A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams

Rezaiee‐Pajand, Mohammad; Mokhtari, Mohamed

doi:10.1007/s40430-019-1799-3

Cited by 10 publications

(4 citation statements)

References 72 publications

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“…Wang et al [46] employed meshless method and moving least squares approximation to analyze vibrational behavior of simply supported nanobeam based on strain gradient Euler beam model. Rezaiee-Pajand and Mokhtari [47] used the symmetric smoothed particle hydrodynamics (SSPH) meshless method to analyze buckling and free vibration of two-directional functionally graded nanobeams by Reddy-Bickford beam theory. Ghadiri Rad et al [48] developed an EFG method and radial basis function (RBF) interpolation for geometrically nonlinear dynamic analysis of beams considering small-scale effect.…”

Section: Murmu and Adhikarimentioning

confidence: 99%

Vibration analysis of 2D-functionally graded multiple nanobeam system by meshless method

Ahmadi,

Davarpanah,

Sladek

et al. 2023

Preprint

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In this study, the free vibration of two-directional functionally graded (2D-FG) multiple nanobeam system are studied by considering Winkler elastic medium between each nanobeam. Effects of small-scale are considered using the theory of nonlocal elasticity. The material properties of the FG nanobeams are considered to vary over the length and thickness of the nanobeams. The equations of motion are derived using Hamilton's principle and the first order shear deformation beam theory (FSDBT), and a meshless formulation is developed to discreteze the governing equations. Numerical results are obtained for both cases of free-chain and clamped-chain multiple nanobeam system (MNBS). In order to validate the accuracy of the meshless formulation, numerical results for free vibration of 1D-FG single nanobeam are compared with the predictions of various beam theories and solution approaches. Also, free vibration of homogeneous double nanobeam system is analyzed and good agreement is observed while comparing these results with analytical solutions. In the numerical results, the effects of nonlocal parameter, slenderness ratio, power FG indices, elastic medium stiffness, number of nanobeams, boundary conditions and concentrated mass on the free vibration of 1D- and 2D-FG single and multiple nanobeam system are investigated.

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Section: Murmu and Adhikarimentioning

confidence: 99%

Vibration analysis of 2D-functionally graded multiple nanobeam system by meshless method

Ahmadi,

Davarpanah,

Sladek

et al. 2023

Preprint

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“…Meshless methods have been successfully applied to a wide range of problems, such as free surface [38][39][40][41], impact magnetohydrodynamics [42][43], explosion phenomena [44][45], heat conduction [46][47], fracture and crack propagation [48][49], wave propagation [50][51], acoustics and fluid flow [52][53], vibration analysis [54][55][56], beams [57][58], plates and shells [59][60], and nanoscale mechanics [61][62][63][64][65][66]. A methodological study on possible and existing meshfree methods is presented in G. R. Liu [67] to solve the partial differential equations governing solid mechanics problems.…”

Section: Introductionmentioning

confidence: 99%

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

Marius,

Jacques,

MINSILI

2023

Numerical Methods in Civil Engineering

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In this paper, the computational design of box culverts are compared using Kleinlogel's formulas and three-dimensional models based on Winkler and Modified Vlasov Foundation (MVF) by Radial Point Interpolation method (RPIM). In order to extend the RPIM to the study of box culverts, a method of decomposition is made by subdomain and creation of a fictitious rotation. Similar results are observed between the RPIM_Winkler and STAAD PRO (FEM software), with fewer nodes in the case study. Kleinlogel's formulas or the Winkler model gives a maximal increase in stresses at the middle of the raft of 5% and 12 times increased displacement. Finally, it emerges that for the same type of soil and a single structure, the reaction and shear modulus of the soil is highly depends on the distribution of loads on the structure.

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“…Pajand and Mokhtari [18] developed a study on the bending, buckling and free vibration of two-directional FGM nanobeams based on Reddy-Bickford beam theory. Material properties were described by an arbitrary power-law form in both the axial and thickness directions.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Free Vibrations of Metallic FGM Beams

2022

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This work aims to analyse the free-vibration response of functionally graded, simply supported beams with different gradient directions, taking into account nonlocal effects. To this purpose, the first-order shear deformation theory and the nonlocal elasticity theory of Eringen are used, in order to assess the influence of size dependency effects on the free-vibration responses of those beams. The influence of other factors such as the aspect ratio of the beams and the evolution of the constituents’ mixture through the beam thickness and along its length is also considered. In this last case, a mixture distribution is proposed, accounting for the boundary conditions’ characteristics. The finite element model is first verified against existing alternative solutions, to assess and illustrate its performance. Based on the conclusions achieved, a set of parametric studies is then developed. The results are discussed considering the material distribution profiles, and conclusions are drawn with respect to their relative performance under the analysed conditions.

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A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams

Cited by 10 publications

References 72 publications

Vibration analysis of 2D-functionally graded multiple nanobeam system by meshless method

Vibration analysis of 2D-functionally graded multiple nanobeam system by meshless method

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

Nonlocal Free Vibrations of Metallic FGM Beams

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