Isogeometric analysis of size-dependent Bernoulli–Euler beam based on a reformulated strain gradient elasticity theory

Yin, Shuohui; Xiao, Zhibing; Deng, Yang; Zhang, Gongye; Liu, Jingang; Gu, Sijia

doi:10.1016/j.compstruc.2021.106577

Cited by 28 publications

(10 citation statements)

References 70 publications

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“…Based on the reformulated strain-gradient elasticity theory proposed by Zhang and Gao [30], the stored strain energy U is defined as [54]:…”

Section: Reformulated Strain-gradient Elasticity Theorymentioning

confidence: 99%

“…In the reformulated strain-gradient elasticity theory, the constitutive relations between stress and strain quantities are given by Yin et al [54] as:…”

Section: Reformulated Strain-gradient Elasticity Theorymentioning

confidence: 99%

“…Form I expresses the strain energy density function in terms of the infinitesimal strain and the second displacement gradient; Form II describes the strain energy density function in terms of the infinitesimal strain and the first strain gradient; and Form III represents the strain energy density function in terms of the infinitesimal strain, the symmetric part of the second displacement gradient; and the rotation gradient (curvature tensor). Several researchers [5,30,38,[50][51][52][53][54] have formulated their own strain-gradient elasticity models based on these three forms (Form I, Form II, and Form III). As the simplest variant of the strain-gradient elasticity theory, the simplified strain-gradient elasticity theory of Altan and Aifantis [51] is constructed based on Form II but can account only for the strain gradient along the longitudinal direction.…”

Section: Introductionmentioning

confidence: 99%

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Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems

et al. 2022

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This study presents a newly developed size-dependent beam-substrate medium model for bending, buckling, and free-vibration analyses of nanobeams resting on elastic substrate media. The Euler-Bernoulli beam theory describes the beam-section kinematics and the Winkler-foundation model represents interaction between the beam and its underlying substrate medium. The reformulated strain-gradient elasticity theory possessing three non-classical material constants is employed to address the beam-bulk material small-scale effect. The first and second constants is associated with the strain-gradient and couple-stress effects, respectively while the third constant is related to the velocity-gradient effect. The Gurtin-Murdoch surface elasticity theory is adopted to account for the surface-free energy. To obtain the system governing equation as well as corresponding boundary conditions, Hamilton’s principle is called for. Three numerical simulations are presented to characterize the influences of the material small-scale effect, the surface-energy effect, and the surrounding substrate medium on bending, buckling, and free vibration responses of nanobeam-substrate medium systems. The first simulation focuses on the bending response and shows the ability of the proposed model to eliminate the paradoxical characteristic inherent to nanobeam models proposed in the literature. The second and third simulations perform the sensitivity investigation of the system parameters on the buckling load and the natural frequency, respectively. All analytical results reveal that both material small-scale and surface-energy effects consistently stiffen the system response while the velocity-gradient effect weakens the system response. Furthermore, these sized-scale effects are more pronounced when the underlying substrate medium becomes softer.

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“…Based on the reformulated strain-gradient elasticity theory proposed by Zhang and Gao [30], the stored strain energy U is defined as [54]:…”

Section: Reformulated Strain-gradient Elasticity Theorymentioning

confidence: 99%

“…In the reformulated strain-gradient elasticity theory, the constitutive relations between stress and strain quantities are given by Yin et al [54] as:…”

Section: Reformulated Strain-gradient Elasticity Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems

et al. 2022

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“…In [ 19 ], Bernoulli-Euler beams are analysed using IGA. This is an efficient and accurate numerical approach for static bending and vibration analysis.…”

Section: Current Status Of the Issuementioning

confidence: 99%

Comparison of Structural Analysis of Thin-Walled Structures Accomplished by Isogeometric Analysis and the Finite Element Method

et al. 2022

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Isogeometric analysis (IGA) represents a relatively new method of problem-solving in engineering practice. A huge advantage of this method over the finite element method (FEM), is the reduction of the simulation execution time. Non-uniform rational B-splines (NURBS) allow the use of higher-order basis functions, thus increasing the accuracy of the solution. This paper deals with the comparison of structural analysis of thin-walled structural elements using isogeometric analysis and the finite element method. The investigated objects are modelled using a single patch in MATLAB. The basic functions are created from NURBS, which were previously used in the creation of an accurate geometric model. The paper contains a comparison of the results obtained by the above-mentioned methods. All computations are performed in the elastic domain.

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“…Among three kinds of structure like beam, plate and shell, beam has always considered the interests of researchers because of its applications. There are many different beam theories used to analyze beam structures like simple beam theory [14][15], classical beam theory [16][17], first-order shear deformation theory [18][19] or higher-order shear deformation theory [20][21][22]. However, using a simple model helps us to reduce the computational cost with the resulting error within the allowable range.…”

Section: Introductionmentioning

confidence: 99%

Effect of porosity on free vibration of functionally graded porous beam based on simple beam theory

To¹

2022

TJDU

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In this paper, the natural frequencies of functionally graded porous (FGP) beam are determined associated with two kinds of porosity. The simple beam theory is applied in this study with various boundary conditions. The results obtained in this paper are presented and compared with other results in the references to verify the correctness in implementing the formula and writing the Matlab code. Last but not least, this article can help researchers to have an overview of the free vibration characteristics of the functionally graded porous beams.

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Isogeometric analysis of size-dependent Bernoulli–Euler beam based on a reformulated strain gradient elasticity theory

Cited by 28 publications

References 70 publications

Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems

Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems

Comparison of Structural Analysis of Thin-Walled Structures Accomplished by Isogeometric Analysis and the Finite Element Method

Effect of porosity on free vibration of functionally graded porous beam based on simple beam theory

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