Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory

Şi̇mşek, Mesut; Kocatürk, Turgut; Akbaş, Şeref Doğuşcan

doi:10.1016/j.compstruct.2012.08.036

Cited by 126 publications

(26 citation statements)

References 54 publications

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“…Before presentation of the numerical results, the material properties of core and piezoelectric face-sheets may be presented as ( [8,[18][19][20][21]25]…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The dimensionless deflection according to reference [8] is calculated asŵ ¼ 100EI qL 4 w. Figures 2 and 3 show the dimensionless deflectionŵ in terms of non-homogeneity index, n for L h ¼ 10; 50, respectively. One can conclude that both comparisons presented in Figures 2 and 3 are in good agreement with reference [8].…”

Section: Comparison and Verificationmentioning

confidence: 99%

“…For verification, the work of Simsek et al [8] is selected. Figures 2 and 3 present comparisons between current results and previous results of Ref [8].…”

Section: Comparison and Verificationmentioning

confidence: 99%

“…For verification, the work of Simsek et al [8] is selected. Figures 2 and 3 present comparisons between current results and previous results of Ref [8]. The dimensionless deflection according to reference [8] is calculated asŵ ¼ 100EI qL 4 w. Figures 2 and 3 show the dimensionless deflectionŵ in terms of non-homogeneity index, n for L h ¼ 10; 50, respectively.…”

Section: Comparison and Verificationmentioning

confidence: 99%

“…Bending analysis of a microscale functionally graded (FG) Timoshenko beam was studied by Simsek et al [8] based on the modified couple stress theory. They assumed that material properties are graded along the thickness direction based on the MoriTanaka homogenization technique and the classical rule of mixture.…”

Section: Introductionmentioning

confidence: 99%

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Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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In this paper, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler-Bernoulli beam theory. The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials. A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam. Hamilton principal is used to derive governing differential equations of motion. Three behaviors of sandwich microbeam including free vibration, wave propagation, and bending analyses are studied in this paper. Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index, applied voltage, parameters of foundation, and material length scales. The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied. ARTICLE HISTORY

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“…Before presentation of the numerical results, the material properties of core and piezoelectric face-sheets may be presented as ( [8,[18][19][20][21]25]…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Comparison and Verificationmentioning

confidence: 99%

“…For verification, the work of Simsek et al [8] is selected. Figures 2 and 3 present comparisons between current results and previous results of Ref [8].…”

Section: Comparison and Verificationmentioning

confidence: 99%

Section: Comparison and Verificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

Ghanbari

Rashidi

2020

Polymer Composites

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An analytical multiscale model is presented in this article for the analysis of functionally graded nanocomposites. The multiscale scheme is composed of a microscale problem whose solution provides the constitutive model for the macroscale problem. For nanoparticle‐reinforced composites, the microscale problem consists of three phases, namely the nanoparticle, the matrix, and an interphase layer between the matrix and the nanoparticle. An analytical micromechanical model based on Green's function is employed to solve the triple‐phase microscale problem. The homogenized properties of the FG nanocomposite are determined by the micromechanical problem and used in the macroscale level, at every macroscopic material point in which the constitutive model is required. As an example, a nanocomposite beam under bending is considered as the macroscale problem which is investigated by classical, first‐order, and third‐order shear deformation theories. The results obtained from the presented method are compared with the relevant data for similar problems using various higher‐order elasticity theories. By comparing the results of higher‐order theories and those obtained by the presented multiscale method, the internal length parameter of the higher‐order theories is correlated to the volume fraction of the interphase layer between the nanoparticle and the matrix.

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