• 한국해안해양공학회지
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• 제11권4호
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• pp.231-237
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• 1999

다절점 케이블요소를 이용하여 조류하중을 받는 해양 케이블의 자유진동해석을 수행한다. 등매개 곡선 케이블요소(isoparametric cable element)의 접선강성행렬과 질량행렬을 유도하고, 하중증분법을 이용하여 지점 변위를 일으키고 자중, 부력, 그리고 조류력을 받는 케이블의 초기평형 상태를 결정한다. 초기의 정적평형상태를 기준으로 부가질량을 고려한 해양케이블의 자유진동해석을 수행한다. 수중케이블의 자유진동해석을 통하여 얻은 해석결과와 기존의 문헌의 결과를 비교, 검토함으로써 본 논문에서 제시한 이론 및 해석방법의 타당성을 입증한다.

• Advances in nano research
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• 제13권4호
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• pp.351-368
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• 2022

Recently, promising structural technologies like multi-function, ultra-load bearing capacity and tailored structures have been put up for discussions. Finite Element (FE) modelling is probably the best-known option capable of treating these superior properties and multi-domain behavior structures. However, advanced materials such as Functionally Graded Material (FGM) and nanocomposites suffer from problems resulting from variable material properties, reinforcement aggregation and mesh generation. Motivated by these factors, this research proposes a unified shape function for FGM, nanocomposites, graded nanocomposites, in addition to traditional isotropic and orthotropic structural materials. It depends not only on element length but also on the beam's material properties and geometric characteristics. The systematic mathematical theory and FE formulations are based on the Timoshenko beam theory for beam structure. Furthermore, the introduced element achieves C1 degree of continuity. The model is proved to be convergent and free-off shear locking. Moreover, numerical results for static and free vibration analysis support the model accuracy and capabilities by validation with different references. The proposed technique overcomes the issue of continuous properties modelling of these promising materials without discarding older ones. Therefore, introduced benchmark improvements on the FE old concept could be extended to help the development of new software features to confront the rapid progress of structural materials.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1990년도 봄 학술발표회 논문집
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• pp.12-17
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• 1990

Stepped bean with immovable ends for large amplitude of vibration including effects of longitudinal displacement, shear deformation and rotary inertia is investigated for free and forced vibration using finite element method. Modified harmonic force matrix is introduced for analysis of vibration with finite amplitude of the stepped beam under uniform hamonic loading and beam with nonuniform harmonic loading. Numerical examples of stepped beam with various support conditions are analysed for deflections and natural frequencies. Results show that the proposed method is valid and efficient.

• 동력기계공학회지
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• 제21권2호
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• pp.70-76
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• 2017

When Timoshenko arcs considering the shear deformation and rotatory inertia have elastic supports, the authors analyze in-plane free vibration of them by the transfer influence coefficient method. This method finds the natural frequencies of them using the transfer of influence coefficient after obtaining the transfer matrix of arc element from numerical integration of the differential equations governing the vibration of arc. In this study, two computer programs were made by the transfer influence coefficient method and the transfer matrix method for analyzing free vibration of Timoshenko arcs. From numerical results of four computational models, we confirmed that the transfer influence coefficient method is a reliable method when analyzing the free vibration of Timoshenko arcs. In particular, the transfer influence coefficient method is a effective method when analyzing the free vibration of arcs with rigid supports.

• Steel and Composite Structures
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• 제30권6호
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• pp.493-516
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• 2019

This paper is dedicated to nonlinear static and free vibration analysis of Uniform Distributed Carbon Nanotube Reinforced Composite (UD-CNTRC) structures under in-plane loading. The authors have suggested an efficient six-node triangular element. Mixed Interpolation of Tensorial Components (MITC) approach is employed to alleviate the membrane locking phenomena. Moreover, the behavior of the well-known LST element is considerably improved by applying an additional linear interpolation on the strain fields. Based on the rule of mixture, the properties of CNTRC are obtained. In this study, only the uniform distributed CNTs are employed through the thickness direction of element. To achieve the natural frequencies and shape modes, the eigenvalue problem is also solved. Using Total Lagrangian Principles, large amplitude free vibration is considered based on the first normalized mode shape of structure. Different well-known plane problem benchmarks and some proposed ones are studied to validate the accuracy and capability of authors' formulations. In addition, the effects of length to the height ratio of beam, CNT's characteristics, support conditions and normalized amplitude parameter on the linear and nonlinear vibration parameters are investigated.

