• Journal of the Earthquake Engineering Society of Korea
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• v.28 no.4
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• pp.165-170
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• 2024

This study investigated the impact of soil-structure interaction on multi-degree-of-freedom structures using the shallow-foundation Winkler model, known as the BNWF model. The model's period was determined through eigenvalue analysis and compared to results obtained from FEMA's formula. Results indicated that considering the soil, the structure's period increased by up to 8.7% compared to the fixed-base model, aligning with FEMA's calculations. Furthermore, with adequate ground acceleration, roof displacement increased by 3.4% to 3.8%, while base shear decreased by 4% to 10%. However, roof displacement and base shear increased in some earthquake scenarios due to spectral shape effects in regions with extended structural periods. Foundation damping effects, determined through the foundation's moment-rotation history, grew with higher ground acceleration. This suggests that accounting for period elongation and foundation damping can enhance the seismic design of multi-degree-of-freedom structures.

• Advances in nano research
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• v.17 no.4
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• pp.315-321
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• 2024

Here, vibration of double walled carbon nanotubes is evaluated using Euler-Bernoulli beam model. These tubes are placed on Winkler elastic foundation. A simple Galerkin's approach is presented to solve the tube governing equations and for extracting of vibration eigen-frequencies of double walled carbon nanotubes. The procedure is easy for computer programming with various combinations of boundary conditions. The frequency influence is observed with different parameters. Effects of Winkler foundation versus frequencies with varying lengths is examined for a number of boundary conditions. It is noticed that the frequencies are lower for higher length on increasing the Winkler foundation. The frequencies of clamped-clamped are higher than that of clamped simply supported end condition. The obtained results are compared with some experimental ones.

• Geomechanics and Engineering
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• v.32 no.1
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• pp.69-84
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• 2023

This paper proposes a novel frame element on Winkler-Pasternak foundation for analysis of a non-ductile reinforced concrete (RC) member resting on foundation. These structural members represent flexural-shear critical members, which are commonly found in existing buildings designed and constructed with the old seismic design standards (inadequately detailed transverse reinforcement). As a result, these structures always experience shear failure or flexure-shear failure under seismic loading. To predict the characteristics of these non-ductile structures, efficient numerical models are required. Therefore, the novel frame element on Winkler-Pasternak foundation with inclusion of the shear-flexure interaction effect is developed in this study. The proposed model is derived within the framework of a displacement-based formulation and fiber section model under Timoshenko beam theory. Uniaxial nonlinear material constitutive models are employed to represent the characteristics of non-ductile RC frame and the underlying foundation. The shear-flexure interaction effect is expressed within the shear constitutive model based on the UCSD shear-strength model as demonstrated in this paper. From several features of the presented model, the proposed model is simple but able to capture several salient characteristics of the non-ductile RC frame resting on foundation, such as failure behavior, soil-structure interaction, and shear-flexure interaction. This confirms through two numerical simulations.

• Advances in nano research
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• v.17 no.3
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• pp.197-211
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• 2024

This work investigates the thermo-mechanical vibration frequencies of an embedded composite nano-beam restrained with elastic springs at both ends. Composite nanobeam consists of a matrix and short fibers as reinforcement elements placed inside the matrix. An approach based on Fourier sine series and Stokes' transform is adopted to present a general solution that can examine the elastic boundary conditions of the short-fiber-reinforced nanobeam considered with the Halpin-Tsai model. In addition to the elastic medium effect considered by the Winkler model, the size effect is also considered on the basis of nonlocal strain gradient theory. After creating an eigenvalue problem that includes all the mentioned parameters, this problem is solved to examine the effects of fiber and matrix properties, size parameters, Winkler stiffness and temperature change. The numerical results obtained at the end of the study show that increasing the rigidity of the Winkler foundation, the ratio of fiber length to diameter and the ratio of fiber Young's modulus to matrix Young's modulus increase the frequencies. However, thermal loads acting in the positive direction and an increase in the ratio of fiber mass density to matrix mass density lead to a decrease in frequencies. In this study, it is clear from the eigenvalue solution calculating the frequencies of thermally loaded embbeded short-fiber-reinforced nanobeams that changing the stiffness of the deformable springs provides frequency control while keeping the other properties of the nanobeam constant.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.69-86
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• 2007

