Nonlinear Mechanical Analysis Of FGM Structures

Functionally graded material is a kind of composite materials that are microscopically inhomogeneous,taking advantage of the merits of constituent materials adequately. By gradually varying the volume fraction of the constituent materials,FGM possesses the gradient in properties, which eliminates the mismatch of mechanical properties induced by the interface.So,FGM structures can be used in various special environments and can bear complex loads.In this thesis,bending,post-buckling and vibration response of bended or postbuckled configurations of FGM beams and circular plates subjected to uniform thermal loads are investigated.It is assumed that the properties of functionally graded materials vary continuously through the thickness of the structures and obey a simple power law related to the volume fraction of the constituents.Based on the classical and first-order shear deformation beam and plate theory, the basic equations of FGM beams and circular plates are derived using the physical neutral surface concept.A shooting method is employed to numerically solve the resulted equations.The main contents are as following:1.We briefly introduced the basic principle,definition and development as well as research status of FGM.At the same time,numerical solution used in this paper named shooting method was simply introduced.2.Static mechanical behavior of FGM beam.Effects of material constant,temperature dependent material properties,transverse shear deformation and thermal loads are discussed in details on bending and post-buckling of a FGM beam.Numerical results obtained herein showed that the post-buckling deformations can be caused for a clamped FGM beam subjected to thermal loads,but the more complex thermal bending deformations for a simple supported beam.Bifurcation buckling cannot occur for FGM beams with simply supported edges subjected to the same thermal loads and the beams will be produce multiple solution branches.3.Dynamic mechanical behavior of FGM beam.The results show that with increase of the thermal load,the natural frequencies of a simple supported and a clamped FGM beam decrease,then with an increasing.But the natural frequencies of a simple supported beam don't close to zero. While thermal load be close to the buckling thermal load,the natural frequencies of a clamped beam approach zero.4.Temperature dependent material properties and transverse shear deformation have different effect on the response dynamic mechanical behavior of the FGM beams.When taking into account these two factors, this effect will be particularly significant.And,with increase of slenderness ratio,the influence decrease.So,load-frequency relationship of FGM beams become complex is attributed to temperature dependent material properties and transverse shear deformation.5.Static mechanical behavior of FGM circular plates.Numerical results obtained herein showed that the post-buckling deformations can be caused for a clamped FGM circular plate subjected to thermal loads,but the more complex thermal bending deformations for a simple supported circular plate.