Variational Formulations and Isogeometric Analysis of Timoshenko–Ehrenfest Microbeam Using a Reformulated Strain Gradient Elasticity Theory

Yin, Shuohui; Xiao, Zhibing; Liu, Jingang; Xia, Zixu; Gu, Shuitao

doi:10.3390/cryst12060752

Cited by 3 publications

(2 citation statements)

References 80 publications

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“…This study revealed that microbeams based on non-classical theories, particularly GSGET, exhibit greater stiffness than models based on classical theory. Based on (RSGET), the vibration governing equations for Timoshenko-Ehrenfest beam were acquired by [21]. The proposed analytical solution revealed a reduced deflection and a higher natural frequency in the nonclassical model utilized.…”

Section: Introductionmentioning

confidence: 99%

Reformulated Strain Gradient (Rsg) Elasticity Theory for Free Vibration of Thermal Bi-Directional Fg Microbeam

Majeed,

Elaikh,

Ugla

2024

Jurnal Teknologi

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This research examines the vibrational response of a micro-scale Euler beam made from two-directional functionally graded (2D-FG) materials and subjected to thermal effects. By employing a reformulated strain gradient elasticity (RSGE) approach, the equations of motion using Hamilton’s principle for clamped -clamped and clamped-simply boundary conditions are derived and solved them using Galerkin's approach. The investigation explores the impact of temperature, gradient index, and parameters length scale materials on the bidirectional graded microbeam's dynamic characteristics. Furthermore, the normalized frequency, as based on the current reformulated strain gradient elasticity microbeam model, consistently emerges as higher than that derived from the classical model.

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Section: Introductionmentioning

confidence: 99%

Reformulated Strain Gradient (Rsg) Elasticity Theory for Free Vibration of Thermal Bi-Directional Fg Microbeam

Majeed,

Elaikh,

Ugla

2024

Jurnal Teknologi

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“…Based on the nonlocal plasticity theory, the nonlocalized variables of the material indirectly consider the changes and interactions of the internal microstructure of the material. Rawat et al [6] proposed a nonlocal plastic damage model for quasi-brittle materials in 2020 and used the method of geometric analysis [9] to avoid the problems of computational accuracy and computational efficiency that would occur during the process of finite element analysis. The application of strain gradient theory in beam bending was proposed by Li et al [7] in 2022.…”

Section: Introductionmentioning

confidence: 99%

Plasticity constitutive theory considering material length parameters

Gong,

Han,

et al. 2024

J. Phys.: Conf. Ser.

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The traditional continuous medium theory introduces the homogenization assumption that the material remains constant from the macroscopic to the microscopic view, which has been successfully applied to the analysis of the macroscopic mechanical properties. When the dimensions are reduced to the microscopic view, the internal defects of the material start to appear, leading to the inhomogeneity of the material properties, which is, in practice, manifested as a ruler effect. Therefore, it is necessary to introduce the material length parameter into the structural theory to model the mechanical response of new materials. Based on the theory of size effect, many scholars have carried out a large number of studies. The most widely used theories are strain gradient theory and differential nonlocal model, mainly the first strain gradient theory, the second strain gradient theory, and the simplified strain gradient theory. Some scholars define it from the kinetic point of view, but most of these consider the intrinsic relationship of elastic materials. To further investigate the plasticity intrinsic theory, some scholars have proposed the gradient plasticity theory, the nonlocal plasticity theory, and so on. In this paper, based on the previous research results, we briefly summarize the development and outlook of the plasticity eigenstructure theory under the consideration of the length parameter of the material. Then, we derive the plasticity eigenstructure relation equation, the full-volume theoretical model, and the yield criterion corresponding to the Mises material under the consideration of the endowment size of the material from the perspective of the gradient theory of plasticity, and finally, put forward a new plasticity eigenstructure theory-higher-order nonlocal gradient theory. A new plasticity constitutive theory, the higher-order nonlocal gradient theory, is finally proposed, and the defining equations and their constitutive relations are derived in detail. The proposed theory is intended to provide a theoretical basis for analyzing the microdefects in materials.

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Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis

et al. 2022

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This paper proposes an analytical solution and isogeometric analysis numerical approach for buckling analysis of size-dependent beams based on a reformulated strain gradient elasticity theory (RSGET). The superiority of this method is that it has only one material parameter for couple stress and another material parameter for strain gradient effects. Using the RSGET and the principle of minimum potential energy, both non-classical Euler–Bernoulli and Timoshenko beam buckling models are developed. Moreover, the obtained governing equations are solved by an exact solution and isogeometric analysis approach, which conforms to the requirements of higher continuity in gradient elasticity theory. Numerical results are compared with exact solutions to reveal the accuracy of the current isogeometric analysis approach. The influences of length–scale parameter, length-to-thickness ratio, beam thickness and boundary conditions are investigated. Moreover, the difference between the buckling responses obtained by the Timoshenko and Euler–Bernoulli theories shows that the Euler–Bernoulli theory is suitable for slender beams.

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Variational Formulations and Isogeometric Analysis of Timoshenko–Ehrenfest Microbeam Using a Reformulated Strain Gradient Elasticity Theory

Cited by 3 publications

References 80 publications

Reformulated Strain Gradient (Rsg) Elasticity Theory for Free Vibration of Thermal Bi-Directional Fg Microbeam

Reformulated Strain Gradient (Rsg) Elasticity Theory for Free Vibration of Thermal Bi-Directional Fg Microbeam

Plasticity constitutive theory considering material length parameters

Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis

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