• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.555-559
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• 2009

난류응력은 순간속도성분을 시간평균성분과 편차성분의 합으로 보고 Navier-Stokes 방정식으로부터 Reynolds 방정식을 유도할 때 나타나게 된다. Reynolds 방정식으로부터 수심 적분된 천수방정식을 유도하는 과정에서 시간 평균된 유속성분을 수심 적분된 유속성분과 편차성분의 합으로 본다면, 분산응력 (dispersion stress)이라고 하는 추가적인 새로운 항이 잔류하게 된다. 점성응력, 난류응력, 그리고 분산응력을 통칭하여 유효응력 (effective stress)이라고 한다. 일반적으로 수심에 비해 수로 폭이 넓은 개수로에서는 유효응력이 흐름특성의 수치 근사해에 큰 영향을 미치지 못한다고 가정하여 2차원 수심적분 모형에서 유효응력을 생략하기도 한다. 또한 유효응력을 적용하더라도, 점성응력이 난류응력에 비해 무시할 만큼 작다고 가정하여 난류응력만을 적용하며, 분산응력은 무시된다. 하지만 만곡부에서는 원심력과 편수위로 인한 횡방향 압력의 불균형이 발생하기 때문에, 만곡부의 이차류가 발생되며, 유속의 연직방향 분포도 일정하지 않게 된다. 따라서 본 연구의 목적은 만곡부의 이차류 특성을 수심적분 2차원 모형에 반영하기 위해 분산응력을 고려한 모형의 개발 및 검증이다. 불규칙한 모의영역을 원활히 나타낼 수 있도록 곡선좌표계를 사용하는 여타 모형들과 달리 유한유소법을 이용하여 수치해를 구하며, 따라서 x, y 좌표축을 사용하는 데카르트 좌표계를 사용하여 지배방정식을 나타낸다. 분산응력의 유 무에 따른 수치결과를 Rozovskii의 $180^{\circ}$ 만곡수로 실내실험 자료와 비교하여 개발 모형을 검증한다.

• The Journal of Korean Academy of Prosthodontics
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• v.48 no.2
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• pp.111-121
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• 2010

Purpose: This 3D-FEA study was performed to investigate the influence of marginal bone loss pattern around the implant to the stress distribution. Material and methods: From the right second premolar to the right second molar of the mandible was modeled according to the CT data of a dentate patient. Teeth were removed and an implant ($\Phi\;4.0{\times}10.0mm$) was placed in the first molar area. Twelve bone models were created; Studied bone loss conditions were horizontal bone loss and vertical bone loss, assumed bone loss patterns during biologic width formation, and pathologic vertical bone loss with or without cortification. Axial, buccolingual, and oblique force was applied independently to the center of the implant crown. The Maximum von Mises stress value and stress contour was observed and von Mises stresses at the measuring points were recorded. Results: The stress distribution patterns were similar in the non-resorption and horizontal resorption models, but differed from those in the vertical resorption models. Models assuming biologic width formation showed altered stress distribution, and weak bone to implant at the implant neck area seams accelerates stress generation. In case of vertical bone resorption, contact of cortical bone to the implant may positively affect the stress distribution.

• The Journal of Korean Academy of Prosthodontics
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• v.36 no.1
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• pp.1-17
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• 1998

