Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates

Abstract

An effective, simple, and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first-order shear deformation theory (S-FSDT), which was recently presented in Composite Structures (2013; 101:332-340), is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C 1 -continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA).Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated.

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

“…Akbari et al [19] used Meshless Local Petrov-Galerkin method to simulate propagation of a thermoelastic wave through FGM plate and presented results for dynamic displacement and stress fields under transient thermal field. Yin et al [20] studied bending, buckling and free vibration of FGM plate and formulated a simple and efficient plate element method for functionally graded plates. Rahimabadi et al [21] presented results for vibration of FGM plates with cutout and crack in thermal environment using an enriched shear flexible 4-noded quadrilateral element with a Heaviside function.…”

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

“…After more ten years of development, IGA has been widely applied in engineering and among them with FGM plate structures. For example, Valizadeh et al [40] and Yin et al [41] employed this method to study the static and dynamic behaviours of FGM plates based on FSDT. Tran et al.…”

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

“…Thai and Choi [305][306] simplified the FSDT for FG plates [305] and laminated composite plates [306]. This simplified FSDT was later employed by Yu et al [307] and Yin et al [308] for the IGA of FG plates accounting for geometric nonlinearity. Thai et al [309] also developed another simplified FSDT for FG sandwich plates using the assumptions from Shimpi et al [310].…”