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".      

This investigation presents material nonlinear analysis of a cantilever bar element made of Functionally graded material with porosity properties. The material properties of bar element are considered as changing though axial direction based on the Power-Law distribution and uniform porosity distribution. The stress-strain relation of the material is considered as a nonlinear property according to a Power-Law function. The cantilever bar element is subjected to a point load at the free end. In order to obtain more realistic solution for the nonlinear problem and axially material distribution, nonlinear finite element method is used. In the obtaining of finite element equations, the virtual work principle is used and, after linearization step, the tangent stiffness matrix and residual vector are obtained. In the nonlinear solution process, the incremental force method is implemented and, each load step, the nonlinear equations are solved by using the Newton-Raphson iteration method. In the numerical results, effects of material nonlinearity parameters, porosity coefficients, material distribution parameter and aspect ratios on nonlinear static deflections of the bar are presented and discussed. The obtained results show that the material nonlinear behaviour of the bar element is considerably affected with porosity and material graduation.

In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A Functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi models, in which the thermophysical properties are temperature dependent. The governing equations are expressed in Laplace-Fourier double transform domain and solved in that domain. Then the inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand are obtained numerically in complex domain by using Laguerre’s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the thermal displacement, temperature and thermal stress are obtained for a hypothetical material. Finally, the obtained results are presented graphically to show the effect of non-local fractional parameter on thermal displacement, temperature and thermal stress. A comparison of the results for different theories (three-phase-lag model, GN model II, GN model III) is presented and the effect of non-homogeneity is also shown. The results, corresponding to the cases, when the material properties are temperature independent, agree with the results of the existing literature.

In the present paper, the buckling problem of rectangular Functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. The plate is subjected to bi-axial compression loading. Mechanical properties of FG plate are assumed to vary continuously along the thickness of the plate according to different volume of fraction functions of constituents. These functions are assumed to have power law distributions. The displacement function is assumed to have the form of double Fourier series, of which derivatives are legitimized using Stokes’ transformation method. The advantage of using this method is the capability of considering effect of any possible combination of boundary conditions on the buckling loads. The out-plane displacement distribution is assumed using Fourier Sinus Series. This results in a general eigenvalue problem which can be used for evaluating the buckling load under different edge conditions, plate aspect ratios and various volume fraction functions. For generality of problem, plate is elastically restrained using some rotational and translational springs at four edges. Some numerical examples are presented and compared the to numerical results of finite element method using ABAQUS and other researchers’ results to validate the proposed method. It has been shown that there is good agreement between them.

The present study deals with the elastic analysis of concave thickness rotating disks made of Functionally graded materials (FGMs).The analysis is carried out using element based gradation of material properties in radial direction over the discretized domain. The resulting deformation and stresses are evaluated for free-free boundary condition and the effect of grading index on the deformation and stresses is investigated and presented. The results obtained show that there is a significant reduction of stresses in FGM disks as compared to homogeneous disks and the disks modeled by power law FGM have better strength.

The pipes conveying fluid are capable of displaying complex dynamical behaviors. In this paper, the dynamic behavior of a simply supported fluid-conveying pipe made of Functionally graded material in thickness direction, is analysed. The Young Modulus are assumed to be graded along the thickness direction according to a simple power law and equations of motion of the Euler– Bernoulli beam are derived. The partial differential equation is discretized to ordinary differential equations by the Galerkin method. The natural frequencies are obtained for different dimensionless parameters and compared with a homogenious pipe conveying fluid, and the effect of gradually changed material has been studied. Dimensionless critical flow velocities which couse instability are obtained for particular mass parameter and different distribution of Young Modulus. The results show that by increasing Young Modulus from inner to outer surface of pipe, the natural frequencies of system increase and instability is occurred in higher critical velocities.

A mesh-free method based on moving least squares approximation (MLS) and weak form of governing equations including two dimensional equations of motion and Maxwell’ s equation is used to analyze the free vibration of Functionally graded piezoelectric material (FGPM) beams. material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the transformation method. The mesh-free method is verified by comparison with a finite element method (FEM) which performed for FGPM beams. Comparisons showed that this model has a good accuracy. After validation of the presented model, a parametric study was carried out to investigate the effect of mechanical and electrical boundary conditions, slenderness ratio and distribution of constituent materials on natural frequencies of FGPM beams. It is concluded that slenderness ratio has more significant effect on lower frequencies. On the other hand, higher frequencies are affected by the volume fraction power index much more than lower frequencies.