• 동력기계공학회지
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• 제3권1호
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• pp.74-79
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• 1999

This paper describes formulation for algorithm of time historical response analysis of vibration for straight-line structure. This method is derived from a combination of the transfer stiffness coefficient method and the Newmark method. And this present method improves the computational accuracy of the transient vibration response analysis remarkably owing to several advantages of the transfer stiffness coefficient method. We regarded the structure as a lumped mass system here. The analysis algorithm for the time historical response was formulated for the straight-line structure containing crooked, tree type system. The validity of the present method compared with the transfer matrix method and the Finite Element Method for transient vibration analysis is demonstrated through the numerical computations.

• Journal of Mechanical Science and Technology
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• 제19권12호
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• pp.2187-2196
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• 2005

In this paper, the stiffness and the mass matrices for the in-plane motion of a thin circular beam element are derived respectively from the strain energy and the kinetic energy by using the natural shape functions of the exact in-plane displacements which are obtained from an integration of the differential equations of a thin circular beam element in static equilibrium. The matrices are formulated in the local polar coordinate system and in the global Cartesian coordinate system with the effects of shear deformation and rotary inertia. Some numerical examples are performed to verify the element formulation and its analysis capability. The comparison of the FEM results with the theoretical ones shows that the element can describe quite efficiently and accurately the in-plane motion of thin circular beams. The stiffness and the mass matrices with respect to the coefficient vector of shape functions are presented in appendix to be utilized directly in applications without any numerical integration for their formulation.

• 한국공간구조학회:학술대회논문집
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• 한국공간구조학회 2006년도 춘계 학술발표회 논문집 제3권1호(통권3호)
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• pp.256-264
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• 2006

This paper describes the formulation of rectangular flat shell element that is modeled with the six degree of freedoms including a rotational degree of freedom. The rectangular finite element matrix with a rotational degree of freedom is developed using a beam stiffness matrix and compared with other methods. The outputs of the quantity of vertical deflection of cantilever beam show us the improving evidence of the Frame-Shell finite element matrix in a calculation of vertical deflections of cantilever beam.

• 한국산학기술학회논문지
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• 제11권7호
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• pp.2661-2669
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• 2010

본 연구에서는 매트릭스가 손상된 적층복합판의 비선형 거동을 분석하기 위한 일차전단변형이론에 기초한 유한요소 정식을 유도하였다. Duan and Yao가 제안한 Matrix 균열의 강성 치환 방법을 적용하여 다방향 강성저하식을 구성하였다. 발생된 Matrix 균열은 탄성계수, 전단탄성계수 및 프아송비의 변화로 표현할 수 있으며, 이를 이용하여 판의 국부 강성 변화를 예측할 수 있다. 가정된 자연변형률 방법을 적용한 쉘요소를 이용하여 면내 및 전단잠김 현상이 발생하지 않았다. 적층복합판의 선형해석은 물론 비선형 해석결과들은 참고문헌의 결과들에 수렴되었다. 매트릭스가 손상된 적층복합판의 해석 결과들은 향후 연구에 비교자료로 활용될 수 있을 것이다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집B
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• pp.355-360
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• 2001

By using Frenet formulation and Timoshenko beam theory, the partial differential equations of motion are derived for a helical spring having a doubly symmetrical cross section subjected to the pre-load axially. These equations of motion are solved to give the dispersion relationship and dynamic stiffness matrix is assembled. Natural frequencies are obtained from the receptance of the system. The results of the dynamic stiffness method are compared with those of the transfer matrix method from published examples and finite element method.

• Steel and Composite Structures
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• 제39권5호
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• pp.543-564
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• 2021

In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

• Architectural research
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• 제13권1호
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• pp.17-24
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• 2011

Isogeometric solution of Poisson equation is provided. NURBS (NonUniform B-spline Surface) is introduced to express both geometry of structure and unknown field of governing equation. The terms of stiffness matrix and load vector are consistently derived with very accurate geometric definition. The validity of the isogeometric formulation is demonstrated by using two numerical examples such as square plate and L-shape plate. From numerical results, the present solutions have a good agreement with analytical and finite element (FE) solutions with the use of a few cells in isogeometric analysis.

• 터널과지하공간
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• 제10권2호
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• pp.173-179
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• 2000

절리면의 전단거동에서 나타나는 응력 및 변위의 비선형 특성을 탄소성해석에 의해 모사하는 경우 소성유동법칙이 해석결과에 미치는 영향을 검토하였다. Plesha의 절리구성모델을 적용하여 일정수직응력조건과 일정수직변위조건에서 수치직접전단시험을 실시하였다. 연상유동법칙을 적용하면 과도한 수직팽창이 예측되는 반면에 비연상유동법칙을 적용한 해석은 실제 절리거동을 잘 모사하고 있음을 보였다. 비연상유동법칙의 적용으로 강성행렬이 비대칭이 피는 단점을 보완하기 위해 비연상유동법칙을 적용하는 경우라도 요소의 접선강성행렬을 대칭화시키는 수치해석 기법이 제안되었다. 본래의 절리면과 동일한 소성변형을 일으키지만 연상유동법칙을 따르는 등가의 절리면을 가정함으로써 대칭인 탄소성행렬을 유도하였다. 일정수직음력조건에서 수티 직접전단시험을 실시하여 제안된 강성행렬 대칭화 기법의 유효성을 검증하였다.

• Structural Engineering and Mechanics
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• 제17권1호
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• pp.113-140
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• 2004

A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.

• Interaction and multiscale mechanics
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• 제1권2호
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• pp.231-250
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• 2008

The statistical two-order and two-scale method is developed for predicting the mechanics parameters, such as stiffness and strength of core-shell particle-filled polymer composites. The representation and simulation on meso-configuration of random particle-filled polymers are stated. And the major statistical two-order and two-scale analysis formulation is briefly given. The two-order and two-scale expressions for the strains and stresses of conventionally strength experimental components, including the tensional or compressive column, the twist bar and the bending beam, are developed by means of their classical solutions with orthogonal-anisotropic coefficients. Then a new effective mesh generation algorithm is presented. The mechanics parameters of core-shell particle-filled polymer composites, including the expected stiffness parameters, minimum stiffness parameters, and the expected elasticity limit strength and the minimum elasticity limit strength, are defined by means of the stiffness coefficients and elasticity strength criterions for core, shell and matrix. Finally, the numerical results for predicting both stiffness and elasticity limit strength parameters are compared with the experimental data.