• 대한토목학회논문집
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• 제26권3A호
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• pp.447-455
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• 2006

순수변위 비선형 4절점 쉘요소의 정식화를 제안하여 철근 콘크리트, 강재및 복합재료등 범용 목적의 구조물의 해석에 적합하도록 하였다. 기하강성의 정식은 2차 운동역학적 관계를 이용하여 쉘이 중립면에서 정의되었고 이러한 기하강성은 면내응력, 휨 모멘트와 수직 전단력의 형태로 구성되어 두꺼운 판 및 쉘의 해석에 효과적이다. 가정된 자연 변형률 방법을 사용하여 전단잠김 문제를 제거한 복합 쉘 요소는 얇은 판및 쉘의 경우에도 정확한 해를 구할 수 있다. 콘크리트 경우 소성이론 및 탄소성 파괴역학에 근거한 비탄성 해석이 가능하며 강재경우 폰미스의 항복이론과 이바노브의 항복이론을 이용한 소성해석이 가능하다. 복합 재료의 수직전단 강성 행렬은 평형방정식으로부터 유도하여 구성하였다. 본 연구에서 제안한 쉘 요소는 해석 예제들이 참고문헌과 잘 일치하여 정확성이 입증되었으며 범용목적의 박판구조 해석에 적합한 것으로 사료 되었다.

• 한국전산구조공학회논문집
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• 제19권4호
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• pp.407-418
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• 2006

본 논문에서는 일차전단변형이론(FSDT)을 이용한 복합재료 적층평판의 고정밀 해석기법을 소개한다. 전단수정계수가 자동적으로 포함되도록 횡방향 전단 변형에너지를 혼합변분이론(mixed variational theorem)을 이용하여 개선하였다. 혼합변분이론에서는 변분을 횡방향 응력들에 대해서만 취하였다. 가정된 횡방향 전단응력은 효율적인 고차이론(Cho and Parmerter, 1993)으로부터 구하였다 횡방향 수직응력은 3차 다항식으로 가정하였고, 무전단 응력조건과 평판의 윗면과 아랫면에서의 응력을 만족하는 조건을 부과함으로써 얻었다. 한편, 변위들에 대해서는 일차전단변형이론의 변위장을 사용하였다. 이렇게 해서 얻어진 변형 에너지를 본 논문에서는 EFSDTM3D이라고 명명 하였다. 본 논문에서 개발된 EFSDTM3D는 변위와 응력의 계산에서 고전적인 FSDT와 같은 정도의 계산 효율을 가지면서, 동시에 변위와 응력의 두께방향의 정확도를 면내 방향 응력들에 대한 최소오차자승법에 기초하여 응력 회복 과정을 적용함으로써 개선하였다. 계산된 결과는 고전적인 FSDT, 3차원 탄성해, 그리고 참고문헌 중에서 이용 가능한 결과들과 비교하여 검증하였다.

• Steel and Composite Structures
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• 제29권3호
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• pp.363-377
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• 2018

An efficient and free of shear locking finite element model is developed and employed to study free vibration of tapered bidirectional functionally graded material (BFGM) beams. The beam material is assumed to be formed from four distinct constituent materials whose volume fraction continuously varies along the longitudinal and thickness directions by power-law functions. The finite element formulation based on the first-order shear deformation theory is derived by using hierarchical functions to interpolate the displacement field. In order to improve efficiency and accuracy of the formulation, the shear strain is constrained to constant and the exact variation of the cross-sectional profile is employed to compute the element stiffness and mass matrices. A comprehensive parametric study is carried out to highlight the influence of the material distribution, the taper and aspect ratios as well as the boundary conditions on the vibration characteristics. Numerical investigation reveals that the proposed model is efficient, and it is capable to evaluate the natural frequencies of BFGM beams by using a small number of the elements. It is also shown that the effect of the taper ratio on the fundamental frequency of the BFGM beams is significantly influenced by the boundary conditions. The present results are of benefit to optimum design of tapered FGM beam structures.

• 대한기계학회논문집
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• 제16권2호
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• pp.248-258
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• 1992

Three-dimensional rigid-plastic finite element formulation based on the membrane theory was described and a computer program for large deformation analysis was developed. In the formulation, normal and planar anisotropy of sheet material and rotation of the principal axes of anisotropy was taken into consideration. Sheet metal was assumed to be rigid-plastic material obeying Hill's quadratic yield criterion and its associated flow rule. Deep drawing process, as a preliminary test, for normal anisotropic material was analyzed in order to examine the validity of developed finite element program. The results were consistent with the existing finite element solutions or experimental data. The present study was mainly concerned with the influence of planar anisotropy on deformation behaviour. Finite element analysis and experiment were carried out for the whole process of deep drawing of planar anisotropic material. The computational and experimental results on the shape of ear, strain distribution and punch load were in good agreement.

