La Trobe

File(s) under embargo





until file(s) become available

Vibration of cracked functionally graded microplates by the strain gradient theory and extended isogeometric analysis

journal contribution
posted on 17.11.2020, 04:06 by HX Nguyen, E Atroshchenko, T Ngo, H Nguyen-Xuan, Thuc Vo
© 2019 Elsevier Ltd In this study, the vibration behaviours of functionally graded microplates with cracks are investigated by means of a simple yet rigorous version of Mindlin's generialised continuum and the extended isogeometric analysis (XIGA). The simplified strain gradient theory which includes one material length parameter and an additional micro-inertia term is employed to capture the size effects. Meanwhile, the displacement field of the plates is described using the refined plate theory with four unknowns and the XIGA in which enrichment functions are involved to effectively predict the responses of microplates with cracks. In addition, the IGA approach with highly smooth basis functions of non-uniform rational B-spline (NURBS) ensures a clean and efficient treatment of higher continuity requirements in the strain gradient theory. The benchmark numerical results show significant departure from those analysed by the classical continuum elasticity. Indeed, they reveal strong influences of microstructural characteristics on the vibration responses of microplates which are not shown in the platform of the classical theory and the influences are more pronounced as the size of the plates becomes comparable with the material length parameter.


The first and last authors gratefully acknowledge the financial support from the Northumbria University via the Researcher Development Framework. The second and the first authors would like to acknowledge the financial support from CONICYT REDI170090 and the Santander Universities Mobility Grant for the research visit at the University of Chile in March 2018.

Northumbria University via the Researcher Development Framework


Santander Universities Mobility Grant


Publication Date



Engineering Structures




16p. (p. 251-266)





Rights Statement

The Authors 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.