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

Abstract

Thuc (2017) A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory. Computer Methods in Applied Mechanics and Engineering, 313. pp. 904-940.

Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

“…In this example, the equivalent axial load caused by the thermal stress is calculated with/without the transverse thermal stress Further verification is carried out for mechanical and thermal buckling behaviours of FG plates in Tables 7 and 8. As can be seen in Table 7, the present results of mechanical buckling agree well with those obtained from refined plate theories (RPT) [26,28] and quasi-3D theory [28]. It is also shown that the inclusion of normal stretching effect leads to the higher critical buckling loads for macroplates but less significant to microplates.…”

“…Lou et al [27] then developed this model for a unified framework including the von Karman's geometric nonlinearity. It should be noted that above studies [26][27][28][29][30], the normal strain or normal deformation, which becomes significant for thick plates, is not included. In order to take into account both shear and normal deformation effects, Nguyen et al [28] presented four-variable quasi-3D model to analyse the bending, vibration and buckling behaviours of FG microplates using the isogeometric solutions.…”

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

“…Recent studies on the developments and applications of nonlocal theory to nanobeams and nanopaltes could be found in the works of Li et al [26][27][28][29], Nguyen et al [30], and Phung-Van et al [31]. Based on the MCT, numerous studies have been also carried out to investigate the behaviour of micro beams and plates [32][33][34][35][35][36][37][38][39][40][41][42][43][44][45]. For nonlinear analysis in accordance with the MCT, Reddy and Kim [41] developed a model based on a general third-order shear deformation plate theory, which can be specialized to classical, first-order shear deformation, the Reddy third-order plate theories and accounts for both von Kármán nonlinearity and FGMs.…”

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

“…The MCST sinusoidal shear deformation model was also developed by Thai and Vo [47] for deflections and natural frequencies of simply supported microplates. Some other refined plate models [48,49] and quasi-3D [50][51][52] were also employed the MCST for FG microplates. In addition, the thermal effects are examined for the FG microplates in many publications.…”