• Structural Engineering and Mechanics
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• 제68권6호
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• pp.721-733
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• 2018

The modal frequency responses of functionally graded (FG) sandwich doubly curved shell panels are investigated using a higher-order finite element formulation. The system of equations of the panel structure derived using Hamilton's principle for the evaluation of natural frequencies. The present shell panel model is discretised using the isoparametric Lagrangian element (nine nodes and nine degrees of freedom per node). An in-house MATLAB code is prepared using higher-order kinematics in association with the finite element scheme for the calculation of modal values. The stability of the opted numerical vibration frequency solutions for the various shell geometries i.e., single and doubly curved FG sandwich structure are proven via the convergence test. Further, close conformance of the finite element frequency solutions for the FG sandwich structures is found when compared with the published theoretical predictions (numerical, analytical and 3D elasticity solutions). Subsequently, appropriate numerical examples are solved pertaining to various design factors (curvature ratio, core-face thickness ratio, aspect ratio, support conditions, power-law index and sandwich symmetry type) those have the significant influence on the free vibration modal data of the FG sandwich curved structure.

• Smart Structures and Systems
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• 제16권5호
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• pp.853-872
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• 2015

Numerical analysis of large amplitude free vibration behaviour of laminated composite spherical shell panel embedded with the piezoelectric layer is presented in this article. For the investigation purpose, a general nonlinear mathematical model has been developed using higher order shear deformation mid-plane kinematics and Green-Lagrange nonlinearity. In addition, all the nonlinear higher order terms are included in the present mathematical model to achieve any general case. The nonlinear governing equation of freely vibrated shell panel is obtained using Hamilton's principle and discretised using isoparametric finite element steps. The desired nonlinear solutions are computed numerically through a direct iterative method. The validity of present nonlinear model has been checked by comparing the responses to those available published literature. In order to examine the efficacy and applicability of the present developed model, few numerical examples are solved for different geometrical parameters (fibre orientation, thickness ratio, aspect ratio, curvature ratio, support conditions and amplitude ratio) with and/or without piezo embedded layers and discussed in details.

• Structural Engineering and Mechanics
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• 제21권3호
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• pp.315-332
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• 2005

The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares interpolation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this interpolation the obtained shape functions do not fulfill the interpolation conditions, which causes additional numerical effort for the application of the boundary conditions. In this paper a new weighting function is presented, which was designed for meshless shape functions to fulfill these essential conditions with very high accuracy without any additional effort. Furthermore this interpolation gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than existing weighting function types.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.1033-1049
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• 2014

The free vibration of functionally graded material (FGM) beams on an elastic foundation and spring supports is investigated. Young's modulus, mass density and width of the beam are assumed to vary in thickness and axial directions respectively following the exponential law. The spring supports are also taken into account at both ends of the beam. An analytical formulation is suggested to obtain eigen solutions of the FGM beams. Numerical analyses, based on finite element method by using a beam finite element developed in this study, are performed in order to show the legitimacy of the analytical solutions. Some results for the natural frequencies of the FGM beams are given considering the effect of various structural parameters. It is also shown that the spring supports show the greatest effect on the natural frequencies of FGM beams.

• Structural Engineering and Mechanics
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• 제85권1호
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• pp.135-145
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• 2023

This study presents the free vibrational responses of bi-directional axially graded cylindrical shell panels using 3D graded finite element approximation under a temperature field. The cylindrical shell panel is graded in two directions and made of metal-ceramic materials. To extract material properties, the Voigt model is combined with a Power-law material distribution. Convergence and validation studies are performed on the developed computational model to ensure its accuracy and effectiveness. Furthermore, a parametric study is performed to evaluate the developed model, which demonstrates that geometrical parameters, imperfect materials (porosity), support conditions, and surface temperature all have a significant impact on the free vibration responses of a bi-directional axially graded cylindrical shell panel in a thermal environment.