• Structural Engineering and Mechanics
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• 제66권5호
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• pp.665-676
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• 2018

In this study, a four-node quadrilateral partial mixed plate element with low degrees of freedom (dofs) is developed for static and free vibration analysis of functionally graded material (FGM) plates rested on Winkler-Pasternak elastic foundations. The formulation of the presented finite element model is based on a parametrized mixed variational principle which is developed recently by the first author. The presented finite element model considers the effects of shear deformations and normal flexibility of the FGM plates without using any shear correction factor. It also fulfills the boundary conditions of the transverse shear and normal stresses on the top and bottom surfaces of the plate. Beside these capabilities, the number of unknown field variables of the plate is only six. The presented partial mixed finite element model has been validated through comparison with the results of the three-dimensional (3D) theory of elasticity and the results obtained from the classical and high-order plate theories available in the open literature.

• Advances in materials Research
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• 제5권4호
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• pp.223-244
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• 2016

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

• 한국전산구조공학회논문집
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• 제28권5호
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• pp.553-561
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• 2015

지수 함수 및 멱 법칙 함수를 이용한 점진기능재료(FGM) 판의 전단 및 두께 방향 변형을 고려한 이론을 정식화하여 동적 평형방정식을 유도하였다. 지수 함수 및 멱 법칙 함수는 두께 방향으로 재료의 변화를 고려할 수 있고 3차원 해석방법은 전단 및 두께 방향 변형을 고려함으로써 점진기능재료의 정확한 구조적 특성을 고려할 수 있다. Pasternak탄성지반 위에 놓인 4변이 단순 지지되고 전단 및 두께 방향 변형이 고려된 점진기능재료 판의 지배방정식을 풀기 위해 Navier 방법을 사용하였다. 거듭제곱 지수와 3차원 해석의 효과를 나타내기 위한 지수 및 멱 법칙 점진기능재료 판의 동적 해석결과를 제시하였다. 기존의 2차원 고차전단변형 이론 및 3차원 이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 (i) 거듭제곱 지수, (ii) 폭-두께 비, 그리고 (iii) 탄성지반 계수, 등이 점진기능재료 판의 자유진동수에 미치는 효과에 대하여 관찰하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였다.

• 한국전산구조공학회논문집
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• 제17권2호
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• pp.119-129
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• 2004

3차원 해석법을 이용하여 반경방향으로 비선형적 두께 변분을 가진 두꺼운 원형판과 환형판의 고유진동수를 결정하였다. 수학적으로 2차원적인 전통적 판 이론과는 달리 본 연구에서는 3차원적 등 탄성방정식을 근간으로 하였다. 반경방향, 두께방향, 원주방향으로의 변위 성분인 u/sub s/, u/sub z/, u/sub θ/를 시간에 대해서는 정현적으로, θ에 대해서는 주기적으로, s와 z방향으로는 대수 다항식의 형태로 취하였다. 판의 위치(변형률) 에너지와 운동 에너지를 정식화하고, 리츠법을 이용하여 고유치 문제를 해결하였으며, 진동수의 최소화과정을 통해 엄밀해에 대해서 상위경계치의 진동수를 구하였다. 다항식의 차수를 증가시키면 진동수는 엄밀해에 수렴하게 된다. 판의 최하위 5개의 진동수에 대한 유효숫자 4자리까지의 수렴성 연구가 이루어졌다. 수치결과로 두께가 일정하거나, 선형적 또는 2차 곡선적 변분을 갖는 자유경계의 두꺼운 원형판과 환형판의 무차원 진동수를 제공하였다. 또한 이미 발표된 2차원적인 박판이론에 의한 결과와 본 연구의 3차원 해석에 의한 결과를 서로 비교하였다.

• Smart Structures and Systems
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• 제5권6호
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• pp.591-612
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• 2009

New insights are presented in simplified modeling and analysis of free vibrations of piezoelectric - based smart structures and systems. These consist, first, in extending the wide used piezoelectric-thermal analogy (TA) simplified modeling approach in currently static actuation to piezoelectric free-vibrations under short-circuit (SC) and approximate open-circuit (OC) electric conditions; second, the popular piezoelectric strain induced - potential (IP) simplified modeling concept is revisited. It is shown that the IP resulting frequencies are insensitive to the electric SC/OC conditions; in particular, SC frequencies are found to be the same as those resulting from the newly proposed OC TA. Two-dimensional plane strain (PStrain) and plane stress (PStress) free-vibrations problems are then analyzed for above used SC and approximate OC electric conditions. It is shown theoretically and validated numerically that, for both SC and OC electric conditions, PStress frequencies are lower than PStrain ones, and that 3D frequencies are bounded from below by the former and from above by the latter. The same holds for the modal electro-mechanical coupling coefficient that is retained as a comparator of presented models and analyses.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1999년도 봄 학술발표회 논문집
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• pp.159-168
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• 1999

