The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates

A review of theories for the modeling and analysis of functionally graded plates and shells

“…It is found that the RMVT-based model is slightly superior to the PVD-based one in predicting the global responses of orthotropic, laminate and FG plates. Based on the RMVT and PVD, Wu and Li [337] developed finite layer models for 3D bending analysis of multilayered and FG plates. In these models, the plate was divided into a number of finite layers in which trigonometric functions and Lagrange polynomials were respectively used to interpolate the in-plane and transverse variations of the field variables of each individual layer.…”

Reissner’s mixed variational theorem-based nonlocal Timoshenko beam theory for a single-walled carbon nanotube embedded in an elastic medium and with various boundary conditions

“…Most of the above-mentioned nonlocal continuum models are based on the PVD, rather than the Reissner mixed variational theorem (RMVT) [33,34], even though RMVT-based theories have been demonstrated to be superior to the PVD-based ones for the analysis of macro-and micro-scaled structures with regard to the accuracy and convergence rate by Carrera [35][36][37], Carrera and Ciuffreda [38,39] and Wu and Li [40,41], Wu and Chiu [42] and Wu et al [43]. In the PVD, the generalized displacements are regarded as the primary variables subject to variation, while in the RMVT, these are both the generalized displacements and the generalized force resultants.…”

Enhanced modeling approach for multilayer anisotropic plates based on dimension reduction method and Hellinger–Reissner principle

“…Also Carrera and Demasi [26] derive a plate-theory based on RMVT and, more recently, Demasi [27][28][29][30][31] develop a generalized unified formulation with the aims to investigate the RMVT based theories and compare a variety of mixed first-and high-order shear deformation theories as well as global, zig-zag, and layerwise theories. Wu and Li [32,33] investigate the static behavior of simply supported multilayer composite and functionally graded material plate. In particular, they consider both RMVT and the principle of virtual displacement in order to develop a RMVT-based Shear Deformation Theory.…”