두개의 임플랜트로 지지되는 overdenture를 이용한 하악무치악환자의 치료법은 경제적이면서, 실용적인 치료로 인정을 받고 있다. 하지만 해부학적인 조건으로 임플랜트를 설측 혹은 후방에 식립해야 되는 경우에는 일반적인 bar설계는 bar가 구강저 상방을 지나게 되어 혀운동, 발음, 위생관리 등에 많은 문제점을 부여한다. 이에 대한 해결방법으로 전방부 치조제 상에 보철물의 회전을 허용하는 angular bar를 설계할 수 있다. 하지만 이 설계는 임플랜트에 불리한 moment를 유발한다. 그럼에도 불구하고 뛰어난 유지력과 지지능력, 경제적인 면 때문에 angular bar는 임상에서 많이 사용되고 있다. 이에 본 연구는 angular bar의 전방 cantilever양을 달리하여 임플랜트 및 주변조직에 미치는 영향을 삼차원 유한요소분석법을 통해서 알아보고자 하였다. 이공사이의 하악골을 단순화시킨 준하악골모형에 직경 3.75mm인 브로네마르크 임플랜트 2개를 길이가 13,15mm인 경우로 설정하여 제 1소구치 부위에 식립하였다. 두 임플랜트를 연결하는 bar는 전방부 cantilever양을 0-5mm, 1mm씩 하여 6가지 경우를 가정하고 제작하였다. 각각 bar 중앙부에 수직압 (90도) 35N, 경사압(120도) 70N, 수평압(0도) 10N을 가하였으며 이때 나타나는 응력 분산형태와 임플랜트의 골유착에 불리하게 작용하는 최대주응력(인장력)과 변위량을 살펴보았다. 연구결과 다음과 같은 결론을 얻었다. 1. Cantilever양이 증가할수록 주변피질골과 임플랜트로 응력이 집중되었으며 상부 보철물의 변위량도 커졌다. 2. Cantilever양에 대한 수평압의 영향은 크지 않았으며 임플랜트 길이가 긴 것이 변위량과 응력이 작았다. 3. 경사압에 대한 응력의 변화는 cantilever양의 증가에 따라 급격히 증가하는 양상을 띠었으며 임플랜트길이가 응력 및 변위의 양에 미치는 영향은 없었다. 4. 수직압에 대한 응력의 변화는 초기에는 완만한 증가를 보이다가 일정 시점 지난 후에는 증가율이 커지는 경향을 띠었다. 증가현상이 두드러지기 전에는 길이의 증가가 응력의 분산효과는 가져왔으나 이후에는 길이의 응력분산 효과는 없었다. 5. 응력분포양상은 cantilever양이 증가할수록 골조직을 통한 분산정도는 작아지고 특정부위의 피질골과 임플랜트, 상부보철물에 집중되는 경향을 보였다. 6. 임플랜트와 주변 골조직으로의 응력분산능력이 예후를 좌우한다는 점에서 angular bar는 적합치 못하며 부득이한 경우는 임플랜트 길이를 길게 하고 최대한 3mm이내로 cantilever양을 제한하는 것이 추천된다.

• The Journal of Korean Academy of Prosthodontics
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• v.25 no.1
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• pp.281-302
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• 1987

의치상 재료 종류에 따라 의치, 점막 및 하악골에 발생되는 변위 및 응력을 연구하기 위하여 컴퓨터를 이용한 수치적 해석인 2차원 유한 요소법을 이용하였다. 2차원 유한 요소 모형으로선 표준 크기의 하악골 및 의치를 고려하여 231개의 사변형 요소 및 268개의 절점으로 분할한 후 각 구성 성분의 물리적 성질인 탄성률 및 프와송비를 대입시켰다. 사용된 의치로서는 일반 합성수지의치, 2mm후경의 탄성재를 의치상 하부에 이장한 합성수지의치, 2mm후경의 탄성재를 치아와 의치상 중앙에 삽입한 합성수지의치 및 0.5mm후경의 금속상의치의 4종류였으며, 하중시에 하악의 고정 부위로선 생체와 동일 조건을 부여하기 위하여 교근, 내측익돌근, 측두근등의 하악 폐구근이 부착되는 하악각 부위 및 하악 근돌기 부위의 16절점을 고정점으로 하였다. 하중 조건으로선 하악 제1대구치의 일점에 10kg의 수직 집중하중, 하악 중절치의 일점에 7kg의 수직 집중하중 및 하악 제 1소구치로 부터 하악 제2대구치까지의 교합면에 10kg의 수직 분산하중을 부여하여 분석한 결과는 다음과 같다. 1. 하중이 의치 교합면위의 가해진 부위에 따라 다양한 의치 회전 및 강하 현상을 보였으며, 탄성재를 이장 및 삽입한 합성 수지 의치의 변위가 일반 합성수지의치 및 금속상 의치의 변위보다 더 컸다. 2. 주응력을 고려할때 점막 부위에는 주로 압축 응력이 작용하였으며 치조제 부위는 압축응력과 인장 응력이 함께 작용하였다. 3. 탄성재를 삽입한 합성수지의치에 최고 등가 응력이 집중되었으며 그 다음은 탄성재를 이장한 합성수지의치, 일반 합성수지의치의 순이였으며 금속상의 경우는 금속을 따라서 높은 등가 응력이 넓게 분산되었다. 4. 의치상 종류에 관계없이 동일 하중 조건하에선 점막에 나타나는 등가 응력의 크기 및 분산양태는 유사하였다. 5. 하악골에서 등가 응력은 의치지지 부위에만 국한되지 않고 넓게 분산 되었으며 의치상 종류 및 하중 조건에 관계없이 치조제 후방 및 하악연의 후방 부위에 특히 높은 등가응력이 집중되었다. 6. 하악 중절치의 일점에 수직 하중을 가한 경우가 다른 하중 조건에 비하여 지지점과의 거리차이로 인하여 하악골에 가장 높은 등가 응력을 유발하였다. 7. 의치상 재료에 따른 하악 골에 발생되는 응력의 크기 및 분산에는 큰 차이가 없으나 금속상의 경우가 교합압을 분산하는데는 효과적이었다.

