La Trobe
Manuscript_FGM_MCS_IGA_rev2.pdf (6.18 MB)

A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory

Download (6.18 MB)
journal contribution
posted on 2021-01-15, 05:12 authored by HX Nguyen, TN Nguyen, M Abdel-Wahab, SPA Bordas, H Nguyen-Xuan, Thuc VoThuc Vo
The isogeometric analysis associated with a novel quasi-3D shear deformation theory is proposed to investigate size-dependent behaviours of functionally graded microplates. The modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The proposed approach is successfully applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions in which some benchmark numerical examples are presented. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and aspect ratios on the responses of the microplates.


The first and last authors gratefully acknowledge the financial support from the Northumbria University via the Researcher Development Framework. The fifth author would like to thank the support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.02-2014.24. The third and fourth authors both thank the support of the INTER/FWO/15/10318764 grant. The fourth author also thanks partial support for his time from the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) entitled 'Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery'.


Publication Date



Computer Methods in Applied Mechanics and Engineering




37p. (p. 904-940)





Rights Statement

The Author reserves all moral rights over the deposited text and must be credited if any re-use occurs. Documents deposited in OPAL are the Open Access versions of outputs published elsewhere. Changes resulting from the publishing process may therefore not be reflected in this document. The final published version may be obtained via the publisher’s DOI. Please note that additional copyright and access restrictions may apply to the published version.