• 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 the Computational Structural Engineering Institute of Korea
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• v.20 no.5
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• pp.533-541
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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.19 no.4 s.74
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• pp.429-440
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• 2006

This paper comprises two specific objectives. The first is to examine the applicability of ordinary kriging interpolation(OK) to the p-adaptivity of the finite element method that is based on variogram modeling. The second objective Is to present the adaptive procedure by the hierarchical p-refinement in conjunction with a posteriori error estimator using the modified S.P.R. (superconvergent patch recovery) method. The ordinary kriging method that is one of weighted interpolation techniques is applied to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by experimental and theoretical variograms for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In the p-refinement, the analytical domain has to be refined automatically to obtain an acceptable level of accuracy by increasing the p-level non-uniformly or selectively. To verify the performance of the modified S.P.R. method, the new error estimator based on limit value has been proposed. The validity of the proposed approach has been tested with the help of some benchmark problems of linear elastic fracture mechanics such as a centrally cracked panel, a single edged crack, and a double edged crack.

• Journal of Korean Association for Spatial Structures
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• v.8 no.4
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• pp.81-90
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• 2008

This paper presents a finite element formulation for the three-dimensional hierarchical solid element using Integrals of Legendre polynomials. The proposed hexahedral solid element is composed of four different modes including vertex, edge, face, and internal mode, respectively. The eigenvalue and patch test have been carried out to confirm the zero-energy mode and constant strain condition. In addition to these, a posteriori error estimation has been studied for the p-adaptive finite element analysis that is based on a smoothing technique to compute a post-processed solution from the finite element solution. The uniform p-refinement and non-uniform p-refinement are compared in terms of convergence rate as the number of degree of freedom is increased. The simple cantilever beam is tested to show the performance of the proposed solid element.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.4A
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• pp.677-687
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• 2006

Kriging interpolation is one of the generally used interpolation techniques in Geostatistics field. This technique includes the experimental and theoretical variograms and the formulation of kriging interpolation. In contrast to the conventional least square method for stress recovery, kriging interpolation is based on the weighted least square method to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by variogram modeling for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In addition to this, the p-level is increased non-uniformly or selectively through a posteriori error estimation based on SPR (superconvergent patch recovery) technique, proposed by Zienkiewicz and Zhu, by auto mesh p-refinement. The cut-out plate problem under tension has been tested to validate this approach. It also provides validity of kriging interpolation through comparing to existing least square method.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.151-160
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• 1993

This paper is concerned with formulations of the hierarchical $C^{\circ}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element based on Integrals of Legendre shape functions is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method are proposed to verify the superior convergence and algorithmic efficiency with the help of the simply supported L-shaped plate problems.

• Journal of Life Science
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• v.17 no.3 s.83
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• pp.368-374
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• 2007

The purpose of this study was to investigate the effects of different type of triglycerides (MCT & LCT) on weight, survival time, energy substrate (FFA, TG, pyruvate, lactate), insulin and lipase in the trained rats. Fifty-four Sprague-Dawley rats were divided into 3 groups: control group (CG, n=18), MCT supplement group (MG, n=18), and LCT supplement group (LG, n=18). They also were divided into 3 periods: trained resting (R, n=6) and trained & exercise load (E, n=6), and survival time test was performed to know the supplemented effects. Body weight of all animals was checked every week, MCT group and LCT group received supplementary MCT and LCT orally and preliminary swimming training for 6 days before the start of main experiment. All animals received 15-minute swimming training 5 times during first week of experiment, and swimming training time was increased 15 minutes every week until it reached 90 minutes at last 9th week. After last swimming training, animals were fasted for 12 hours and blood samples were taken from abdominal aorta in the Department of Animal Medicine at the D university Animal Center. Among the CGE, MGE, and LGE groups, the MGE had the greatest increase in physical performance time. In the FFA levels, there was significant differences(p<.05) in CG, MG and LG groups, and also there was major difference of FFA levels in the MG and LG. In the lipase levels, there was signifi.ant differences (p<.05) in CG, MG and LG groups. MG was the greatest than the other groups. In the insulin hormone levels, there was the great differences (p<.05) in LG compare to CG groups, whereas there was no significant difference in the CG and MG. In conclusion, these results suggest that regular prolonged physical training with MCT supplementation, improves exercise performance time through the increase of energy substrate utilization, lipase activity and FFA levels, irrespective of insulin hormone responses.

• Journal of Chest Surgery
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• v.32 no.7
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• pp.621-627
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• 1999

Background: Sixty five cases with congenitally corrected transposition of the great arteries (CCTGA) indicated for biventricular repair were operated on between 1984 and september 1998. Comparison between the results of the conventional(classic) connection(LV-PA) and the anatomic repair was done. Material and Method: Retrospective review was carried out based on the medical records of the patients. Operative procedures, complications and the long-term results accoding to the combining anomalies were analysed. Result: Mean age was 5.5$\pm$4.8 years(range, 2 months to 18years). Thirty nine were male and 26 were female. Situs solitus {S,L,L} was in 53 and situs inversus{I,D,D} in 12. There was no left ventricular outflow tract obstruction(LVOTO) in 13(20%) cases. The LVOTO was resulted from pulmonary stenosis(PS) in 26(40%)patients and from pulmonary atresia(PA) in 26(40%) patients. Twenty-five(38.5%) patients had tricuspid valve regurgitation(TR) greater than the mild degree that was present preoperatively. Twenty two patients previously underwent 24 systemic- pulmonary shunts previously. In the 13 patients without LVOTO, 7 simple closure of VSD or ASD, 3 tricuspid valve replacements(TVR), and 3 anatomic corrections(3 double switch operations: 1 Senning+ Rastelli, 1 Senning+REV-type, and 1 Senning+Arterial switch opera tion) were performed. As to the 26 patients with CCTGA+VSD or ASD+LVOTO(PS), 24 classic repairs and 2 double switch operations(1 Senning+Rastelli, 1 Mustard+REV-type) were done. In the 26 cases with CCTGA+VSD+LVOTO(PA), 19 classic repairs(18 Rastelli, 1 REV-type), and 7 double switch operations(7 Senning+Rastelli) were done. The degree of tricuspid regurgitation increased during the follow-up periods from 1.3$\pm$1.4 to 2.2$\pm$1.0 in the classic repair group(p<0.05), but not in the double switch group. Two patients had complete AV block preoperatively, and additional 7(10.8%) had newly developed complete AV block after the operation. Other complications were recurrent LVOTO(10), thromboembolism(4), persistent chest tube drainage over 2 weeks(4), chylothorax(3), bleeding(3), acute renal failure(2), and mediastinitis(2). Mean follow-up was 54$\pm$49 months(0-177 months). Thirteen patients died after the operation(operative mortality rate: 20.0%(13/65)), and there were 3 additional deaths during the follow up period(overall mortality: 24.6%(16/65)). The operative mortality in patients underwent anatomic repair was 33.3%(4/12). The actuarial survival rates at 1, 5, and 10 years were 75.0$\pm$5.6%, 75.0$\pm$5.6%, and 69.2$\pm$7.6%. Common causes of death were low cardiac output syndrome(8) and heart failure from TR(5). Conclusion: Although our study could not demonstrate the superiority of each classic or anatomic repair, we found that the anatomic repair has a merit of preventing the deterioration of tricuspid valve regurgitations. Meticulous selection of the patients and longer follow-up terms are mandatory to establish the selective advantages of both strategies.