A four-noded plate bending quadrilateral (PBQ4) and an eight-noded plate bending quadrilateral (PBQ8) element based on Mindlin plate theory have been adopted for modeling the thick plates on elastic foundations using Winkler model. Transverse shear deformations have been included, and the stiffness matrices of the plate elements and the Winkler foundation stiffness matrices are developed using Finite Element Method based on thick plate theory. A computer program is coded for this purpose. Various loading and boundary conditions are considered, and examples from the literature are solved for comparison. Shear locking problem in the PBQ4 element is observed for small value of subgrade reaction and plate thickness. It is noted that prevention of shear locking problem in the analysis of the thin plate is generally possible by using element PBQ8. It can be concluded that, the element PBQ8 is more effective and reliable than element PBQ4 for solving problems of thin and thick plates on elastic foundations.

• Steel and Composite Structures
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• v.27 no.2
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• pp.177-184
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• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like structures on elastic foundations by using classic plate theory. Multi-material optimal topology and shape are produced as an alternative to provide reasonable material assignments based on stress distributions. Multi-material topology optimization problem is solved through an alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to thin plate potential strain energy are derived in terms of multiphase design variables and Winkler-Pasternak parameters considering elastic foundation to apply to the current topology optimization. Numerical examples verify efficiency and diversity of the present topology optimization method of elastic thin plates depending on multiple materials and Winkler-Pasternak parameters with the same amount of volume fraction and total structural volume.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.27-34
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• 2002

In the case of reinforced concrete structures, the knowledge of load transfer in the long-term behavior analysis considering construction sequence is very important. Even though long-term behavior of concrete structures has been widely studied, the studies on the time-dependent axial force variation of shore have been scarce to date. In order to investigate the shore behaviors under actual construction conditions, a three-story test frame was constructed on a construction site. The entire construction schedule for the test frame was made to follow the schedule of an actual three-story frame. To analyze the data collected from the test frame, an analysis method based on the Winkler foundation model was developed. This analysis method accurately Predicts the time-dependent behavior of shore. The analysis results coincide well with those obtained by the Midas GENw program

• Advances in materials Research
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• v.7 no.3
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• pp.163-174
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• 2018

This article studies the free and forced vibrations of the carbon nanotubes CNTs embedded in an elastic medium including thermal and dynamic load effects based on nonlocal Euler-Bernoulli beam. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The non-local Euler-Bernoulli beam model predicts lower resonance frequencies. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the temperature change on the non-dimensional natural frequency.

• Geomechanics and Engineering
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• v.24 no.4
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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.

• Journal of the Korean GEO-environmental Society
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• v.15 no.9
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• pp.47-58
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• 2014

This study explores methods for modeling the foundation-seabed interaction needed for the load analysis of an offshore wind energy system. It comprises the comparison study of foundation design load analyses for NREL 5 MW turbine according to various soil-foundation interaction models by conducting the load analysis with GH-Bladed, analysis software for offshore wind energy systems. Furthermore, the results of the aforementioned load analysis were applied to foundation analysis software called L-Pile to conduct a safety review of the foundation cross-section design. Differences in the cross-section of a monopile foundation were observed based on the results of the fixed model, winkler spring and coupled spring models, and the analysis of design load cases, including DLC 1.3, DLC 6.1a, and DLC 6.2a. Consequently, under all design load conditions, the diameter and thickness of the monopile foundation cross-section were found to be 7 m and 80 mm, respectively, using the fixed and coupled spring models; the results of the analysis conducted using the winkler spring model showed that the diameter and thickness of the monopile foundation cross-section were 5 m and 60 mm, respectively. The study found that the soil-foundation interaction modeling method had a significant impact on the load analysis results, which determined the cross-section of a foundation. Based on this study, it is anticipated that designing an offshore wind energy system foundation taking the above impact into account would reduce the possibility of a conservative or unconservative design of the foundation.