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Research Papers

A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar Plates

[+] Author and Article Information
R. Ansari

Department of Mechanical Engineering,
University of Guilan,
Rasht 3756, Iran
e-mail: r_ansari@guilan.ac.ir

A. H. Shakouri, M. Bazdid-Vahdati, A. Norouzzadeh

Department of Mechanical Engineering,
University of Guilan,
Rasht 3756, Iran

H. Rouhi

Department of Engineering Science,
Faculty of Technology and Engineering,
East of Guilan,
University of Guilan,
Rudsar-Vajargah 44891-63157, Iran

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 15, 2015; final manuscript received August 16, 2016; published online November 22, 2016. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 12(1), 011019 (Nov 22, 2016) (12 pages) Paper No: CND-15-1131; doi: 10.1115/1.4034678 History: Received May 15, 2015; Revised August 16, 2016

Based on the micropolar elasticity theory, a size-dependent rectangular element is proposed in this article to investigate the nonlinear mechanical behavior of plates. To this end, a novel three-dimensional formulation for the micropolar theory with the capability of being used easily in the finite element approach is developed first. Afterward, in order to study the micropolar plates, the obtained general formulation is reduced to that based on the Mindlin plate theory. Accordingly, a rectangular plate element is developed in which the displacements and microrotations are estimated by quadratic shape functions. To show the efficiency of the developed element, it is utilized to address the nonlinear bending problem of micropolar plates with different types of boundary conditions. It is revealed that the present finite element formulation can be efficiently employed for the nonlinear modeling of small-scale plates by considering the micropolar effects.

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Figures

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Fig. 1

Schematic view of the micropolar plate

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Fig. 2

Rectangular micropolar plate element

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Fig. 3

Mesh grids of elements for the SSSS micropolar plate in case I (a) before and (b) after deflection

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Fig. 4

Variation of dimensionless maximum deflection of micropolar plates with different boundary conditions against the dimensionless length scale parameter in case I (P=500N/m2)

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Fig. 5

Variation of dimensionless maximum deflection of micropolar plates with different boundary conditions against the dimensionless length scale parameter in case II (P=1N)

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Fig. 9

Variation of Φ2,max against the applied load for (a) SSSS and (b) CCCC micropolar plates (————: Linear, ——●—— : Nonlinear) in case II

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Fig. 8

Variation of Φ2,max against the applied load for (a) SSSS and (b) CCCC micropolar plates (————: Linear, ——●—— : Nonlinear) in case I

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Fig. 7

Effect of dimensionless length scale parameter on the dimensionless transverse deflection and microrotation component of (a) SSSS, and (b) CCCC micropolar plates in case II (P=1 N)

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Fig. 6

Effect of dimensionless length scale parameter on the dimensionless transverse deflection and microrotation component of (a) SSSS and (b) CCCC micropolar plates in case I (P=500N/m2)

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