A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory
journal contributionposted 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'.
JournalComputer Methods in Applied Mechanics and Engineering
Pagination37p. (p. 904-940)
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Science & TechnologyTechnologyPhysical SciencesEngineering, MultidisciplinaryMathematics, Interdisciplinary ApplicationsMechanicsEngineeringMathematicsIsogeometric analysisFunctionally graded microplatesModified couple stress theoryRefined plate theoryQuasi-3D theorySHEAR DEFORMATION-THEORYHIGHER-ORDER SHEARLAMINATED COMPOSITE PLATESFREE-VIBRATION ANALYSISTHERMAL BUCKLING ANALYSISREISSNER-MINDLIN PLATESFINITE-ELEMENT-ANALYSISSIMPLE 4-UNKNOWN SHEARSANDWICH PLATESBENDING ANALYSISApplied Mathematics