Behaviours of functionally graded sandwich micro-beams and plates

Trinh, Luan (2017) Behaviours of functionally graded sandwich micro-beams and plates. Doctoral thesis, Northumbria University.

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Abstract

Functionally graded materials (FGMs) are a novel class of materials having unique characteristics formed of two or more constituent phases with a continuously variable composition. The introduction of these materials to the sandwich structures creates more potentials to the structural applications with the ability of tailoring the material properties as well as the possibility of avoiding the delamination and stress concentration in conventional sandwich structures. With the rapid development of technology, it is now common to use FGMs in micro/nanoelectromechanical systems, e.g. thin films, sensors, actuators and other devices. At these scales, the use of experimentation to understand the structural behaviours is difficult and highly time-consuming, whilst the molecular modelling is computationally very expensive for the scales that are popular to structural engineers. Therefore, higher-order continuum theories, which were developed from the classical continua, become very popular in modelling micro/nano-scale structures. Based on one of these higher-order continuum theories namely the modified couple stress theory, this thesis aims to develop the analytical methods, i.e. Navier and state space based solutions, to analyse the static, free vibration and buckling behaviours of FG and FG-sandwich beams and plates. The governing equations and appropriate boundary conditions are developed for these structural behaviours of beams and plates at both micro and macro- scales using the variational principle. Numerical results are computed using MATLAB and verified with the published results to demonstrate the accuracy and efficiency of the developed theoretical formulation. The numerical applications include:
 the free vibration and buckling behaviours of FG and FG sandwich macrobeams under arbitrary boundary conditions and mechanical/thermal loads,
 the static, free vibration and buckling behaviours of simply supported FG microbeams, and the free vibration behaviour of bidirectional FG microbeams under arbitrary boundary conditions,
 the static, free vibration and buckling behaviours of simply supported FG-sandwich microplates under mechanical/thermal loads,
 the static, free vibration and buckling behaviours of FG-sandwich microplates with two opposite simply supported edges and various boundary conditions for other edges.

The outcomes from this thesis emphasize the need of including couple stress in analyzing the structural behaviours of FG beams and plates at microscales. Some of them are presented at the first time and can be used as the benchmark results for numerical methods. These analytical methods can also be combined with other strong form methods to analyse various types of complex structures.

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