Generalized foundation Timoshenko beam and its calculating methods

Xia, Guiyun

doi:10.1007/s00419-021-02090-1

Cited by 5 publications

(2 citation statements)

References 39 publications

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“…Ninik et al [21] proposed an embedded beam formulation for discrete independent finite element (FE) analysis of pile foundations or rock anchors interacting with the surrounding soil in geotechnical and tunnelling engineering. Xia et al [22] derived that the lateral deflection of the generalized foundation Timoshenko beam is more sensitive to the compressive stiffness of the Winkler foundation than to the stiffness of the shear layer and rotating springs of the foundation. Horizontal interfacial friction due to foundation adhesion has the same effect as foundation cohesion.…”

Section: Introductionmentioning

confidence: 99%

Large Deformation Settlement Series Solution and Numerical Simulation for Underpass Project Track

Chen

Peng

2023

Applied Sciences

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The settlement of track in a railroad underpass project was studied by theoretical analysis and numerical simulation, based on the model of winkle beam on elastic foundation. Taking the settlement of roadbed as a nonlinear boundary condition, the control differential equation of the track large deformation settlement was established and solved by the Fourier series method; the numerical solution was obtained by establishing a numerical model based on an actual project and compared and analyzed with the series solution and cosine function solution. The correlation coefficients of the track settlement curves obtained from the series solution and the numerical solution were higher than those of the cosine function solution while the numerical solution with the maximum track settlement difference was only 0.8% of the maximum settlement of the track numerical solution. The accuracy of the series solution method is higher in this paper, and the track settlement curve obtained from theoretical calculation reflects and predicts the track settlement well when the track settlement cannot be measured directly.

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Section: Introductionmentioning

confidence: 99%

Large Deformation Settlement Series Solution and Numerical Simulation for Underpass Project Track

Chen

Peng

2023

Applied Sciences

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“…However, practical engineering often encounters beams with relatively high span ratios, where shear deformation significantly impacts lateral displacement. Conventional Bernoulli-Euler beam theory does not account for this effect [8]. To address the effect of shear stiffness in beam structures and enhance the constructive equation, scholars have proposed nonlinear beam theories [10].…”

Section: Introductionmentioning

confidence: 99%

Variable-Section Functional Gradient Beams on Pasternak Foundations: An Enhanced Interaction Theory for Construction Applications

Ling

Huang

et al. 2023

Preprint

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Functional gradient materials are ubiquitous in construction projects. Enhancing the theory of interaction between variable-section functional gradient beams (FGBs) and soil holds significant implications for engineering applications. Based on the variational principle and the transfer matrix method, this paper formulates semi-analytical solutions for displacement and internal force in the Timoshenko beam model (P-T model). The model features variable-section axial functional gradients on a Pasternak foundation. It accounts for the shear effects in the FGB structure and the soil's continuity and shear strength influences. Next, the semi-analytical solution is compared with finite difference decomposition results from existing studies. The comparison validates the proposed computational theory's precision and accuracy. The P-T model can degenerate to the Winkler-Timoshenko model (W-T model) when the foundation's shear layer stiffness is zero. Examining the displacement and internal force change when the beam stiffness varies along the axial direction reveals that an asymmetrical stiffness distribution on both sides of the midspan increases the displacement in the midsection. Moreover, when the beam stiffness gradient follows a Gaussian distribution along the axial direction, displacement sharply increases at the boundary position. Finally, the proposed method is incorporated with the Mindlin stress solution to assess the impact of construction on a tunnel existing within a foundation pit project in Shenzhen. We compare theoretical calculations, monitoring data, and numerical simulation results. The results show considerable agreement across the three methods. The tunnel's overall deflection follows an "M" shape, and the calculation using the variable-section FGB predicts the existing tunnel's deformation trend more accurately. This method reduces the calculation error from 35% to 8.3% in comparison to the traditional normal section beam.

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Free vibration of axially FG curved beam on orthotropic Pasternak foundation via mixed FEM

Ermis

Kutlu

Eratlı

et al. 2022

J Braz. Soc. Mech. Sci. Eng.

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Generalized foundation Timoshenko beam and its calculating methods

Cited by 5 publications

References 39 publications

Large Deformation Settlement Series Solution and Numerical Simulation for Underpass Project Track

Large Deformation Settlement Series Solution and Numerical Simulation for Underpass Project Track

Variable-Section Functional Gradient Beams on Pasternak Foundations: An Enhanced Interaction Theory for Construction Applications

Free vibration of axially FG curved beam on orthotropic Pasternak foundation via mixed FEM

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