Vibration of cracked functionally graded microplates by the strain gradient theory and extended isogeometric analysis. (15th May 2019)

• Record Type: Journal Article
• Authors: Nguyen, Hoang X.; Atroshchenko, Elena; Ngo, Tuan; Nguyen-Xuan, H.; Vo, Thuc P.
• Is Part Of: Engineering structures. Volume 187(2019)
• Page Start: 251
• Page End: 266
• Publication Date: 2019-05-15
• Subjects: Strain gradient theory -- Extended isogeometric analysis -- Vibration analysis -- Functionally graded microplates; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2019.02.032
• Languages: English
• ISSNs: 0141-0296

Abstract

Highlights: A new approach for cracked microplates with size effects based on strain gradient theory and extended isogeometric analysis. An efficient NURBS-based extended isogeometric analysis for vibration of cracked microplates with elements of C 2 -continuity. New enrichment functions for near-tip asymptotic field in strain gradient regime. Benchmarking results for vibration of cracked microplates with size effects. Abstract: 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.