Modelling of bidirectional functionally graded plates with geometric nonlinearity: A comparative dynamic study using whole domain and finite element method

Present work attempts to study the nonlinear dynamic behaviour of bidirectional functionally graded plates (BFG) along with unidirectional functionally graded plates (UFG). For BFG plates the material is graded along the thickness and length simultaneously and two types of UFG plates are considered namely thickness-wise (TFG) and length-wise (AFG) plates. The dynamic problem is formulated using two different methods namely, whole domain method and finite element method. The constitutive relation for the former is generated using classical plate theory whereas Mindlin plate theory is used in the later. Geometric nonlinearity is addressed here by using Von Karman type strain-displacement relation. Both clamped and simply supported boundary conditions are considered and the plate is assumed to be under action of uniformly distributed external load. The results of free and forced vibration analyses are presented as backbone curves and frequency response curves respectively. The results show that all three plates exhibit hardening type nonlinearity. It is also seen that the effect of material gradation parameters is more profound in simply supported plates compared to clamped plates. Specifically, these parameters do not seem to have much effect on BFG clamped plates in free vibration. The outcome of the analysis is compared with those in existing literature and fair agreement is observed between them.

Automated summary

This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.