• 대한토목학회논문집
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• 제3권3호
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• pp.129-135
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• 1983

토목설계(土木設計), 토지이용조사(土地利用調査) 및 지질조사(地質調査)에 있어서, 사진측량(寫眞測量)과 사진판독(寫眞判讀)에 의한 지형정보(地形情報)는 계획수립(計劃樹立)에 중요(重要)한 역할(役割)을 한다. 종래(從來)에 발표(發表)된 경사(傾斜)와 주향결정방법(走向決定方法)들에서는 사진(寫眞)의 기하학적(幾何學的)인 조건(條件)에 대한 특성(特性)을 정확하게 고려(考慮)하지 못하였기 때문에, 이를 보완(補完)하는 올바른 공식유도(公式誘導)가 필요(必要)하게 되었다. 이에 본(本) 논문(論文)에서는 삼각법(三角法)에 의한 기하학적(幾何學的)인 모델과 평면방정식(平面方程式)에 의해 유도(誘導)되는 수학적(數學的) 모델의 두가지 측면(側面)에서 이론적(理論的)으로 고찰(考察)하므로서, 경사(傾斜)진 면(面)의 경사(傾斜)와 주향결정(走向決定)에 사진측정방법(寫眞測定方法)을 이용(利用)하는 하나의 기법(技法)을 제시(提示)하고자 한다.

• Smart Structures and Systems
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• 제8권5호
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• pp.433-447
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• 2011

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

• Structural Engineering and Mechanics
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• 제19권4호
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• pp.401-411
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• 2005

The influence of cracks on the elastic deflection and ultimate bearing capacity of eccentric thin-walled columns with both ends pinned was studied in this paper. First, a method was developed and applied to determine the elastic deflection of the eccentric thin-walled columns containing some model-I cracks. A trigonometric series solution of the elastic deflection equation was obtained by the Rayleigh-Ritz energy method. Compared with the solution presented in Okamura (1981), this solution meets the needs of compatibility of deformation and is useful for thin-walled columns. Second, a two-criteria approach to determine the stability factor ${\varphi}$ has been suggested and its analytical formula has been derived. Finally, as an example, box columns with a center through-wall crack were analyzed and calculated. The effects of cracks on both the maximum deflection and the stability coefficient ${\varphi}$ for various crack lengths or eccentricities were illustrated and discussed. The analytical and numerical results of tests on the columns show that the deflection increment caused by the cracks increases with increased crack length or eccentricity, and the critical transition crack length from yielding failure to fracture failure ${\xi}_c$ is found to decrease with an increase of the slenderness ratio or eccentricity.

• Structural Engineering and Mechanics
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• 제70권5호
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• pp.525-534
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• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Advances in nano research
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• 제10권2호
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• pp.101-114
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• 2021

An analytical investigation has been performed on the mechanical performance of waves propagated in a Single-Layered Graphene Sheet (SLGS) when an In-plane Varying Bending (IVB) load is interacted. It has been supposed that the Graphene Sheet (GS) is located on an elastic medium. Employing a two-parameter elastic foundation, the effects of elastic substrate on the GS behavior are modeled. Besides, the kinematic equations are derived by the means of a trigonometric two-variable refined plate theory. Moreover, in order to indicate the size-dependency of the SLGS, a Nonlocal Strain Gradient Theory (NSGT) was considered. The nonlocal governing differential equations are achieved in the framework of Hamilton's Principle (HP). Also, an analytical approach was used to detect the unknowns of the final eigenvalue equation. Finally, the effects of each parameters using some dispersion charts were determined.

