A New Mathematical Model of Functionally Graded Porous Euler–Bernoulli Nanoscaled Beams Taking into Account Some Types of Nonlinearities

Krysko, Anton V.; Папкова, И. В.; Rezchikov, A. F.; Krysko, Vadim A.

doi:10.3390/ma15207186

Cited by 4 publications

(2 citation statements)

References 51 publications

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“…In [13], based on the modified theory of pair stresses, a mathematical model of Euler-Bernoulli beams was developed, and the deformation theory of plasticity was applied. For metal beams, taking into account geometric and physical nonlinearity, the phenomenon of changing boundary conditions, i.e., structural nonlinearity, was discovered.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Determining the patterns of asymmetric interaction of plastic medium with counter-directional metal flow

Chigirinsky,

Naizabekov,

Lezhnev

et al. 2024

EEJET

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The plane problem of rolling theory is analytically solved using the method argument of functions of a complex variable. The solution to the plane problem has been strengthened from the point of view of the asymmetry of the process, which made it possible to consider the applied problem as the interaction of differently directed zones in the deformation zone. The interaction of lagging and advancing zones is represented as a combination of multidirectional processes in a single deformation zone. With a change in kinematic, power characteristics in local zones, the process parameters change in the entire deformation zone. Stressed states of intermediate loading schemes between stable and unstable rolling are considered. A feature of the interaction of zones with the opposite flow of metal is the analogy with the action of back tension on the deformation zone in literally all parameters - this is the presence of tensile stresses in the lagging zone, a decrease in local specific pressures, a shift in maximum normal stresses towards the exit from the rolls, a change in the length of the advance zone, reduction in rolling force. The studies confirm and repeat the generally accepted provisions of the theory of rolling but reveal the effects of changes in the stress state under different loading models. The results of the work make it possible to determine the modes of rolling processes visually and computationally under conditions of strong and weak interaction of zones with an oppositely directed metal flow. The effects of plastic deformation with a decrease in the total effort in the processes that are within the reach of the limiting focus of crimping under conditions of increasing kinematic load when the gripping angles vary between 0,077…0,168 are given

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Determining the patterns of asymmetric interaction of plastic medium with counter-directional metal flow

Chigirinsky,

Naizabekov,

Lezhnev

et al. 2024

EEJET

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“…Size-dependent models can be classified into various frameworks [ 12 , 13 ] such as the nonlocal elasticity theory, which is intertwined with Eringen’s ground-breaking 1984 work [ 14 ] on evaluating the mechanical response of micro/nano-structures. This theory has been exploited for investigations of elastic waves lattice dispersion, wave propagation in nano-composites, dislocation mechanics, fracture mechanics, surface tension fluids, and other related topics.…”

Section: Introductionmentioning

confidence: 99%

A Review on Nonlocal Theories in Fatigue Assessment of Solids

2023

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A review of nonlocal theories utilized in the fatigue and fracture modeling of solid structures is addressed in this paper. Numerous papers have been studied for this purpose, and various nonlocal theories such as the nonlocal continuum damage model, stress field intensity model, peridynamics model, elastic-plastic models, energy-based model, nonlocal multiscale model, microstructural sensitive model, nonlocal lattice particle model, nonlocal high cycle fatigue model, low cycle fatigue model, nonlocal and gradient fracture criteria, nonlocal coupled damage plasticity model and nonlocal fracture criterion have been reviewed and summarized in the case of fatigue and fracture of solid structures and materials.

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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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A New Mathematical Model of Functionally Graded Porous Euler–Bernoulli Nanoscaled Beams Taking into Account Some Types of Nonlinearities

Cited by 4 publications

References 51 publications

Determining the patterns of asymmetric interaction of plastic medium with counter-directional metal flow

Determining the patterns of asymmetric interaction of plastic medium with counter-directional metal flow

A Review on Nonlocal Theories in Fatigue Assessment of Solids

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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