Magneto-electro-elastic node-based smoothed point interpolation method for micromechanical analysis of natural frequencies of nanobeams

Zhou, Liming; Ren, Shuhui; Nie, Bin; Yang, Hongrong; Liu, Peng

doi:10.1007/s00707-019-02489-6

Cited by 5 publications

(3 citation statements)

References 71 publications

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“…where g, H, and E were determined from equations (88) to (90); c, e, m, e, q, and m were the matrices of effective factors for MEE nanomaterials computed by equations (34)-(39) with AHM; b, Q, and R are the surface load, surface density of free charge, and the magnetic field on the boundary, respectively. And the discretization equations can be expressed (Zhou et al, 2019b)…”

Section: Weakened Weak Form and Discretization Equationsmentioning

confidence: 99%

“…In order to solve the complex MEE micromechanical problem, a new efficient and accurate method without the defects of traditional FEM is extremely needed. The frequency of MEE nanomaterials was explored with NS-PIM combined with AHM (Zhou et al, 2019b), which showed the accuracy and reliability of AHM for micromechanical problems. With the RPIM shape function that satisfies the delta function property, the moment matrix of NS-RPIM with AHM is nonsingular and the basic boundary requirements can be decided easily (Li and Liu, 2019).…”

Section: Introductionmentioning

confidence: 99%

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Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

Zhou

Nie

Ren

et al. 2020

Journal of Intelligent Material Systems and Structures

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The node-based smoothed radial point interpolation method combined with the asymptotic homogenization method was proposed, as an addition to the finite element method, to address the static and dynamic reactions of magneto-electro-elastic coupling micromechanical problems. First, several basic equations for relevant problems were derived. Second, asymptotic homogenization method was utilized to determine the material properties of magneto-electro-elastic nanomaterials. Third, node-based smoothed radial point interpolation method was applied to obtain the discrete equations of magneto-electro-elastic nanostructures. Then, the Newmark method was introduced to solve the response of microcosmic problems. Finally, several numerical examples were calculated to prove the accuracy, convergence, and reliability of node-based smoothed radial point interpolation method by comparing the results of node-based smoothed radial point interpolation method with those of finite element method.

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Section: Weakened Weak Form and Discretization Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

Zhou

Nie

Ren

et al. 2020

Journal of Intelligent Material Systems and Structures

Self Cite

View full text Add to dashboard Cite

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“…Generally, lightweight design of automobile can be conducted by structural analysis and optimization, 5–21 material substitution, 22–24 and new forming process. 25–27 For decades, structural optimization has been maturely applied in automobile industry.…”

Section: Introductionmentioning

confidence: 99%

Equivalent substitution criteria of aluminum for steel and its application in automobile structures

Bai

Wang

et al. 2020

Advances in Mechanical Engineering

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Lightweight automobile body structure, made of aluminum, can extend the endurance mileage of electric automobile. However, the mechanisms for the application of aluminum in automobile body structure are not clear until now. The main contribution of this work is to propose a method of equivalent substitution criteria of aluminum for steel. This method researches small deformation and large deformation under bending mode. First, formulations of cross-sectional properties, including open, single-cell, double-cell, three-cell, and four-cell sections, are derived, and equivalent substitution criteria in the case of small deformation, which include equal stiffness design and equal strength design, are initially proposed. Second, in the case of large deformation, the steel circular tube and channel tube are substituted by aluminum tube under equivalent stiffness. The bending resistance of five types of tubes, including rectangular hollow section, rectangular hollow section with double-cell, rectangular hollow section with triple-cell, mild steel, and high-strength steel tube, are, respectively, compared considering crashworthiness under equal mass. Third, the side frame and chassis frame examples verify the effectiveness of the proposed method, which is universal and can also be applied in aerospace structures.

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Stabilized node‐based smoothed radial point interpolation method for micromechanical analysis of the magneto‐electro‐elastic structures in thermal environment

Ren

Meng

et al. 2020

Math Methods in App Sciences

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In this paper, the stabilized node‐based smoothed radial point interpolation method (SNS‐RPIM) is combined with asymptotic homogenization method (AHM) to investigate the static and transient responses of magneto‐electro‐elastic (MEE) structures in thermal environment. Stabilization terms are applied to construct a “close‐to‐exact” stiffness for the model; the temporal instability is also cured. To study the microscopic multi‐physics coupling problems more accurately, the effective material parameters related to the volume fraction of fiber are obtained based on AHM. Through numerical calculation, it is confirmed that SNS‐RPIM could simulate the responses of MEE structures well when combined with AHM. Therefore, the combination of SNS‐RPIM and AHM has great potential in studying nanostructures including nanobeams, nanoplates, and nanotubes.

show abstract

Magneto-electro-elastic node-based smoothed point interpolation method for micromechanical analysis of natural frequencies of nanobeams

Cited by 5 publications

References 71 publications

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

Equivalent substitution criteria of aluminum for steel and its application in automobile structures

Stabilized node‐based smoothed radial point interpolation method for micromechanical analysis of the magneto‐electro‐elastic structures in thermal environment

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