Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

Gan, Buntara Sthenly; Kien, Nguyen Dinh

doi:10.3130/jaabe.13.649

Cited by 12 publications

(10 citation statements)

References 23 publications

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“…Partial differential equations are used for mathematical representation of beams resting on the linear or nonlinear elastic foundation. [15][16][17][18][19][20] Generally, finding an exact solution for nonlinear vibration equations is very difficult. Javanmard et al 21 implemented Energy Balance Method (EBM) to the Euler-Bernoulli beam resting on an elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of Axially Loaded Railway Track Systems Using Analytical Approach

Bayat

Pakar

Ziehl

2021

Journal of Low Frequency Noise, Vibration and Active Control

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In this paper, the nonlinear vibration of railway track systems resting on elastic foundation has been studied. An axially loaded simply supported Euler–Bernoulli beam resting on a flexible foundation has been considered to provide a mathematical representation of the railway track system. Winkler springs have been used to model the elastic foundation. Nonlinear partial differential equation of the system has been presented and solved. A new approximate analytical solution called Improved Amplitude–Frequency Formulation (IAFF) is proposed to obtain nonlinear frequency of the system and an accurate analytical solution for the whole domain. The first iteration of the IAFF leads to a highly accurate solution in comparison with the exact frequency of the problem. The exact frequency of the problem is also presented, and the results of IAFF are compared and verified. Sensitive analysis of the soil stiffness and loading condition is studied for different parameters. A full comparison of the IAFF and exact solution results are illustrated. It has been proved that the IAFF can be potentially extended to highly nonlinear conservative problems.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of Axially Loaded Railway Track Systems Using Analytical Approach

Bayat

Pakar

Ziehl

2021

Journal of Low Frequency Noise, Vibration and Active Control

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“…Shen and Wang 6 investigated the large amplitude vibration, nonlinear bending and thermal postbuckling of FGB resting on an elastic foundation in thermal environments. Gan and Kien 7 studied a finite element procedure for the large deflection analysis of FGB resting on a two-parameter elastic foundation. Li and Shao 8 discussed nonlinear bending problem of functionally graded cantilever beams resting on a Winkler elastic foundation under distributed load.…”

Section: Introductionmentioning

confidence: 99%

Accurate solution for functionally graded beams with arbitrarily varying thicknesses resting on a two-parameter elastic foundation

Huang

2020

The Journal of Strain Analysis for Engineering Design

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This work presents analytical solutions for bending deformation and stress distributions in functionally graded beams with arbitrarily and continuously variable thicknesses and resting on a two-parameter Pasternak elastic foundation. Based on two-dimensional elasticity theory directly, the general solutions of displacements and stresses which completely satisfy the differential equations governing the equilibrium for arbitrarily varying thickness functionally graded beams are derived for the first time. The undetermined coefficients in the general solution are obtained using Fourier series expansion along the upper and lower surfaces. The accuracy and efficiency of the proposed method are verified through several typical examples. The effects of mechanical and geometry parameters on the stress and displacement distributions of varying thickness functionally graded beams resting on a two-parameter Pasternak elastic foundation are discussed further.

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“…A new finite element formulation was developed to study the shallow and the raft foundation response eliminating the limits of Winkler model (Mullapudi 2010). In the way to study large deflections of functionally graded beam resting on two-parameter elastic foundation, a finite element procedure was developed (Gan and Kien 2014). Finally, the effect of material nonhomogeneity and the two-parameter elastic foundation were used to quantify the response of simply supported beams.…”

Section: Introductionmentioning

confidence: 99%

Static interaction analysis between beam and layered soil using a two-parameter elastic foundation

Souad

Khalfallah

Bilotta³

2019

Int J Adv Struct Eng

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The work presents a finite element modeling of beam resting on a two-parameter layered soil. The behavior of the soil continuum and the beam are assumed to be linear and homogeneous isotropic. Using the strain energy expressions, the shear strain of the beam element and the soil foundation are taken together in the analysis. In this approach, the stiffness matrix of each component is elaborated and integrated in the finite element analysis. First, various examples are elaborated to show the effectiveness of the proposed approach and the ability of the numerical program developed for this concern. Second, the analysis is widened to study the influence of the soil properties on the interface continuum and on the beam responses. Third, a parametric study is carried out to highlight the effect of the position of springs at the interface continuum, the properties of soil, the deepest of the soil foundation and the ballast layer on the response of the interface and the beam itself. Moreover, shear deformations are presented to show the crucial influence on the beam, on the structure and on the interface behaviors. Obtained results show pertinent results corresponding to the interface continuum and the beam responses.

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Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

Cited by 12 publications

References 23 publications

Nonlinear Vibration of Axially Loaded Railway Track Systems Using Analytical Approach

Nonlinear Vibration of Axially Loaded Railway Track Systems Using Analytical Approach

Accurate solution for functionally graded beams with arbitrarily varying thicknesses resting on a two-parameter elastic foundation

Static interaction analysis between beam and layered soil using a two-parameter elastic foundation

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