Nonlinear bending analysis of functionally graded porous beams using the multiquadric radial basis functions and a Taylor series-based continuation procedure

Fouaidi, Mustapha; Jamal, Mohammad; Belouaggadia, Naoual

doi:10.1016/j.compstruct.2020.112593

Cited by 27 publications

(4 citation statements)

References 34 publications

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Section: Discussionmentioning

confidence: 99%

“…To create a non-singular moment matrix, radial basis functions (RBF) are introduced in a PIM formulation to construct shape functions using local nodes. The RPIM is obtained by combining PIM and RBF (Fouaidi et al, 2020a, 2020b). Using the n local nodes, the RPIM approximation of the variable field u h ( x ) is expressed as: Where a i is the coefficient of the radial basis R i ( x ) which is described in Table A2.…”

Section: A1 Moving Least Square Methods Mlsmentioning

confidence: 99%

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Analysis of the elasto-magnetic wave propagation in a smart magnetostrictive actuator using a mesh-free method

Belfallah

laasri

Fouaidi

et al. 2022

Journal of Intelligent Material Systems and Structures

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This work aims to propose an implicit algorithm for solving the magnetoelastic wave propagation in a magnetostrictive actuator. This algorithm is built by combining meshless methods with the Newmark implicit time scheme. The mathematical formulation of vibrations of the actuator is performed by modeling the experimental actuator device by a monodimensional magnetostrictive cylindrical rod attached to an elastic spring, subjected to an axial magnetic field. The formulation of the problem is carried out using the rod model. The study is carried out taking into account mechanical and magnetic effects described by a linear model of strain-stress magnetoelastic relations, whose coefficients depend on the square of the magnetic field, elastic, magnetostrictive, and magnetoelastic characteristics of the elastomagnetic material of which the rod is made. The dynamic equation which describes the magnetoelastic wave propagation in the actuator is obtained by applying the Lagrangian formalism based on the least action principle. The wave propagation is governed by a spatio-temporal partial differential equation whose coefficients are a function of on elastic, magnetostrictive, and magnetic characteristics and implicitly depends on time. The resolution of the dynamic equation is made by adopting two numerical approaches developed by combining the mesh-free collocation methods, the Moving Least Squares (MLS), and the Radial Point Interpolation Method (RPIM) with the Newmark implicit scheme temporal integration. By performing the spatial discretization of the displacement, we obtain a system of linear second-order ordinary differential equations (ODEs), then transform it into a system of first-order ordinary differential equations after integrating Newmark’s implicit time scheme. A comparison of results computed by the proposed numerical approaches RPIM and MLS with experimental data available in the literature is presented. The stability and the solutions qualities of two meshless methods, RPIM and MLS, are also studied. The influence of magnetical and mechanical parameters as well as the coupling coefficients on the performance of the magnetostrictive actuator is also made.

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Section: Discussionmentioning

confidence: 99%

Section: A1 Moving Least Square Methods Mlsmentioning

confidence: 99%

Analysis of the elasto-magnetic wave propagation in a smart magnetostrictive actuator using a mesh-free method

Belfallah

laasri

Fouaidi

et al. 2022

Journal of Intelligent Material Systems and Structures

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“…In recent years, functionally graded structures have been used in many modern engineering applications due to varying material properties over dimensions which allow them to improve the strength of material, high resistance to temperature shocks and high strength to weight ratio. Authors [1][2][3][4][5][6][7][8][9][10][11][12] devoted a considerable number of studies to predicting and to understanding the mechanics of functionally graded structures. In [1], the main idea of this paper's developed method was the control over the produced gradient and did not require burning binder phase.…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear bending analysis of FGP beams was investigated using an efficient numerical algorithm associating a meshless collocation technique uses the multiquadric radial basis function approximation method and a higher-order Taylor series-based continuation procedure. Material properties of the FGP beams were described by adopting a modified power-law function taking into account the effect of porosities as in [2]. Besides, the [3] was aimed to develop an efficient and highperformance four-node iso-parametric beam element, which was composed of FGM.…”

Section: Introductionmentioning

confidence: 99%

Mechanical Behavior of 2D FGP Beam with Uneven Porosity Distribution

Hoang That Ton

2023

jaer

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A new modified Bessel‐type radial basis function for meshless methods: Utilized in the analysis of free vibration in 2D functionally graded Euler–Bernoulli beams

Hosseini,

Abbaspour,

Nazari

2024

Int J Numerical Modelling

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Radial basis functions (RBFs) are extensively employed in mesh‐free methods owing to their distinct properties. This study presents a novel RBF formulation based on a modified first‐kind Bessel function, introduced for the first time. The efficacy and precision of the proposed function are assessed through an examination of the free vibrations of Euler–Bernoulli beams composed of two‐directional functionally graded materials. Longitudinal and thickness property variations are modeled in polynomial and exponential forms, respectively. The performance of the novel RBF is scrutinized under various boundary conditions (clamped, simply supported, and free), and comparative analyses are conducted against similar investigations and an RBF based on the first‐kind Bessel function. Convergence analysis of the proposed modified first‐kind Bessel function‐based RBF reveals superior convergence rates compared to the first‐kind Bessel function‐based RBF. Moreover, a comparison between results obtained from modeling using the proposed RBF and exact solutions underscores the adequacy of this approach, with a maximum discrepancy of 4.933% observed under clamped‐free boundary conditions. In essence, the findings suggest that the proposed modified first‐kind Bessel function‐based RBF holds promise for analyzing the free vibrations of functionally graded Euler–Bernoulli beams. The primary aim of this research is to introduce and validate a new RBF based on a modified first‐kind Bessel function for the analysis of free vibrations in Euler–Bernoulli beams made of two‐directional functionally graded materials. The study focuses on evaluating the performance and accuracy of this novel RBF in comparison with existing RBFs and exact solutions. By addressing the limitations of conventional RBFs and proposing an innovative approach, this research aims to enhance the accuracy and efficiency of meshless methods in structural vibration analysis.

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Nonlinear bending analysis of functionally graded porous beams using the multiquadric radial basis functions and a Taylor series-based continuation procedure

Cited by 27 publications

References 34 publications

Analysis of the elasto-magnetic wave propagation in a smart magnetostrictive actuator using a mesh-free method

Analysis of the elasto-magnetic wave propagation in a smart magnetostrictive actuator using a mesh-free method

Mechanical Behavior of 2D FGP Beam with Uneven Porosity Distribution

A new modified Bessel‐type radial basis function for meshless methods: Utilized in the analysis of free vibration in 2D functionally graded Euler–Bernoulli beams

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