On the use of Chebyshev polynomials in the Rayleigh-Ritz method for vibration and buckling analyses of circular cylindrical three-dimensional graphene foam shells

Ye, Chao; Wang, Yan Qing

doi:10.1080/15397734.2019.1704776

Cited by 24 publications

(8 citation statements)

References 53 publications

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“…There are several ways to approach finite element theory, one of the main ways to elucidate FEA, is through the Rayleigh-Ritz procedure [ 20 ]. Where it is one of the most intuitive and didactic methods, which allows the approximation of problem-solving through the principle of virtual work [ 28 , 29 ].…”

Section: Literature Reviewmentioning

confidence: 99%

“…The method makes this possible, based on the hypothesis that the displacements are a function of a finite number of indeterminate coefficients that must be determined. The problem becomes the determination of these coefficients [ 29 , 33 , 34 ].…”

Section: Literature Reviewmentioning

confidence: 99%

“…The solution to the problem is to find an expression for the potential energy of the system in terms of A the constant of the equations that describe the beam strain, differentiate this equation concerning A and equal to zero, according to the boundary conditions ( Table 2 ) [ 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ].…”

Section: Literature Reviewmentioning

confidence: 99%

“…For static structural problems, the finite element method results in part of a complex problem transforming it into several simple equations that can be expressed in the formula ( Figure 5 ) [ 29 ].…”

Section: Literature Reviewmentioning

confidence: 99%

“…The finite element method employs interconnected elements, so a displacement function is attached to each finite element [ 29 ]. As far as it is concerned, each element is interconnected through common interfaces, that is, by nodes [ 30 , 31 , 35 , 36 , 37 ].…”

Section: Literature Reviewmentioning

confidence: 99%

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Bioengineering Tools Applied to Dentistry: Validation Methods for In Vitro and In Silico Analysis

et al. 2022

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This study aimed to evaluate the use of bioengineering tools, finite element analysis, strain gauge analysis, photoelastic analysis, and digital image correlation, in computational studies with greater validity and reproducibility. A bibliographic search was performed in the main health databases PUBMED and Scholar Google, in which different studies, among them, laboratory studies, case reports, systematic reviews, and literature reviews, which were developed in living individuals, were included. Therefore, articles that did not deal with the use of finite element analysis, strain gauge analysis, photoelastic analysis, and digital image correlation were excluded, as well as their use in computational studies with greater validity and reproducibility. According to the methodological analysis, it is observed that the average publication of articles in the Pubmed database was 2.03 and with a standard deviation of 1.89. While in Google Scholar, the average was 0.78 and the standard deviation was 0.90. Thus, it is possible to verify that there was a significant variation in the number of articles in the two databases. Modern dentistry finds in finite element analysis, strain gauge, photoelastic and digital image correlation a way to analyze the biomechanical behavior in dental materials to obtain results that assist to obtain rehabilitations with favorable prognosis and patient satisfaction.

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Section: Literature Reviewmentioning

confidence: 99%