• Journal of Mechanical Science and Technology
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• 제16권8호
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• Structural Engineering and Mechanics
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• 제64권5호
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• pp.591-610
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• 2017

This paper is concerned with the static analysis of variable thickness of two directional functionally graded porous materials (FGPM) circular plate resting on a gradient hybrid foundation (Horvath-Colasanti type) with friction force and subjected to compound mechanical loads (e.g., transverse, in-plane shear traction and concentrated force at the center of the plate).The governing state equations are derived in terms of displacements based on the 3D theory of elasticity, assuming the elastic coefficients of the plate material except the Poisson's ratio varying continuously throughout the thickness and radial directions according to an exponential function. These equations are solved semi-analytically by employing the state space method (SSM) and one-dimensional differential quadrature (DQ) rule to obtain the displacements and stress components of the FGPM plate. The effect of concentrated force at the center of the plate is approximated with the shear force, uniformly distributed over the inner boundary of a FGPM annular plate. In addition to verification study and convergence analysis, numerical results are displayed to show the effect of material heterogeneity indices, foundation stiffness coefficients, foundation gradient indices, loads ratio, thickness to radius ratio, compressibility, porosity and friction coefficient of the foundation on the static behavior of the plate. Finally, the responses of FG and FG porous material circular plates to compound mechanical loads are compared.

• Geomechanics and Engineering
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• 제31권5호
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• pp.489-503
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• 2022

A 1257-m-long irregular deep foundation pit located in the central of Nanjing, China was constructed using the combined full-width and half-width top-down method. Based on the long-term field monitoring data, this study analyzed the evolution characteristics of the vertical movement of the columns, internal force of the struts, and axial force of the structural beam and slab. The relevance of the three mentioned above and their relationship with the excavation process, structural system, and geological conditions were also investigated. The results showed that the column uplift was within the range of 0.08% to 0.22% of the excavation depth, and the embedded depth ratio of the diaphragm wall and the bottom heave affected significantly on the column uplift. The differential settlement between the column and diaphragm wall remained unchanged after the base slab was cast. The final settlement of the diaphragm wall was twice the column uplift. The internal force of the struts did not varied monotonically but was related to numerous factors such as the excavation depth, number of struts, and environmental conditions. Additionally, the dynamic force and deformation of the columns, beams, and slabs were analyzed to investigate the inherent relationship and variation patterns of the responses of different parts of the structure.

• 한국전산구조공학회논문집
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• 제33권1호
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• pp.9-16
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• 2020

본 연구는 쿨롱마찰을 갖는 동적시스템의 기초적인 연구로써 단자유도계의 자유진동응답에 대한 닫힌 해를 제공하는 것을 목적으로 한다. 쿨롱마찰을 포함하는 동적시스템의 운동방정식은 운동방향에 따른 마찰력의 부호변화로 인하여 비선형 미분방정식의 형태로 표현되기 때문에 닫힌 형태의 해를 얻기가 매우 어려운 특성이 있다. 이를 해결하기 위한 기존의 방법으로는 수치적분법에 의해 비선형 미분방정식을 직접 계산하거나 또는, 쿨롱마찰에 의한 감쇠효과를 등가점성감쇠로 치환한 선형 미분방정식을 이용하여 간접적으로 해를 구하는 방법이 사용되고 있다. 그러나 이러한 방법들은 수학적인 측면에서 닫힌 해를 제공하지 않는다. 따라서 본 연구에서는 운동방정식에서 반주기 구간마다 반전되는 마찰력의 부호변화를 고려하고, 이를 멱급수를 이용하여 전 구간으로 확장시킴으로써 쿨롱마찰을 고려한 단자유도계의 자유진동응답에 대해서 수학적으로 닫힌 해를 유도하였다. 또한, 마찰력의 크기가 강성에 의한 복원력의 크기보다 커지는 순간에 자유진동 운동이 정지하는 조건을 이용함으로써 주어진 초기조건에 대해서 예측되는 자유진동 반주기의 수와 운동이 정지하는 순간의 정확한 응답 값을 제안하였다

• 한국수학사학회지
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• 제21권3호
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• pp.1-30
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• 2008

뉴턴의 중력이론의 성공은 수학물리학을 태동시키는 바, 최초로 19세기 초의 분자력의 모델성립에 중요한 요소로 등장하였다. 라플라스는 여기서 회전타원체의 작용이라는 모델을 이용하였고 회전타원체의 작용은 이계편미분방정식으로 표현이 되었다. 이것을 풀어서 유체를 담은 용기의 기하학적 모습과 와 유체와 고체의 접촉각에 대응시켰다. 알 수 없는 분자간거리는 추상적이고 미지의 힘 함수 $\varphi(f)$를 써서 표현하여, 분자 작용반경이라는 개념을 도입하여 이론적인 포텐셜 함수의 이론적인 토대를 구축하였다. 뉴턴의 중력이론은 라플라스이론에서 완성을 이루었고, 이후 분자력의 모델로서 작용을 하였다. 라플라스-영의 모세관이론은 수학적으로는 극소 곡면론에서 물리학적으로는 표면장력현상으로 설명이 된다.