• 한국산학기술학회논문지
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• 제19권2호
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• pp.608-616
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• 2018

일반적으로 비선형 시스템은 1차와 2차 시스템의 곱의 형태로 선형화되며, 시스템의 근은 1차 시스템의 근과 2차 시스템의 중근, 서로 다른 두 실근, 복소근으로 구성된다. 그리고 LQ(Linear Quadratic) 제어는 성능지수함수를 최소화하는 제어법칙을 설계하는 방법으로 시스템의 안정성을 보장하는 장점과 가중행렬 조정으로 시스템의 근의 위치를 조정하는 극배치 기능이 있다. 가중행렬에 의해 LQ 제어는 시스템의 근의 위치를 임의로 이동시킬 수 있지만 시행착오 방법으로 가중행렬을 설정하는 어려움이 있다. 이것은 해밀토니안(Hamiltonian) 시스템의 특성방정식을 이용하여 해결 할 수 있다. 또한 제어가중행렬이 상수의 대칭행렬이면 제어법칙을 반복적으로 적용하여 시스템의 여러 근을 원하는 폐루프 근으로 이동시킬 수 있다. 이 논문은 해밀토니안 시스템의 특성방정식을 이용하여 조단 블록을 갖는 시스템의 중근을 두 실근으로 이동시키는 상태가중행렬과 제어법칙을 계산하는 방법을 제시한다. 삼각함수로 표현된 상태가중행렬로 해밀토니안 시스템의 특성방정식을 구한다. 그리고 이동된 두 실근이 특성방정식의 근이라는 조건에서 중근과 상태가중행렬의 관계식(${\rho},\;{\theta}$)을 유도한다. 상태가중행렬이 양의 반한정행렬이 될 조건에서 중근의 이동범위를 구한다. 그리하여 이동범위에서 선택한 두 실근을 관계식에 대입하여 상태가중행렬과 제어법칙을 계산한다. 제안한 방법을 간단한 3차 시스템의 예제에 적용해본다.

• 대한의용생체공학회:의공학회지
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• 제28권4호
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• pp.520-529
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• 2007

An efficient method for implementing image reconstruction algorithms for Compton cameras is presented. Since Compton scattering formula establishes a cone surface from which the incident photon must have originated, it is crucial to implement a computationally efficient cone-surface integration method for image reconstruction. In this paper we assume that a cone is made up of a series of ellipses (or circles) stacked up one on top of the other. In order to reduce computational burden for tracing ellipses formed by the intersection of a cone and an image plane, we propose a new method using a series of imaginary planes perpendicular to the cone axis so that each plane contains a circle, not an ellipse. In this case the cone surface integral can be performed by simply accumulating the circles along the cone axis. To reduce the computational cost of tracing circles, only one of the circles in the cone is traced and the rest are determined by using simple trigonometric ratios. For our experiments, we used the three different schemes for tracing ellipses; (i) using the samples generated by the ellipse equation, (ii) using the fixed number of samples along a circle on the imaginary plane, and (iii) using the fixed sampling interval along a circle on the imaginary plane. We then compared performance of the above three methods by applying them to the two reconstruction algorithms - the simple back-projection method and the expectation-maximization algorithm. The experimental results demonstrate that our proposed methods (ii) and (iii) using imaginary planes significantly improve reconstruction accuracy as well as computational efficiency.

• 대한조선학회지
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• 제14권1호
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• pp.1-10
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• 1977

The major objects of this report are to supplement data of natural frequencies of thin elastic rectangular plates to the available data, and to give an experimental verification for natural frequencies obtained by Rayleigh-Ritz method, the generation set of which are eigenfunctions of Euler beams. For the first object the following five models, for which data only for the fundamental mode or data only for square plates are available, are adopted; (1) two opposed edges are clamped and the other two opposed edges simply supported (C-C, S-S), (2) one edge is simply supported and the other three edges clamped (C-C, C-S), (3) one edge is free and the other three edges clamped (C-C, C-F), (4) two adjacent edges are clamped and the other two adjacent edges free (C-F, C-F). For the (C-C, S-S) model the frequency equation obtained with the mode shapes assumed as of a single trigonometric series is solved. And for the other four models Rayleigh-Ritz method taking eigenfunctions of Euler beams as the generating set is applied. The numerical examples are obtained up to the fourth, the fifth or the sixth order depending on the range of the aspect ratio (0.1-10.0). The number of terms in the generating set for Rayleigh-Ritz method is fifteen for all models. For the experiment three models made of 3.2mm thickness mild steel plate for general structure use were prepared in following size; $300mm{\times}600mm,\;600mm{\times}600mm\;and\;900mm{\times}600mm$. Their boundary conditions are made to fit (C-C, C-F) condition. From the experiment mechanical impedance curves based on the frequency response method were obtained together with phase relation diagrams. The experimental data are resulted in good conformity to calculated values.

