Bending and Buckling Analysis of Functionally Graded Microplates using Isogeometric Approach
Hoang Nguyen  1@  , Thuc Vo  1, *@  , Hung Nguyen-Xuan  2, *@  
1 : Department of Mechanical and Construction Engineering
Northumbria University, Newcastle Upon Tyne NE1 8ST -  United Kingdom
2 : Center for Interdisciplinary Research in Technology (CIRTech)
Ho Chi Minh City Univeristy of Technology (HUTECH), Ho Chi Minh City 70000 -  Vietnam
* : Corresponding author

This study aims at investigating size-dependent effects of functionally graded (FG) microplates for bending and buckling problems using isogeometric analysis (IGA). While displacement field of the microplates is established based on the refined plate theory (RPT) with four variables, the modified couple stress (MCS) theory is used to capture small scale effects of the microplates. The RPT, which requires C1-continuity element, not only is able to improve the accuracy of the analysis but also helps to describe the non-linear distribution of shear stress through plate thickness without using shear correction factors. The MCS, which has advantages of including asymmetric couple stress tensor and using only one material length scale parameter, would be able to effectively capture the size-dependent effects in small-scale structures rather than classical theories. Bending and buckling analysis of rectangular and circular FG microplates based on these two theories are solved in the platform of IGA. This recently developed method utilises the non-uniform rational B-splines (NURBS) functions to establish approximation functions and describe geometry domains. In addition, NURBS functions, by its nature, could satisfy high-order continuity which is required in RPT theory without any difficulty. A number of numerical examples conducting for rectangular and circular FG microplates reveal that the consideration of small scale effects is followed by the increase in plates' stiffnes. Consequently, transverse deflection and buckling load of the FG microplates will be decreased and risen, respectively.

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