• The Journal of Korean Academy of Prosthodontics
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• v.46 no.2
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• pp.157-168
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• 2008

Statement of problem: Over the past two decades, implant supported fixed prosthesis have been widely used. However, there are few studies conducted systematically and intensively on the splinting effect of implant systems in mandible. Purpose: The purpose of this study was to investigate the changes in stress distributions in the mandibular implants with splinting or non-splinting crowns by performing finite element analysis. Materials and methods: Cortical and cancellous bone were modeled as homogeneous, transversely isotropic, linearly elastic. Perfect bonding was assumed at all interfaces. Implant models were classified as follows. Group 1: $Br{{\aa}}nemark$ length 8.5mm 13mm splinting type Group 2: $Br{{\aa}}nemark$ length 8.5mm 13mm Non-splinting type Group 3: ITI length 8.5mm 13mm splinting type Group 4: ITI length 8.5mm 13mm Non-splinting type An load of 100N was applied vertically and horizontally. Stress levels were calculated using von Mises stresses values. Results: 1. The stress distribution and maximum von Mises stress of two-length implants (8.5mm, 13mm) was similar. 2. The stress of vertical load concentrated on mesial side of implant while the stress of horizontal load was distributed on both side of implant. 3. Stress of internal connection type was spreading through abutment screw but the stress of external connection type was concentrated on cortical bone level. 4. Degree of stress reduction was higher in the external connection type than in the internal connection type.

• The Journal of Korean Academy of Prosthodontics
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• v.50 no.2
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• pp.119-127
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• 2012

Purpose: This study was performed to compare the stress distribution pattern of abutment-fixture connection area using 3-dimensional finite element model analysis when 5 different implant systems which have internal connection. Materials and methods: For the analysis, a finite element model of implant was designed to locate at first molar area. Stress distribution was observed when vertical load of 200 N was applied at several points on the occlusal surfaces of the implants, including center, points 1.5 mm, 3.0 mm away from center and oblique load of 200 N was applied $30^{\circ}$ inclined to the implant axis. The finite element model was analyzed by using of 3G. Author (PlassoTech, California, USA). Results: The DAS tech implant (internal step with no taper) showed more favorable stress distribution than other internally connected implants. AS compare to the situations when the loading was applied within the boundary of implants and an oblique loading was applied, it showed higher equivalent stress and equivalent elastic strain when the loading was applied beyond the boundary of implants. Regardless of loading condition, the abutments showed higher equivalent stress and equivalent elastic strain than the fixtures. Conclusion: When the occlusal contact is afforded, the distribution of stress varies depending on the design of connection area and the location of loading. More favorable stress distribution is expected when the contact load was applied within the diameter of fixtures and the DAS tech implant (internal step with no tapering) has more benefits than the other design of internally connected implants.

• Journal of Dental Rehabilitation and Applied Science
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• v.24 no.1
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• pp.67-76
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• 2008