• Structural Engineering and Mechanics
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• 제22권2호
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• pp.169-184
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• 2006

A close form solution of the maximum deflection for cracked columns with rectangular cross-sections was developed and thus the elastic buckling behavior and ultimate bearing capacity were studied analytically. First, taking into account the effect of the crack in the potential energy of elastic systems, a trigonometric series solution for the elastic deflection equation of an arbitrary crack position was derived by use of the Rayleigh-Ritz energy method and an analytical expression of the maximum deflection was obtained. By comparison with the rotational spring model (Okamura et al. 1969) and the equivalent stiffness method (Sinha et al. 2002), the advantages of the present solution are that there are few assumed conditions and the effect of axial compression on crack closure was considered. Second, based on the above solutions, the equilibrium paths of the elastic buckling were analytically described for cracked columns subjected to both axial and eccentric compressive load. Finally, as examples, the influence of crack depth, load eccentricity and column slenderness on the elastic buckling behavior was investigated in the case of a rectangular column with a single-edge crack. The relationship of the load capacity of the column with respect to crack depth and eccentricity or slenderness was also illustrated. The analytical and numerical results from the examples show that there are three kinds of collapse mechanisms for the various states of cracking, eccentricity and slenderness. These are the bifurcation for axial compression, the limit point instability for the condition of the deeper crack and lighter eccentricity and the fracture for higher eccentricity. As a result, the conception of critical transition eccentricity $(e/h)_c$, from limit-point buckling to fracture failure, was proposed and the critical values of $(e/h)_c$ were numerically determined for various eccentricities, crack depths and slenderness.

• 대한토목학회논문집
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• 제4권4호
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• pp.95-103
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• 1984

본(本) 연구(硏究)에서는 기준점측량(基準點測量)의 기하학적(幾何學的)인 조건(條件)을 최적(最適)으로 하는 각조건(角條件)을 제시함으로써 기준점((基準點)들의 정확도(正確度)를 향상시키는데 목적(目的)이 있다. 이를 위해 임의의 데오돌라이트 관측점(觀測點)에서 관측(觀測)한 기준점좌표(基準點座標)의 정확도(正確度)를 평가할 수 있는 식(式)을 유도하고, 이를 적분(積分)하여 여러 좌표(座標)들의 평균오차(平均誤差)를 구하였으며, 이로부터 최적(最適)의 데오돌라이트 관측점(觀測點)의 위치(位置)를 결정(決定)하였다. 일반적(一般的)으로 정삼각형(正三角形)이 경우(境遇) 기하학적(幾何學的) 조건(條件)인 것으로 알려져 있으나, 각(各) 변(邊)들의 관측(觀測) 정밀도(精密度)가 틀리므로 밑각이 $52.77^{\circ}$인 이등변삼각형이 최적(最適)이었으며, 삼각수준측량(三角水準測量)의 경우 $45^{\circ}$일 때 최적(最適)이었다. 또한 근거리(近距離) 사진측량(寫眞測量)을 위한 기준점측량시(基準點測量時) 최적기선(最適基線)과 대상물(對象物)까지의 거리연계식(距離關係式)은 $D_0=0.357587-0.357587B_0+0.308555B_0{^2}$ 임을 알 수 있었다.