• 복합신소재구조학회 논문집
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• 제3권3호
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• pp.22-30
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• 2012

This study deals with an enhanced assumed strain (EAS) three-dimensional element for free vibration analysis of laminated composite and sandwich structures. The three-dimensional finite element (FE) formulation based on the EAS method for composite structures shows excellence from the standpoints of computational efficiency, especially for distorted element shapes. Using the EAS FE formulation developed for this study, the effects of side-to-thickness ratios, aspect ratios and ply orientations on the natural frequency are studied and compared with the available elasticity solutions and other plate theories. The numerical results obtained are in good agreement with those reported by other investigators. The new approach works well for the numerical experiments tested, especially for complex structures such as sandwich plates with laminated composite faces.

• Steel and Composite Structures
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• 제4권6호
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• pp.489-507
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• 2004

The flexibility of the connection between steel and concrete largely influences the global behaviour of the composite beam. Therefore the way the connection is modelled is the key issue in its structural analysis. Here we present a new strain-based finite element formulation in which we consider non-linear material and contact models. The computational efficiency and accuracy of the formulation is proved with the comparison of our numerical results with the experimental results of Abdel Aziz (1986) obtained in a full-scale laboratory test. The shear connectors are assumed to follow a non-linear load-slip relationship proposed by Ollgaard et al. (1971). We introduce the notion of the generalized slip, which offers a better physical interpretation of the behaviour of the contact and gives an additional material slip parameter. An excellent agreement of experimental and numerical results is obtained, using only a few finite elements. This demonstrates that the present numerical approach is appropriate for the evaluation of behaviour of planar composite beams and perfect for practical calculations.

• Advances in materials Research
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• 제5권2호
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• pp.107-120
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• 2016

The static analysis of the simply supported functionally graded plate under transverse load by using a new sinusoidal shear deformation theory based on the neutral surface concept is investigated analytically in the present paper. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. The mechanical properties of the FGM plate are assumed to vary continuously through the thickness according to a power law formulation except Poisson's ratio, which is kept constant. The equilibrium and stability equations are derived by employing the principle of virtual work. Results are provided for thick to thin plates and for different values of the gradient index k, which subjected to sinusoidal or uniformly distributed lateral loads. The accuracy of the present results is verified by comparing it with finite element solution. From the obtained results, it can be concluded that the proposed theory is accurate and efficient in predicting the displacements and stresses of functionally graded plates.

• Structural Engineering and Mechanics
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• 제82권3호
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• pp.401-416
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• 2022

The aim of this study is to examine the frictionless double receding contact problem for two functionally graded (FG) layers pressed with a uniformly distributed load and resting on a homogeneous half plane (HP) using analytical and numerical methods. The FG layers are made of a non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layers and FG layer-HP interface is frictionless. The body force of the FG layers and homogeneous HP are ignored in the study. Firstly, an analytical solution for the contact problem has been realized using the theory of elasticity and the Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using the ANSYS package program based on FEM. Numerical results for contact lengths and contact pressures between FG layers and FG layer-HP were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio, and the heights of the FG layers for both methods. The results obtained using FEM were compared with the results found using the analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

• Advances in Computational Design
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• 제2권3호
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

• 한국전산구조공학회논문집
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• 제13권4호
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• pp.449-459
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• 2000

기존의 Mindlin이론을 바탕으로 한 감절점 쉘 요소는 두께가 두꺼운 쉘 구조를 해석할 경우 매우 좋은 결과가 얻어지는 것으로 알려져 있다. 그러나 두께가 얇은 쉘의 경우 전단구속 및 막구속 현상으로 인해 요소의 강성이 과대하게 평가되는 것으로 나타났다. 이러한 문제를 해결하기 위해 본 연구에서는 서로 다른 두 가지 막 및 전단 구속 해결방법을 조합하여 쉘 요소에 적용하였다. 첫 번째 요소는 전단 변형률에 가정된 전단변형률을 적용하였고, 막 변형률에는 감차적분법을 적용하였다. 두 번째 요소의 경우, 막 변형률과 전단 변형률 모두에 가정된 전단 변형률을 적용하여 쉘 구조해석을 수행하였다. 여러 가지 수치 해석을 수행한 결과, 두 가지 쉘 요소가 빠른 수렴성을 가지고 있는 것으로 나타났으며, 막 구속과 전단 구속 현상이 제거된 것을 나타났다.