Thermal buckling and elastic vibration analysis of functionally graded beams and plates using improved third-order shear deformation theory

摘要

Functionally graded materials (FGMs) have been developed for general purpose structural components such as rocket engine components or turbine blades where the components are exposed to extreme temperatures. The earliest FGMs were introduced by Japanese scientists in the mid-1980s as ultra-high temperature-resistant materials for aerospace applications. Recently, these materials have found other uses in electrical devices, energy transformation, biomedical engineering, optics, etc. FGMs are microscopically inhomogeneous spatial composite materials, typically composed of a ceramic-metal or ceramic-polymer pair of materials. Therefore, it is important to investigate the behaviors of engineering structures such as beams and plates made from FGMs when they are subjected to thermal and dynamic loads for appropriate design. The material property profiles of FGMs vary across the graded direction. Therefore, using an improved third order shear deformation theory (TSDT) based on more rigorous kinetics of displacements to predict the behaviors of functionally graded beams and plates is expected to be more suitable than using other theories. Thus, in this research, the improved TSDT is used to investigate thermal buckling and elastic vibration response of functionally graded beams and plates. For the first time in this research temperature dependent material property solutions, are adopted to investigate thermal buckling results of functionally graded beams and plates. Additionally, the research includes natural frequency and forced vibration analysis of functionally graded plates subjected to a uniformly distributed dynamic load acting over the plate domain. To obtain the solutions, the Ritz method using polynomial and trigonometric functions for defining admissible displacements and rotations is applied to solve the governing equations. The numerical results are validated by published and experimental results. To clearly understand functionally graded materials beam specimens were manufactured from alumina-epoxy using a multi-step sequential infiltration technique. These beams were then subject to microscopic analysis to determine the profiles of the constituents. Finally experiments were conducted to determine the vibration characteristics and the results were compared to analysis using the improved TSDT. To compute theoretical parts in this research, the material compositions of the functionally graded beams and plates are assumed to vary smoothly and continuously throughout the thickness according to the power law distribution. Several significant aspects such as thickness and aspect ratios, materials, temperature, added mass etc. which affect analytical results are taken into account and discussed in detail. The original work in this thesis includes the application of the improved TSDT to thermal buckling and elastic vibration problems of functionally graded beams and plates. New critical buckling temperature results for the case of temperature dependent material properties have been solved by an iterative calculation technique. The results reveal that the effect of temperature dependent material on reduced buckling temperatures is more profound for a thicker beam and plate than a thinner one. The relationship between the critical temperatures and natural frequencies of the beam and plate structures are also presented and discussed.