In seismic analysis, there are two main ways - uniform load method and dynamic analysis, dynamic analysis can be divided into response spectrum analysis and time history analysis. In case of which get the complexion of the vibration with 3-axis of coordinate direction in each mode of free vibration mode happened owing to complication of the shape, 3-dimensional dynamic analysis is recommended to perform as multi-mode spectral analysis in standard specification for highway bridge. The purpose of this study is to understand the dynamic behavior by performing multi-mode seismic analysis according to responses analysis and time history anal)'sis in using record of earthquake. In accordance with the criterion of seismic design as defined in standard specification for highway bridge by using modified records of the El Centre and Coyote Lake earthquake, response spectrum was constructed by using the tripartite logarithmic plot. The 3-span continuous space truss bridge was selected as model of numerical analysis. As the result performed time history analysis and analysis of response spectrum for the model of numerical analysis, the result of time history analysis was slightly larger than that of response spectrum analysis. This coincide with the tendency of the result came from the analysis when using a jagged response spectrum analysis, This coincide with the tendency of the result came from the analysis when using a jagged response spectrum for a single excitation. In the Process of performing these two analysis. response spectrum analysis is more effective than time history analysis in saving times in analyzing data.

• Structural Engineering and Mechanics
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• 제12권2호
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• pp.189-200
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• 2001

This paper presents an experimental modal analysis of perforated rectangular plates in air or in contact with water. The penetration of holes in the plates had a triangular pattern with P/D (pitch to diameter) 2.125, 2.500, 3.000 and 3.750. The plate was clamped along the plate edges by a number of bolts and nuts. The natural frequencies of the perforated plates in air were obtained by the analytical method based on the relation between the reference kinetic and maximum potential energies and compared with the experimental results. Good agreement between the results was found for the natural frequencies of the perforated plates in air. Additionally, it was empirically found that the natural frequencies of the perforated plate in air increase with an increase of P/D, on the other hand, the natural frequencies of the perforated plate in contact with water decrease with an increase of P/D.

• Advances in aircraft and spacecraft science
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• 제3권1호
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• pp.15-28
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• 2016

Although the aircraft industry was the first to use fibre composites, now they are increasingly used in a range of structural applications such as flooring, decking, platforms and roofs. Interlayer delamination is a major failure mode which threatens the reliability of composite structures. Delamination can grow in size under increasing loads with time and hence leads to severe loss of structural integrity and stiffness reduction. Delamination reduces the natural frequency and as a consequence may result in resonance. Hence, the study of the effects of delamination on the free vibration behaviour of multilayer composite structures is imperative. The focus of this paper is to develop a 3D FE model and investigate the free vibration behaviour of fibre composite multilayer sandwich panels with interlayer delaminations. A series of parametric studies are conducted to assess the influence of various parameters of concern, using a commercially available finite element package. Additionally, selected points in the delaminated region are connected appropriately to simulate bolting as a remedial measure to fasten the delamination region in the aim of reducing the effects of delamination. First order shear deformation theory based plate elements have been used to model each sandwich layer. The findings suggest that the delamination size and the end fixity of the plate are the most important factors responsible for stiffness reduction due to delamination damage in composite laminates. It is also revealed that bolting the delaminated region can significantly reduce the natural frequency variation due to delamination thereby improving the dynamic performance.

• Steel and Composite Structures
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• 제39권2호
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• pp.149-158
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• 2021

In this research paper, the free vibrational response of laminated composite plates is investigated using a non-polynomial refined shear deformation theory (NP-RSDT). The most interesting feature of this theory is the parabolic distribution of transverse shear deformations while ensuring the conditions of nullity of shear stresses at the free surfaces of the plate without requiring the Shear correction factor "Ks". A fourth-nodded isoparametric element with four degrees of freedom per node is employed for laminated composite plates. The numerical analysis of simply supported square anti-symmetric cross-ply and angle-ply laminated plate is carried out using a special discretization based on four-node finite element method which four degrees of freedom per node. Several numerical results are presented to show the effect of the coupling parameters of the plate such as the modulus ratios, the thickness ratio and the plate layers number on adimensional eigen frequencies. All numerical results presented using the current finite element method (FEM) is presented in 3D curve form.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 추계학술대회 논문집
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• pp.1081-1084
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• 2002

In this study, we perform 3-D reconstruction of human proximal femur from DICOM files by using voxel mesh algorithm. After 3-D reconstruction, the model converted to Finite Element model which developed for automatically making not only 3-D geometrical model but also FE model from medical image dataset. During this job, trabecular pattern, one of characteristic of human bone can be added to the model by means of giving it's own elastic property calculated from intensity in CT scanned image to the each voxel. And then another model is made from same image dataset which have two material properties - one corresponds to cortical bone, another to trabecular bone. Finally, validity of voxel mesh technique is verified through comparing results of FE analysis, free vibration and stress analysis.