• 한국소음진동공학회논문집
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• 제13권12호
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• pp.947-955
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• 2003

This research analyzes the dynamic stability of stiffened plates on elastic foundations using the finite element method. For analyzing the stiffened plates, both the Mindlin plate theory and Timoshenko beam-column theory were applied. In application of the finite element method, 8-nodes serendipity element system and 3-nodes finite element system were used for plate and beam elements, respectively Elastic foundations were modeled as the Pasternak foundations in which the continuity effect of foundation is considered. In order to verify the theory of this study, solutions obtained by this analysis were compared with the classical solutions in open literature and experimental solutions. The dynamic stability legions of stiffened plates on Pasternak foundations were determined according to changes of in-plane stresses, foundation parameters and dimensions of stiffener.

• Journal of Mechanical Science and Technology
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• 제20권4호
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• pp.467-472
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• 2006

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Pasternak foundation and Euler-Bernoulli beam on Pasternak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated.

• 한국전산구조공학회논문집
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• 제17권4호
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• pp.351-363
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• 2004

비보존력을 받는 보-부재의 질량행렬, 탄성강도행릴, circulatory비보존력의 방향변화로 인한 load correction강도행력, 그리고 Winkler 및 Pasternak지반강도행렬을 고려한 운동방정식을 유도하고 divergence 및 flutter에 의한 안정성 해석을 수행한다. 또한 내적 및 외적 감쇠계수를 운동방정식에 포함시킴으로써 감쇠효과를 고려하고, 2차 고유치문제의 해법(quadratic eigen problem solution)을 적용하여 flutter에 미치는 영향을 조사한 후, Beck's column, Leipholz's column 및 Hauger's column에 대하여 비보존력의 방향파라미터 ${\alpha}$에 대한 임계하중의 영향, 내적 및 외적 감쇠계수 및 Winkler 및 Pasternak지반에 의한 임계하중의 영향을 각각 조사한다.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.151-158
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• 2005

본 연구에서는 유한요소법을 이용하여 Pasternak 지반 위에 놓인 보강판의 고유치해석을 수행하였다. 보강판 해석은 Mindlin 판 이론과 Timoshenko 보-기둥 이론을 적용하여 해석하였으며, 유한요소법 적용시 판요소는 8절점 Serendipity 요소계를, 보요소는 3절점 유한요소를 적용하였다. 탄성지반은 지반의 연속성을 고려한 Pasternak 지반으로 모형화하였다. 본 연구의 타당성을 검증하기 위하여 이 연구의 결과를 문헌, 실험 및 SAP 2000의 결과와 비교하였다. 이 연구의 결과로 문헌 해가 존재하지 않는 Pasternak 지반 위에 놓인 보강판의 지반 변수의 변화 및 보강재 크기에 따른 고유진동수를 산정하였다.

• Geomechanics and Engineering
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• 제24권4호
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• pp.371-388
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• 2021

A novel flexibility-based beam-foundation model for inelastic analyses of beams resting on foundation is presented in this paper. To model the deformability of supporting foundation media, the Winkler-Pasternak foundation model is adopted. Following the derivation of basic equations of the problem (strong form), the flexibility-based finite beam-foundation element (weak form) is formulated within the framework of the matrix virtual force principle. Through equilibrated force shape functions, the internal force fields are related to the element force degrees of freedom. Tonti's diagrams are adopted to present both strong and weak forms of the problem. Three numerical simulations are employed to assess validity and to show effectiveness of the proposed flexibility-based beam-foundation model. The first two simulations focus on elastic beam-foundation systems while the last simulation emphasizes on an inelastic beam-foundation system. The influences of the adopted foundation model to represent the underlying foundation medium are also discussed.

• Structural Engineering and Mechanics
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• 제34권3호
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• pp.319-334
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• 2010

The dynamic response of a finite Bernoulli-Euler beam resting on a tensionless Pasternak foundation and subjected to a concentrated harmonic load is investigated in this study. This load may be applied at the center of the beam, or it may be offset from the center. Since the elastic foundation is assumed to be tensionless, the beam may lift off the foundation, resulting in contact and non-contact regions in the system. An analytical/numerical solution is obtained from the governing equations of the contact and non-contact regions to determine the coordinates of the lift-off points. Although there is no nonlinear term in the equations, the problem appears to be nonlinear since the contact regions are not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The results, which represent the symmetric and asymmetric responses of the beam, are presented graphically in this work. They illustrate the effects of the forcing frequency and the beam length on the extent of the contact regions and displacements.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.797-801
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• 2003

This paper has the object of investigating natural frequencies of opening thick plates on Pasternak foundation by means of finite element method and providing Kinematic design data for mat of building structures. Vibration analysis that opening plate subjected to In-plane stress is presented in this paper. Finite element analysis of rectangular opening plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on Pasternak foundation, the Winkler foundation parameter is varied with 0, 10, 102, 103 and the shear foundation parameter is 0, 5, 10, 15. The ratio of In-plane force to critical load is applied as 0.2, 0.8, respectively. This paper analyzed varying opening Position and opening size.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.894-897
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• 2004

This paper has the object of investigating dynamic stability of opening thick plates on Pasternak foundation by means of finite element method and providing Kinematic design data for mat of building structures. Finite element analysis of Tapered Thick plate is done by use of rectangular (mite element with 8-nodes. In order to analysis plate which is supported on Pasternak foundation, the Winkler foundation parameter is varied with $10^2,\;10^3$ and the shear foundation parameter is 5, 10. The ratio of In-plane force to critical load is applied as 0.4, 0.6, respectively. This paper analyzed varying Tapered Ratio.

• Smart Structures and Systems
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• 제16권1호
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• pp.81-100
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• 2015

This paper presents nonlinear analysis of an arbitrary functionally graded circular plate integrated with two functionally graded piezoelectric layers resting on the Winkler-Pasternak foundation. Geometric nonlinearity is considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential is assumed as a quadratic function along the thickness direction. After derivation of general nonlinear equations, as an instance, numerical results of a functionally graded material integrated with functionally graded piezoelectric material obeying two different functionalities is investigated. The effect of different parameters such as parameters of foundation, non homogenous index and boundary conditions can be investigated on the mechanical and electrical results of the system. A comprehensive comparison between linear and nonlinear responses of the system presents necessity of this study. Furthermore, the obtained results can be validated by using previous linear and nonlinear analyses after removing the effect of foundation.

• 한국소음진동공학회논문집
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• 제17권9호
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• pp.835-846
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• 2007

이 논문은 Pasternak 지반으로 지지된 변화폭 원호형 띠기초의 휨 자유진동에 관한 연구이다. 단면폭은 띠기초의 중앙점을 중심으로 대칭 일차 함수를 갖는 변화폭으로 선정하였다. 이 연구에서 지반은 전단층을 갖는 탄성지반인 Pasternak 지반으로 모형화 하였고 회전관성과 전단변형을 고려한 곡선 띠기초의 자유진동을 지배하는 상미분방정식을 유도하였다. 이 상미분방정식을 수치해석하여 고유진동수 및 진동형을 산출하였다. 수치해석 예에서는 회전-회전, 회전-고정 및 고정-고정의 3개의 지점조건을 고려하였다. 띠기초의 무차원 변수들이 고유진동수에 미치는 영향을 분석하였다.