The bamboo structure can be generally viewed as a Functionally Graded composite material constituted by long and aligned cellulose fibres embedded in a lignin matrix. Analysing the transversal section of a bamboo culm, one can observe that the fibre distribution is variable through its thickness. The non-uniform distribution of fibres prevents the direct application of equations used to model the behaviour of composite materials, as the rule of mixtures equations for strength and modulus of elasticity. These equations assume, besides the perfect bonding between fibre and matrix, uniform distribution of the fibres in the matrix. In bamboo, the fibre distribution follows an organized pattern with a higher concentration of fibres on the outer surface of the culm. Establishing how this variation occurs, the basic equations from the composite materials approach can be modified in order to model the mechanical behaviour of bamboo. This paper presents the meso-structure analyses of bamboo culms through Digital Image Analysis. The variation of the volume fraction of the cellulose fibres across the transversal section of the bamboo is established. The developed methodology is successfully applied to study the volume fraction variation of fibres in two different samples of bamboo species Phyllostachys heterocycla pubenscens, commonly know as "Moso".      

In this article, thermal stability of beams made of functionally graded material (FGM) is considered. The derivations of equations are based on the one-dimensional theory of elasticity. The material properties vary continuously through the thickness direction. Tanigawa's model for the variation of Poisson's ratio, the modulus of shear stress, and the coefficient of thermal expansion is considered. The equilibrium and stability equations for the functionally graded beam under thermal loading are derived using the variational and force summation methods. A beam containing six different types of boundary conditions is considered and closed form solutions for the critical normalized thermal buckling loads related to the uniform temperature rise and axial temperature difference are obtained. The results are reduced to the buckling formula of beams made of pure isotropic materials….

Perforated discs have many applications in different parts of industry. By making such disks of functionally graded materials, more capabilities can be obtained from them. Vibration analysis of these kinds of disks can help us make them more efficient. In this paper, modeling and evaluation of disk vibration of functionally graded materials with regard to thickness were carried out using Abaqus software. Since no certain element has been defined regarding functionally graded materials for the design and analysis of a particular element in Abaqus software, molding of such materials has been used in this application. In order to verify the results, the results obtained from ABAQUS analysis have been compared with those available in the literature. The obtained results show that by defining more layers with regard to changes in properties, the obtained results approach the exact solutions.

In this paper, the static bending, free vibration, and dynamic response of functionally graded piezoelectric beams have been carried out by finite element method under different sets of mechanical, thermal, and electrical loadings. The beam with functionally graded piezoelectric material (FGPM) is assumed to be graded across the thickness with a simple power law distribution in terms of the volume fractions of the constituents. The electric potential is assumed linear across the FGPM beam thickness. The temperature field is assumed to be of uniform distribution over the beam surface and through the beam thickness. The governing equations are obtained using potential energy and Hamilton's principle based on the Euler-Bernoulli beam theory that includes thermo-piezoelectric effects. The finite element model is derived based on the constitutive equation of piezoelectric material accounting for coupling between the elasticity and the electric effect by two nodes Hermitian beam element. The present finite element is modelled with displacement components and electric potential as nodal degrees of freedom. The temperature field is calculated by post-computation through the constitutive equation.Results are presented for two-constituent FGPM beam under different mechanical boundary conditions. Numerical results include the influence of the different power law indexes, the effect of mechanical, thermal, and electrical loadings and the type of in-plane boundary conditions on the deflection, stress, natural frequencies, and dynamic response. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.