• Structural Engineering and Mechanics
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• v.38 no.5
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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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• v.42 no.1
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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.

• Journal of Korean Society of Steel Construction
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• v.15 no.3
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• pp.291-298
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• 2003

Recently, as the size of buildings structure becomes large increases, their mat area of building structure is supported or by an inhomogeneous foundation. This paper presents a vibration analysis on thick plates subjected to in-plane force is presented in this paper. The rectangular plate is isotropic, homogeneous, and composed of a linearly elastic material. A vibration analysis of the rectangular thick plate iwas done by useing ofarectangular finite element with 8 nodes and 9 nodes. In this study, the foundation was idealized as a Pasternak foundation model. A Pasternak foundation haves a shear layer on Winkler's model, which idealizes the foundation as a vertical spring. In order tTo analysze the vibration of a plate supported on by an inhomogeneous Pasternak foundation, the value of the Winkler foundation parameter of the central and border zones of the plate awere chosen as WFP1 and WFP2. (fFigure 4.). The Winkler foundation parameter of WFP1 and WFP2 is varied from 0 to 10, $10^2$, and $10^3$ and the shear foundation parameters is were 0, 5, and 10. The ratio of the in-plane force to the critical load iwas applied as 0.4 to 0.8

• Journal of the Korean GEO-environmental Society
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• v.14 no.4
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• pp.59-66
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• 2013

The foundation of offshore wind energy system is generally assumed to be fixed-ended in system analysis for the convenience of calculation and, correspondingly, it might lead a conservative design. If soil-foundation interaction get involved with the analysis, the system characteristics such as natural frequency, shear force, moment and displacement are expected to differ from those of fixed-ended case. In this study, the analysis have been conducted to identify how the response of offshore wind turbine varies upon considering the foundation flexibility with soil-foundation interaction. The model taking account of the flexibility of foundation was compared with fixed-ended model at the seabed. The flexibilities of foundation were obtained by coupled spring model at the seabed and Winkler Spring Model with soil depth. As a result, the first mode of the whole system with the Winkler Spring Model was decreased relative to that with the fixed-ended model. The results showed that the effect of foundation flexibility should be considered when designing the offshore wind energy system.

• Computational Structural Engineering
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• v.1 no.1
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• pp.103-112
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• 1988

In this study, the earthquake response of building structures with foundation uplift was investigated. The Winkler foundation model and two-spring model are widely used to represent the interaction between foundation mat and soil. While the analysis using the Winkler foundation model results in more accurate prediction, it requires a complex procedure and longer computation time. In this study, an equivalent two-spring model(S model) is proposed. The S model can represent the Winkler foundation model more accurately and the analysis using the S model is simpler and more effective. The S model is derived by simplifying the nonlinear moment-rotation relationship of foundation mat. The dynamic responses predicted by the S model gave a good agreement to those of the Winkler foundation model.

• Steel and Composite Structures
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• v.35 no.1
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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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• v.50 no.1
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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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.29 no.2
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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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• v.7 no.2
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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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• v.9 no.6
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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.