Implant requires long lasting, strong osseointegration using bio-mechanical interlocking by bone ingrowth. In regarding the size level for bone ingrowth, the micro-patterning would enhance bone response. Micro-patterning can increase the area contacting the bone tissues. Therefore, it may distribute the load to the surrounding bone tissue, more effectively. This study compared and analyzed the load distributing effect with the shape and number of micro-patterning. For the optimal comparison of threads, the assumptions different from general finite element analysis model were made. It was assumed that the implant was axisymmetric and infinitely long. The implant was assumed to be completely embedded in the infinitely long cortical bone and to have 100% bone apposition. The implant-bone interface had completely fixed boundary conditions and received an infinitely big axial load. The condition of threads were as follows. The reference model 1 had conventional thread. Model 2 had 2 micro-patterns on the upper flank of the thread. Model 3 had 2 micro-patterns on the lower flank of the thread. Model 4 had 2 micro-patterns on the upper and lower flanks of the thread. Model 5 had 3 micro patterns on the upper and lower flanks of the thread. The results were as follows: 1. The thread with micro-patterns distributed stress better than the conventional thread. 2. The thread with micro-patterns on the lower flank distributed stress better than that with micro-patterns on the upper flank. 3. The thread with 3 micro-patterns distributed stress better than that with 2 micro-patterns, However, an area with stress concentration occurred.

• The Journal of Korean Academy of Prosthodontics
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• v.50 no.1
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• pp.1-9
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• 2012

Purpose: The purpose of this study was to investigate the effects of a mouthguard on stress distribution under mandibular impact. Materials and methods: The FEM model of head consisted of skull, maxilla, mandible, articular disc, teeth, and mouthguard. The impact locations on mandible were gnathion, the center of inferior border, and the anterior edge of gonial angle. And the impact directions were vertical, oblique ($45^{\circ}$), and horizontal. The impact load was 800 N for 0.1 sec. Results: When vertical impact was applied, the similar stress and the distribution pattern was occurred without the relation of the mouthguard use (P>.05). The model with mouthguard was dispersed the stress to the teeth, the facial bone and the skull when the oblique ($45^{\circ}$) impacts were happened. However, the stress was centralized on the teeth in the model without mouthguard(P<.05). The model with mouthguard was dispersed the stress to the teeth, the facial bone and the skull when the horizontal impacts was occurred. However, the stress was centralized on the teeth without mouthguard (P<.05). For all impact loads, stress concentrated on maxillary anterior teeth in model without mouthguard, on the contrary, the stress was low in the model with mouthguard and distributed broadly on maxillary anterior teeth, facial bone, and skull. Conclusion: The mouthguard was less effective at shock absorbing when vertical impact was added. However, it was approved that mouthguard absorbed the shock regarded to the oblique ($45^{\circ}$) and horizontal impact by dispersing the shock to the broader areas and decreasing the stress.

• The Journal of Korean Academy of Prosthodontics
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• v.47 no.1
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• pp.70-81
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• 2009

Statement of problem: The position and length of cantilever influence on the stress distribution of implants, superstructure and bone. In edentulous mandible, implant-supported cantilever prostheses that based 4 or 6 implants between mental foramens has been attempted. Excessive bite force loaded at cantilever prosthesis causes bone resorption and breakage of superstructure prosthesis around posterior implants. To complement the cantilever length of conventional prosthesis, In 1992, (McCartney) introduced "cantilever-rest-implant" and Malo reported "All-on-Four" in 2003. Purpose: Analyze and compare the stress distribution of conventional cantilever prostheses with rest implant and All-on-$Four^{TM}$ implant prostheses. Material and method: The external loads(300 N vertically, 75 N horizontally) are applied to first molar area. The stress value, stress distribution and aspect of stress dispersion are analyzed by three-dimensional finite element analysis program, ANSYS ver. 10.0. Results: 1. The rest implant and "All-on-Four" implant system are superior to conventional cantilever prostheses to reduce stress on the bone and the superstructure around implants. 2. The rest implant was of the greatest advantage to stress distribution on bone, implant and superstructure. 3. With same number of implants, distally tilted implants are preferred to conventional cantilever prostheses for reducing the length of cantilever.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.5
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• pp.1785-1795
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• 2013

Most of the previous models for analysis of shallow water flow assumed the uniform velocity distributions over the flow depth so that they produced incorrect velocity prediction at meandering part due to the ignorance of secondary current. In this study, the vertical velocity profiles in longitudinal and transverse direction were decomposed as the mean and variation components, which resulted in additional dispersion stresses terms in momentum equations. The proposed model were applied at the channels with $30^{\circ}$, $90^{\circ}$, $270^{\circ}$ bends, and shallow water flow in curved channel was analyzed using dispersion stresses. The dispersion stresses acted as a sink or source in the momentum equations, which caused the transverse convection of momentum to shift from the inner bank to the outer bank.