• Structural Engineering and Mechanics
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• 제38권5호
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• pp.573-592
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• 2011

Comprehensive and accurate analysis of a finite foundation beam is a challenging engineering problem and an important subject in foundation design. One of the limitation of the traditional Winkler elastic foundation model is that the model neglects the effect of the interface resistance between the beam and the underneath foundation soil. By taking the beam-soil interface resistance into account, a deformation governing differential equation for a finite beam resting on the Winkler elastic foundation is developed. The coupling effect between vertical and horizontal displacements is also considered in the presented method. Using Galerkin method, semi-analytical solutions for vertical and horizontal displacements, axial force, shear force and bending moment of the beam under symmetric loads are presented. The influences of the interface resistance on the behavior of foundation beam are also investigated.

• Structural Engineering and Mechanics
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• 제42권1호
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• pp.39-53
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• 2012

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called "natural" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

• 한국강구조학회 논문집
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• 제15권3호
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• pp.291-298
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• 2003

최근 건축물의 대형화로 구조물의 기초는 비균질지반에 지지된다. 본 연구는 면내력을 받는 후판의 진동해석을 한 것이다. 장방 형판은 등방, 균질의 선형 탄성재료로 구성되었다. 장방형 후판의 진동해석은 8절점과 9절점을 이용한 장방형 유한요소를 사용하여 행하였다. 본 연구에서 기초를 수직스프링으로 이상화한 Winkler지반에 전단지반층을 추가한 Pasternk지반으로 이상화하였다. 지반의 강성을 달리한 비균질 Pasternak지반에 지지된 판을 해석하기 위해 중앙부분과 가장자리 부분의 Winkler지반계수를 WFP1과 WFP2로 선택하였다. (그림 4.) Winkler지반계수 WFP1과 WFP2는 0, 10, $10^2$, $10^3$으로 변환시키고 전단지반강성은 0, 5, 10으로 하였다. 후판의 좌굴응력(${\sigma}_{cr}$)에 대한 면내력의 비는 각각 0.4, 0.8에 대해 적용하였다.

• 한국지반환경공학회 논문집
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• 제14권4호
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• pp.59-66
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• 2013

현재 해상풍력시스템의 거동 해석은 지반을 고정단으로 가정한 채로 수행하는 것이 일반적이라고 알려져 있다. 지반의 연성이 고려될 경우 해상풍력시스템의 고유 주파수뿐만 아니라 기초구조물 설계를 위한 하중 또한 변화할 것이라고 예상되나, 이에 대한 연구는 아직 미미한 실정이다. 이에 따라, 본 연구는 기초구조물의 연성을 고려하여 시스템 해석을 수행할 경우 시스템의 고유 주파수와 하중의 변화를 살펴보기 위한 목적으로 수행되었다. 해상풍력시스템의 해석을 위하여 풍력발전기 해석프로그램인 GH-Bladed를 활용하였으며, 해석 시에는 coupled spring 모델과 winkler spring 모델을 활용하여 기초구조물의 연성효과를 고려하였다. 해석결과 지반의 연성 고려방안 중 winkler spring 모델을 적용하여 산정한 시스템 1차모드 및 하중이 지반을 고정단으로 가정한 해석결과와 비교하여 감소하는 것을 확인하였으며, 이를 통하여 지반의 연성이 시스템의 거동에 미치는 영향을 관찰하였다.

• 전산구조공학
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• 제1권1호
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• pp.103-112
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• 1988

본 연구에서는 기초의 uplift의 영향을 고려하여 지진하중에 대한 건축구조물의 동적 거동을 예측하는 효율적인 방법을 제안하였다. 기초와 지반의 관계에 대한 모델에는 Winker 모델과 Two-Spring 모델이 있다. Winker 모델에 의한 해석방법은 정확하기는 하나 계산 시간이 오래 걸리고 복잡하다는 단점이 있다. 본 연구에서 Winker 모델을 보다 정확하게 나타낼 수 있고 해석이 간편하며 효율적인 등가 Two-Spring 모델(S-모델)을 제안하였다. S 모델은 기초에 정적하중이 작용했을 때의 기초 중앙의 모멘트와 회전각의 비선형 관계를 간단한 5개의 선형적인 관계로 나타냄으로써 유도되며, S모델에 의한 동적해석 결과는 Winker 모델에 의한 해석 결과와 잘 일치하였다.

• Steel and Composite Structures
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• 제35권1호
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• pp.129-145
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• 2020

In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.

• Structural Engineering and Mechanics
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• 제50권1호
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• pp.53-71
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• 2014

A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated.

• 한국농공학회지
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• 제29권2호
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• pp.39-52
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• 1987

This study was to investigate the effects of soil-structure relative stiffness on the structural characteristics of the cylindrical tank supported by soil. A standard example model of the farm silo rested on the Winkler's subsoil model was used for the analysis of soil-structure coupled system. In this paper, Winkler's constants 4,15 and l00kg/cm$^2$/cm were considered and the bottom plate thicknesses of the farm silo 20, 30, 50,100 and 150cm were adopted. For the given model the effects of bottom plate thickness were the most conspicuous at weakest Winkler's constant 4kg/ cm$^2$/cm. While when Winkler's constant is l00kg/cm$^2$/cm, the effect of the bottom plate thickness is almost negligible. On the other hand, when the bottom plate thickness is more than 100cm, the effects of elastic foundation were aknost disappeared. In design practice, it is hoped that the thicknesses of bottom plate should be determined reasonably because of it's considerable effect on the structural characteristics as the lOOcm thickness of bottom plate will not be practical value in usual sites.

• Advances in nano research
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• 제7권2호
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• pp.89-98
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• 2019

In this work, the thermal buckling characteristics of zigzag single-walled boron nitride (SWBNNT) embedded in a one-parameter elastic medium modeled as Winkler-type foundation are investigated using a nonlocal first-order shear deformation theory (NFSDT). This model can take into account the small scale effect as well as the transverse shear deformation effects of nanotubes. A closed-form solution for nondimensional critical buckling temperature is obtained in this investigation. Further the effect of nonlocal parameter, Winkler elastic foundation modulus, the ratio of the length to the diameter, the transverse shear deformation and rotary inertia on the critical buckling temperature are being investigated and discussed. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the thermal buckling properties of boron nitride nanotubes.

• Coupled systems mechanics
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• 제9권6호
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• pp.499-519
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• 2020

The effect of porosity on the thermo-mechanical behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper using new refined hyperbolic shear deformation plate theory. Both even and uneven distribution of porosity are taken into account and the effective properties of FG plates with porosity are defined by theoretical formula with an additional term of porosity. The present formulation is based on a refined higher order shear deformation theory, which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the FG plate and takes into account the various distribution shape of porosity. The elastic foundation is described by the Winkler-Pasternak model. Anew modified power-law formulation is used to describe the material properties of FGM plates in the thickness direction. The closed form solutions are obtained by using Navier technique. The present results are verified in comparison with the published ones in the literature. The results show that the dimensionless and stresses are affected by the porosity volume fraction, constituent volume fraction, and thermal load.