\mathcal{T}^{(p)}_{n,k}$ of $\mathcal{T}^{(p)}_n$, which is the set of p-ary labeled trees whose maximal decreasing subtree has k vertices.

• The Korean Journal of Ceramics
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• v.6 no.3
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• pp.240-244
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• 2000

The three-dimensional orientation distribution function of a conical shaped tungsten liner prepared by the thermo-mechanical forming process was analyzed by 1.525$\AA$ neutrons to carry out the Rietveld refinement. The pole figure data of three reflections, (110)(220) and (211) were measured. The orientation distribution functions for the normal and radial directions were calculated by the WIMV method. The inverse pole figures of the normal and radial directions were obtained from their orientation distribution functions. The Rietveld refinement was performed with the RIETAN program that was slightly modified for the description of preferred orientation effect. We could successfully do the Rietveld refinement of the strongly textured tungsten liner by applying the pole density of each reflection obtained from the inverse pole figure to the calculated diffraction pattern. The correction method of preferred orientation effect based on the inverse pole figures showed a good improvement over the semi-empirical texture correction based on the direct usage of simple empirical functions.

• Journal of Korea Foundry Society
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• v.15 no.4
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• pp.416-421
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• 1995

Recently Al-Cu-P alloys are used to refine primary Si of hypereutectic Al-Si alloys. Because it has inside AlP compound that acts as nucleation site in the melt, Al-Cu-P alloy has good refinement effect in lower holding temperature and after shoter holding times. In this study Al-Cu-P refinement agent was made by mechanical alloying method. When Al-13.5wt%Cu-1.5wt%P was alloyed mechanically for 30hr in Ar atmosphere by high energy ball mill, it had the refinement effect that showed primary Si size of about $30{\mu}m$ in Al-20wt%Si at $760^{\circ}C$, treated for 15min.

• Journal of Korea Foundry Society
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• v.13 no.2
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• pp.168-174
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• 1993

It has been known that the grain refinement of Cu base alloys greatly improved mechanical properties, castability, workability and hot shortness resistance etc. In this study CuZr50, CuP7, CuFe7, CuMg10 binary alloys were added as grain refiners in CuZn36 alloy. The alloys melted in vacuum and controlled in mixed gas conditions and casted at $1050^{\circ}C$. Zr-P-X compound has significantly grain refined but oxygen has been found detrimental to grain refinement. In the case of Zr /B ratio below 4, B acted as grain growth element in this alloy.