• Structural Engineering and Mechanics
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• 제7권3호
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• pp.259-276
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• 1999

An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters.

• 한국소음진동공학회논문집
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• 제21권8호
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• pp.698-707
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• 2011

이 연구는 유한요소법을 이용하여 집중질량을 갖고 비균질한 지반에 놓은 변단변 후판 구조물에 대한 동적 안정해석이다. 해석을 위하여 유한요소법을 이용하여 해당구조물의 고유진동수와 좌굴하중을 구하여 기존해와 비교하여 프로그램을 검증하였다. 비균질 Pasternak 지반에 놓인 변단면으로 집중질량을 갖는후판의 동적안정 해석을 통하여 판의 불안정 영역이 결정된다. 무차원 Winkler 지반강성은 100, 1000을 적용하였고, 무차원 전단지반강성은 5로 하였다. 그리고 변단면율은 0.25, 1.0, 집중질량비는 0.25, 1.0 그리고 면내응력은 $0.4{\sigma}_{cr}$을 적용하여 해석하였다.

• Interaction and multiscale mechanics
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• 제3권1호
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• pp.95-110
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• 2010

In recent years, study of the static response of pavements to moving vehicle and aircraft loads has received significant attention because of its relevance to the design of pavements and airport runways. The static response of beams resting on an elastic foundation and subjected to moving loads was studied by several researchers in the past. However, most of these studies were limited to steady-state analytical solutions for infinitely long beams resting on Winkler-type elastic foundations. Although the modelling of subgrade as a continuum is more accurate, such an approach can hardly be incorporated in analysis due to its complexity. In contrast, the two-parameter foundation model provides a better way for simulating the underlying soil medium and is conceptually more appealing than the one-parameter (Winkler) foundation model. The finite element method is one of the most suitable mathematical tools for analysing rigid pavements under moving loads. This paper presents an improved solution algorithm based on the finite element method for the static analysis of rigid pavements under moving vehicular or aircraft loads. The concrete pavement is discretized by finite and infinite beam elements, with the latter for modelling the infinity boundary conditions. The underlying soil medium is modelled by the Pasternak model allowing the shear interaction to exist between the spring elements. This can be accomplished by connecting the spring elements to a layer of incompressible vertical elements that can deform in transverse shear only. The deformations and forces maintaining equilibrium in the shear layer are considered by assuming the shear layer to be isotropic. A parametric study is conducted to investigate the effect of the position of moving loads on the response of pavement.

• Structural Engineering and Mechanics
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• 제2권1호
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• pp.95-112
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• 1994

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.681-688
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• 2006

This paper has the object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Finite element analysis of rectangular 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 parameter is varied with 10, $10^2,\;10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0 respectively.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 춘계학술대회논문집
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• pp.794-798
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• 2004

This paper is analysis of stiffened opening thick plate on foundation. 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. In this paper, vibration analysis of rectangular opening thick plate is done by use of Serendipity finite element with 8 nodes by considering shearing strain of plate. And vibration analysis of stiffener is done by used of Timoshenko beam-column element wit 3 nodes. It is shown that natural frequencies depend on not only Winkler foundation parameter but also shear foundation parameter, opening position, opening size, stiffener size.

• 한국농공학회지
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• 제45권4호
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• pp.115-125
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• 2003

Shell structures are widely used in a variety of engineering application, and mathematical solution of shell structures are available only for a few special cases. The solution of shell structure is more complicated when it has such condition as winkler foundation, other problems. In this study many simplified methods (analogy of beam on elastic foudation, finite element method and transfer matrix method) are applied to analyze a hemisphere-cylindrical shell structures on elastic foundation. And the transfer matrix method is extensively used for the structural analysis because of its merit in the theoretical backgroud and applicability. Therefore, this paper presents the analysis of hemisphere-cylindrical shell structure base on the transfer matrix method. The technique is attractive for implementation on a numerical solution by means of a computer program coded in FORTRAN language with a few elements. To demonstrate this fact, it gives good results which compare well with finite element method.

• Structural Engineering and Mechanics
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• 제9권6호
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• pp.519-540
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• 2000

In this study, a new functional based on the Reissner theory, for thick plates on a Winkler foundation is obtained. This functional has geometric and dynamic boundary conditions. In deriving the new functional, the $G{\hat{a}}teaux$ differential is used. This functional which is in polar coordinates is also transformable into the classical potential energy equation. Bending and torsional moments, transverse shear forces, rotations and displacements are the basic unknowns of the functional. Two different sectorial elements are developed with $3{\times}8$ degrees of freedom (SEC24) and $4{\times}8$ degrees of freedom (SEC32). The accuracy of the SEC24 and SEC32 elements together are verified by applying the method to some problems taken from literature.

• 한국농촌건축학회논문집
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• 제16권4호
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• pp.59-66
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• 2014

This paper deals with vibration of plates with concentrated mass on elastic foundation. The object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Free vibration analysis that tapered thick plate in this paper. Finite element analysis of rectangular 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 parameter is varied with 10, $10^2$, $10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0. And the Concentrated Mass is applied as P1, Pc, P2 respectively.

• 한국지진공학회논문집
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• 제16권3호
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• pp.13-22
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• 2012

지반-구조물의 상호작용은 구조물의 동적 해석 및 기초 설계에 있어 지대한 영향을 미침에도 불구하고 그 중요성이 간과되어 왔다. 이는 모델링 과정의 복잡성으로 인해 실무자를 위한 적절한 절차가 미비 하다는 점에서 상당부분 그 이유를 찾을 수 있을 것이다. 본 연구에서는 먼저 구조물의 동적 해석이 필수적으로 요구되는 강진지역인 미국 캘리포니아에 위치한 Cal(IT)2 건물을 대상으로 지반 경계조건을 달리했을 시 해석상의 차이가 어느 정도 나는지를 검토해 보았다. 기초 모델링 기법의 하나인 Beam on Nonlinear Winkler Foundation Model을 Linear Matrix Inequalities Model Reduction 기법을 활용하여 보다 간략하게 사용할 수 있도록 하였다. 이렇게 하여 만들어진 대상 건물의 유한요소 모델과 실재 얻어진 가속도 데이터를 비교하여 제시된 방식을 통해 매우 우수한 해석 결과를 얻을 수 있음을 보였다.