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Research Papers

Nonlinear Bending Analysis of First-Order Shear Deformable Microscale Plates Using a Strain Gradient Quadrilateral Element

[+] Author and Article Information
R. Ansari

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

M. Faghih Shojaei, A. H. Shakouri

Department of Mechanical Engineering,
University of Guilan,
P.O. Box 3756,
Rasht, Iran

H. Rouhi

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

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 5, 2014; final manuscript received January 11, 2016; published online February 25, 2016. Assoc. Editor: Daniel J. Segalman.

J. Comput. Nonlinear Dynam 11(5), 051014 (Feb 25, 2016) (18 pages) Paper No: CND-14-1234; doi: 10.1115/1.4032552 History: Received October 05, 2014; Revised January 11, 2016

Based on Mindlin's strain gradient elasticity and first-order shear deformation plate theory, a size-dependent quadrilateral plate element is developed in this paper to study the nonlinear static bending of microplates. In comparison with the classical first-order shear deformable quadrilateral plate element, the proposed element needs 15 additional nodal degrees-of-freedom (DOF) including derivatives of lateral deflection and rotations with respect to coordinates, which means a total of 20DOFs per node. Also, the developed strain gradient-based finite-element formulation is general so that it can be reduced to that on the basis of modified couple stress theory (MCST) and modified strain gradient theory (MSGT). In the numerical results, the nonlinear bending response of microplates for different boundary conditions, length-scale factors, and geometrical parameters is studied. It is revealed that by the developed nonclassical finite-element approach, the nonlinear behavior of microplates with the consideration of strain gradient effects can be accurately studied.

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References

Figures

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Fig. 1

Schematic view of the nine-node quadrilateral microplate element

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Fig. 2

Variation of Wmax of microplates with the number of elements based on MSGT (a/h=10,  h/l=2,  and  Q=100)

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Fig. 3

Variation of Wc of microplates with the number of elements based on MSGT (a/h=10,  h/l=2,  and  Q=100)

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Fig. 4

Comparison between the present results and the analytical solutions of Ref. [38] in predicting the dimensionless maximum deflection of aluminum square plates based on the classical elasticity theory

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Fig. 5

Influence of dimensionless length-scale parameter on the nonlinear bending behavior of microplates with different types of boundary conditions based on MCST (a/h=12)

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Fig. 6

Influence of dimensionless length-scale parameter on the nonlinear bending behavior of microplates with different types of boundary conditions based on MSGT (a/h=12)

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Fig. 7

Influence of side length-to-thickness ratio on the nonlinear bending behavior of microplates with different types of boundary conditions based on MCST (h/l=1.5)

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Fig. 8

Influence of side length-to-thickness ratio on the nonlinear bending behavior of microplates with different types of boundary conditions based on MSGT (h/l=1.5)

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