• 센서학회지
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• 제11권3호
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• pp.171-182
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• 2002

이식형 인공중이에 사용되는 일반적인 전자기 방식의 진동 트랜스듀서에 비하여 두 개의 소형 영구자석을 같은 극끼리 접착한 후 코일내부에 위치시킨 차동 전자 트랜스듀서는 효율이 높고 코일-영구자석간의 공극조정이 필요 없으며 외부의 자기장에 대하여 영향을 받지 않는 특성을 가진다. 본 논문에서는 이러한 차동 전자 트랜스듀서를 이식형 인공중이 시스템에 사용하기 위하여 입력전류에 대하여 진동력의 크기를 최대화시킬 수 있는 효율적인 구조를 제안, 해석하였다. 유한요소 해석을 통하여 가장 효율적인 코일과 자석의 길이 비를 도출하였고 소리신호 전달을 위한 트랜스듀서의 필요 진동력을 산출한 후 트랜스듀서 발생 진동력을 해석하였다. 그리고 실제 이소골에 이식할 수 있는 크기의 트랜스듀서를 제작하기 위한 설계상수를 추출하였다. 계산된 설계상수를 이용하여 이식 가능한 크기로 트랜스듀서를 구현한 후 무부하 실험과 사체 부하 실험을 실시하여 제작된 트랜스듀서가 실제 중등이상 고도난청자를 위한 이식형 인공중이 시스템에 사용될 수 있음을 증명하였다.

• 대한치과교정학회지
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• 제51권1호
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• pp.32-42
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• 2021

Objective: To investigate the three-dimensional forces created by clear aligners on mandibular teeth during differential activation with en-masse retraction and/or intrusion in vitro. Methods: Six sets of clear aligners were designed for differential en-masse retraction and/or intrusion procedures in a first premolar extraction model. Group A0 was a control group with no activation. Groups A1-5 underwent different degrees of retractions and/or intrusions. Each group consisted of 10 aligners. Aligner forces were measured on a multi-axis force/torque transducer measurement system in real-time. Results: In the en-masse retraction groups (A1 and A2), lingual and extrusive forces were observed on the incisors; the canines mainly received distal forces; intrusive forces were seen on the second premolars; and the molars received mesial forces. In the en-masse retraction and intrusion groups (A3, A4, and A5), incisors also received lingual and extrusive forces; canines received distal and intrusive forces; mesial and extrusive forces were seen on the second premolars; and the second molars received distal and intrusive forces. The vertical forces on the incisors did not differ significantly among groups A1, A3, and A5. However, the vertical forces on the second premolars reversed from intrusion in group A1 to extrusion in groups A3 and A5. Conclusions: With clear aligners, the "bowing effect" is seen during en-masse anterior teeth retraction and can be partially relieved by performing en-masse retraction accompanied by anterior teeth intrusion. Vertical control of incisors remained unsolved during en-masse retraction, even when intrusive activation was added to the anterior teeth.

• 대한기계학회논문집
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• 제15권2호
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• pp.630-643
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• 1991

The hydrodynamic stability equations are formulated for buoyancy-induced flows adjacent to a vertical, planar, isothermal surface in cold pure water. The resulting stability equations, when reduced to ordinary differential equation by a similarity transformation, constitute a two-point boundary-value(eigenvalue) problem, which was numerically solved for various values of the density extremum parameter R=( $T_{m}$ - $T_.inf./) / ( $T_{o}$ - $T_.inf./). These stability equations have been solved using a computer code designed to accurately solve two-point boundary-value problems. The present numerical study includes neutral stability results for the region of the flows corresponding to 0.0.leq. R. leq.0.15, where the outside buoyancy force reversals arise. The results show that a small amount of outside buoyancy force reversal causes the critical Grashof number $G^*/ to increase significantly. A further increase of the outside buoyancy force reversal causes the critical Grashof number to decrease. But the dimensionless frequency parameter $B^*/ at $G^*/ is systematically decreased. When the stability results of the present work are compared to the experimental data, the numerical results agree in a qualitative way with the experimental data.erimental data.

• 대한기계학회논문집B
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• 제38권1호
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• pp.9-16
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• 2014

본 논문은 경사진 원형관에서 표면장력과 중력으로 구동되는 비뉴턴 유체(멱법칙 모델)의 유동 및 변위를 이론적으로 연구한 것이다. 그리고 표면장력에 의하여 연속적으로 원형관 내로 유입되는 비뉴턴 유체의 변위를 기술하기 위한 지배방정식을 처음으로 개발하였다. 뉴턴의 운동방정식으로부터 유도된 식은 2계 비선형이며 비제차인 형태의 상미분 방정식이다. 지배방정식의 해를 수평관에서 변위를 시간의 함수로 기술한 식 및 실험과 비교한 결과 정량적으로 동일한 일치를 보였다. 여기에 더하여 정상상태인 힘의 균형식의 결과에 대해서도 정확한 일치로 나타남을 확인할 수 있었다.

• Structural Engineering and Mechanics
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• 제76권3호
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• pp.395-412
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• 2020

In this article, the values of internal force and deformation of a curved beam under any action with the firm or elastic supports are determined by using structural matrices. The article presents the general differential formulation of a curved beam in global coordinates, which is solved in an orderly manner using simple integrals, thus obtaining the transfer matrix expression. The matrix expression of rigidity is obtained through reordering operations on the transfer notation. The support conditions, firm or elastic, provide twelve equations. The objective of this article is the construction of the algebraic system of order twenty-four, twelve transfer equations and twelve support equations, which relates the values of internal force and deformation associated with the two ends of the directrix of the curved beam. This final algebraic system, expressed in matrix form, is divided into two subsystems: twelve algebraic equations of internal force and twelve algebraic equations of deformation. The internal force and deformation values for any point in the curved beam directrix are determined from these values in the initial position. The five examples presented show how to apply the matrix procedures developed in this article, whether they are curved beams with the firm or elastic support.