• 대한토목학회논문집
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• 제14권1호
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• pp.119-129
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• 1994

본 연구에서는 기존의 구조적 프로그래밍 방법의 단점들을 개선한 새로운 객체지향 프로그래밍기법으로 구조물의 정적해석과 자유진동해석이 가능한 PC용 $C^{{+}{+}}$ 구조해석 프로그램을 개발하였다. 객체지향 프로그램은 기존의 구조적 프로그램에 비하여 프로그램의 재사용성 및 확장성이 뛰어나므로 프로그램의 수정과 개발이 용이하고 다양한 지능과 메뉴선택을 제공하며 소프트웨어의 개발시간과 프로그램의 크기를 줄일 수 있다. 본 연구에서 개발한 객체지향 자유진동해석 프로그램은 벡터 및 행렬의 연산을 수행하는 VECTOR 및 MATRIX클래스, 뼈대 구조물의 자유진동해석을 위한 STRU클래스 및 사용자 환경을 위한 GUI클래스로 구성되며 모든 프로그램은 객체지향 언어인 $C^{{+}{+}}$로 작성되었다. 여러가지 예제해석을 통하여 본 연구에서 개발된 객체지향 $C^{{+}{+}}$ 자유진동해석 프르그램의 효율성과 타당성을 검증하였다.

• Structural Engineering and Mechanics
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• 제65권5호
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.513-518
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• 2007

A polygon-wise constant curvature natural element approximation is presented in this paper for the numerical implementation of the abstract Kirchhoff plate model. The strict continuity requirement in the displacement field is relaxed by converting the area integral of the curvatures into the boundary integral along the Voronoi boundary. Curvatures and bending moments are assumed to be constant within each Voronoi polygon, and the Voronoi-polygon-wise constant curvatures are derived in a selective manner for the sake of the imposition of essential boundary conditions. The numerical results illustrating the proposed method are also given.

• 전산구조공학
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• 제10권4호
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• pp.117-130
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• 1997

본 논문에서는 등방성판의 인장이나 전단변형은 물론 굽힘문제에도 적용할 수 있는 3차원 고체요소들 중에서 최소의 자유도를 갖는 수정 10절점 상당요소를 제안하였다. 제안된 수정 10절점 상당요소는 Q11요소나 20절점요소로부터 자유도가 줄어듬에 기인한 과대한 굽힘강성을 나타낸다. 이러한 상대적 강성과잉 현상을 수정하기 위한 효과적인 방법으로 가우스 적분점 수정 방법을 제안하였다. 수정량은 포아송 비의 함수이다. 수정 10절점 상당요소의 효과를 여러 가지 예에 적용하여 검증하였다. 제안된 수정 10절점 상당요소에 의한 등방성판의 정적해석과 자유진동 해석의 결과들은 20절점요소를 사용한 결과들과 잘 일치하였다.

• Computers and Concrete
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• 제26권3호
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• pp.213-226
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• 2020

The present study covenants with the static and free vibration behavior of nanocomposite sandwich plates reinforced by carbon nanotubes resting on Pasternak elastic foundation. Uniformly distributed (UD-CNT) and functionally graded (FG-CNT) distributions of aligned carbon nanotube are considered for two types of sandwich plates such as, the face sheet reinforced and homogeneous core and the homogeneous face sheet and reinforced core. Based on the first shear deformation theory (FSDT), the Hamilton's principle is employed to derive the mathematical models. The obtained solutions are numerically validated by comparison with some available cases in the literature. The elastic foundation model is assumed as one parameter Winkler - Pasternak foundation. A parametric study is conducted to study the effects of aspect ratios, foundation parameters, carbon nanotube volume fraction, types of reinforcement, core-to-face sheet thickness ratio and types of loads acting on the bending and free vibration analyses. It is explicitly shown that the (FG-CNT) face sheet reinforced sandwich plate has a high resistance against deflections compared to other types of reinforcement. It is also revealed that the reduction in the dimensionless natural frequency is most pronounced in core reinforced sandwich plate.

• 한국구조물진단유지관리공학회 논문집
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• 제8권4호
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• pp.107-114
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• 2004

본 논문에서는 복합적층판의 유한요소해석을 위해 직접수정법으로 간단히 개선된 8절점 유한요소를 제안하였다. 우선, 9절점 등매개변수 요소와 동일한 조건하에서 이차다항식을 표현할 수 있도록 형상함수를 수정하며, 이를 외시적(explicit)으로 표현하였다. 전단보정계수를 갖는 1차전단변형이론을 고차전단변형이론에 근거하여 간단히 개선함으로써 두께방향으로 전단응력 및 변형률이 포물선 분포를 가지도록 하였다. 더 이상의 전단보정계수가 필요하지 않다. 따라서 간단한 직접수정법 즉, 형상함수의 수정, 1차전단변형이론의 개선 및 가정변형률을 조합함으로써 8절점 유한요소의 성능을 개선하였다. 제안된 유한요소를 이용하여 복합적층판의 정적, 좌굴 및 자유진동 수치해석을 실시하여 비교 검증하였다.

