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Geometrically nonlinear isogeometric analysis of functionally graded microplates with the modified couple stress theory

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journal contribution
posted on 2021-01-15, 05:08 authored by HX Nguyen, E Atroshchenko, H Nguyen-Xuan, Thuc VoThuc Vo
© 2017 Elsevier Ltd In this study, a new and efficient computational approach based on isogeometric analysis (IGA) and refined plate theory (RPT) is proposed for the geometrically nonlinear analysis of functionally graded (FG) microplates. While the microplates’ size-dependent effects are efficiently captured by a simple modified couple stress theory (MCST) with only one length scale parameter, the four-unknown RPT is employed to establish the displacement fields which are eventually used to derive the nonlinear von Kámán strains. The NURBS-based isogeometric analysis is used to construct high-continuity elements, which is essentially required in the modified couple stress and refined plate theories, before the iterative Newton-Raphson algorithm is employed to solve the nonlinear problems. The successful convergence and comparison studies as well as benchmark results of the nonlinear analysis of FG microplates ascertain the validity and reliability of the proposed approach. In addition, a number of studies have been carried out to investigate the effects of material length scale, material and geometrical parameters on the nonlinear bending behaviours of microplates.


The first and last authors gratefully acknowledge the financial support from the Northumbria University via the Researcher Development Framework. The first author would also like to acknowledge the supports from the Santander Universities Mobility Grant and Prof. E. Atroshchenko for the research visit at the University of Chile in March 2017.


Publication Date



Computers and Structures




18p. (p. 110-127)





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