Numerical study of size effects in micro/nano plates by moving finite elements

Repka, Miroslav�; Sládek, V.; Sládek, J.

doi:10.1016/j.compstruct.2019.01.010

Cited by 11 publications

(5 citation statements)

References 41 publications

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“…Next, how to calculate the above integral becomes the key point, which is also the main point that this article needs to discuss. Some scholars have made some discussions on two‐dimensional problems, 33 so this article focuses on the derivation of three‐dimensional formulas, and degenerates from three‐dimensional problems to two‐dimensional problems. We will start our discussion with the mechanics of functionally graded materials.…”

Section: Zonal Free Element Methodsmentioning

confidence: 99%

“…In order to further improve the accuracy and stability of the block‐based (or zonal‐based) method, a Petrov–Galerkin formulation based on the ZFREM (PG‐ZFREM) is proposed for solid mechanical problems in this article. Similar to the Petrov–Galerkin formulation used in FBM 32 and moving FEM, 33 the main idea of the method is to combine the meshless local Petrov–Galerkin (MLPG) method with the zonal free element method. Besides, the technique used in the previous literature is extended to 3D problems in this article.…”

Section: Introductionmentioning

confidence: 99%

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Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems

Gao

2023

Numerical Meth Engineering

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In this article, a novel weak‐form zonal Petrov–Galerkin free element method is proposed for two‐ and three‐dimensional linear mechanical problems. By absorbing the advantages of finite block method and strong‐form finite element method, the block mapping technique is used in the free element method. Combining the characteristics of the meshless local Petrov–Galerkin method, the local Petrov–Galerkin formulation based on the zonal free element method is formed at last. Besides, the local integral domain selected in the local collocation element is circular or spherical to simplify programming. The transformation of the local integral domain between the physical and normalized spaces is given for two‐ and three‐dimensional problems. The comparison of accuracy and convergence between the new proposed Petrov–Galerkin method and the conventional methods is carried out. Some challenging examples including fracture mechanics problems and a complex 3D problem are given to validate the convergence and accuracy of the proposed method.

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Section: Zonal Free Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems

Gao

2023

Numerical Meth Engineering

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“…4 (c). On the other hand, Repka et al [95] performed a numerical analysis using the moving finite element (FE) to examine the SDE on the bending behavior in nano/microplates (NMPs). However, Salehipour et al [96] presented an analytical solution that focused on exploring the bending behavior of FG NMPs based on EF shown in Fig.…”

Section: Various Composite Nano/microplatesmentioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely studied. Due to the neuroma's advanced technology in various engineering fields and applications, developing small-size structures has become highly demanded for several structural geometries. One of the most important is the nano/micro-plate structure. However, the essential nature of highly lightweight material with extraordinary mechanical, electrical, physical, and material characterizations makes researchers more interested in developing composite/laminated-composite-plate structures. To comprehend the dynamical behavior, precisely the linear/nonlinear-free vibrational responses, and to represent the enhancement of several parameters such as nonlocal, geometry, boundary condition parameters, etc., on the free vibrational performance at nano/micro scale size, it is revealed that to employ all various parameters into various mathematical equations and to solve the defined governing equations by analytical, numerical, high order, and mixed solutions. Thus, the presented literature review is considered the first work focused on investigating the linear/nonlinear free vibrational behavior of plates on a small scale and the impact of various parameters on both dimensional/dimensionless natural/fundamental frequency and Eigen-value. The literature is classified based on solution type and with/without considering the size dependency effect. As a key finding, most research in the literature implemented analytical or numerical solutions. The drawback of classical plate theory can be overcome by utilizing and developing the elasticity theories. The nonlocality, weight fraction of porosity, or the reinforcements, and its distribution type of elastic foundation significantly influence the frequencies.

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“…Babu and Patel [9] used the classical plate theory of Kirchhoff to explore the static bending, free vibration, and buckling of nanoplates with different boundary conditions, in which the static bending problem only gave the maximum deflection result of the plate under static load. Repka et al [10] explored the bending of plates subjected to stationary transversal loading based on a moving finite elements method, and the results focused on vertical deflection w in the direction perpendicular to the plane of plates. ai et al [11] used modified isogeometric analysis (IGA) to analyze the free vibration and bending of nano FGM plates, where the calculation results for the static bending problem just stopped at the static deflection and did not mention the stresses.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Modeling of Stress Behavior of FGM Nanoplates

Giang

2021

Advances in Materials Science and Engineering

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The mechanical response investigation of nanoplates especially the stress distribution plays a very important role in engineering practice, which is a condition to help test the durability as well as design and use the nanoplate structures most effectively. This pioneering paper uses the finite element method to simulate the stress field of FGM nanoplates based on the first-order shear deformation theory of Mindlin. The finite element formulations are derived by taking into account the effect of the nonlocal coefficient to analyze the mechanical response of nanometer-scale plates. This work presents the distribution of stress components in the xy-plane of plates with different boundary conditions. The numerical results also show clearly that the nonlocal coefficient has a significant influence on the deflection and stress of FGM nanoplates. These numerical results are very new and stunning which clearly show the position of the stress reaching the maximum value. This work is also the basis for scientists in testing the durability of FGM nanoplates.

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Numerical study of size effects in micro/nano plates by moving finite elements

Cited by 11 publications

References 41 publications

Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems

Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Finite Element Modeling of Stress Behavior of FGM Nanoplates

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