• 대한토목학회논문집
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• 제3권4호
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• pp.109-122
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• 1983

본(本) 연구(硏究)에서는 전단변형(剪斷變形)(Shear deformation)과 회전관성(回轉慣性)(Rotatory inertia)의 영향(影響)을 고려(考慮)한 4절점(節點) 8자유도(自由度)를 갖는 Timoshenko 보 요소(要素)(TB4)를 3차원(次元) 연속체(連續體)로부터 유도(誘導)하고 있다. TB4보 요소(要素)는 3차(次) 보간함수(補間凾數)(Interpolation function)로 표시(表示)되는 연직(鉛直)처짐(Transverse deflection) W와 평면회전(平面回轉)(Plane rotation) ${\theta}$를 절점(節點)의 자유도(自由度)로 취(取)하고 있다. TB4요소(要素)의 강도(剛度)매트릭스와 질량(質量)매트릭스는 보의 운동방정식(運動方程式)을 Galerkin 가중잔차법(加重殘差法)(Weighted residual method)으로 Discretization하여 3개(個)의 Gauss점(點)을 이용(利用)한 RSI(Reduced shear integration)기법(技法)에 의한 수치적분(數値積分)으로 구해진다. TB4보 요소(要素)의 정확성(正確性)과 수감상태(收歛狀態)를 고찰(考察)하기 위하여 여러 가지 예제(例題)를 해석(解析)한 결과(結果), 보의 L/h 비(比)에 관계없이 보의 정적해석(靜的解析)(Static analysis)이라 자유진동해석(自由振動解析)(Free vibration analysis)에 있어서 TB4보 요소(要素)는 다른 Timoshenko보 요소(要素)들 보다 월등(越等)히 우수(優秀)한 정확도(正確度)와 수감현상(收歛現象)을 보여 주고 있다.

• Steel and Composite Structures
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• 제39권1호
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• pp.1-20
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• 2021

An exact solution based on refined third-order theory (TOT) has been presented for functionally graded porous curved beams having deep curvature. The displacement field of the refined TOT is derived by imposing the shear free conditions at the outer and inner surfaces of curved beams. The properties of the two phase composite are tailored according the power law rule and the effective properties are computed using Mori-Tanaka homogenization scheme. The equations of motion as well as consistent boundary conditions are derived using the Hamilton's principle. The curved beam stiffness coefficients (A, B, D) are obtained numerically using six-point Gauss integration scheme without compromising the accuracy due to deepness (1 + z/R) terms. The porosity has been modeled assuming symmetric (even) as well as asymmetric (uneven) distributions across the cross section of curved beam. The programming has been performed in MATLAB and is validated with the results available in the literature as well as 2D finite element model developed in ABAQUS. The effect of inclusion of 1 + z/R terms is studied for deflection, stresses and natural frequencies for FG curved beams of different radii of curvature. Results presented in this work will be useful for comparison of future studies.

• Journal of Mechanical Science and Technology
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• 제17권1호
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• pp.85-96
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• 2003

In the present investigation, the nonlinear dynamic buckling of a curved plate subjected to sinusoidal loading is examined. By the theoretical analyses, a highly nonlinear snap-through motion of a clamped-free-clamped-free plate and its effect on the overall vibration response are investigated. The problem is reduced to that of a single degree of freedom system with the Rayleigh-Ritz procedure. The resulting nonlinear governing equation is solved using Runge-Kutta (RK-4) numerical integration method. The snap-through boundaries, which vary with different damping coefficient and linear circular frequency of the flat plate are studied and given in terms of force and displacement. The relationships between static and dynamic responses at the start of a snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. 1) small oscillation about the buckled position-softening spring type motion, 2) chaotic motion of intermittent snap-through, and 3) large oscillation of continuous snap-through motion crossing the two buckled positions-hardening spring type. The responses of buckled plate were found to be greatly affected by the snap-through motion. Therefore, better understanding of the snap-through motion is needed to predict the full dynamic response of a curved plate.

• 한국지반환경공학회 논문집
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• 제24권2호
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• pp.13-24
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• 2023

Tunnels may undergo a larger or a smaller response compared with the free-field soil. In the pseudo-static procedure, the response of the tunnel is most often characterized by a curve that relates the racking ratio (R) with the flexibility ratio (F), where R represents the ratio of the tunnel response with respect to the free-field vibration and F is the relative stiffness of the tunnel and the surrounding soil. A set of analytical and empirical curves that do not account for the depth and the aspect ratio of the tunnel are typically used in practice. In this study, a series of dynamic analyses are conducted to develop a set of F-R_m relations for use in a frame analysis method. R_m is defined as an adjusted R where the rocking mode of deformation is removed and only the racking deformation is extracted. The numerical model is validated against centrifuge test recordings. The influence of aspect ratio, buried depth of tunnel on results is investigated. The results show that R_m increases with the increase of the buried depth and the aspect ratio. The widely used F-R relations are highlighted to be different compared with the obtained results in this study. Therefore, the updated F-R_m relations with proposed equations are recommended to be used in practice design. The rocking response decreases with either the decrease of the difference of stiffness between surrounding soil and tunnel or the larger aspect ratio of the tunnel section.