Stress Analysis of Functionally Graded Disk with Exponentially Varying Thickness using Iterative Method

In this paper, variable thickness disk made up of functionally graded material (FGM) under internal and external pressure is analyzed using a simple iteration technique. Thickness of FGM disk and the material property, namely, Young’s modulus are varying exponentially in radial direction. Poisson’s ratio is considered invariant for the material. Navier equation is used to formulate the problem in the differential equation form under plane stress condition. Displacement, stresses, and strains are obtained under the influence of material gradation and variable thickness. Three different material combinations are considered for the FGM disk. The mechanical response of disk obtained for different functionally graded material combinations are compared with the homogenous disk, and results are plotted graphically

Free vibration analysis on axially graded beam resting on variable Pasternak foundation

Free vibration analysis is conducted on axially functionally graded Euler-Bernoulli beam resting on variable Pasternak foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying linearly along the axial direction. Two types of boundary conditions namely; clamped and simply supported are used in the analysis. The problem is formulated using Rayleigh-Ritz method and governing equations are derived with the help of Hamilton’s principle. The numerical results are generated for different material gradation parameter, foundation parameter and boundary conditions and the effect of these parameters on the free vibration behaviour of the beam is discussed.

The flying insect thoracic cuticle is heterogenous in structure and in thickness-dependent modulus gradation

The thorax is a specialized structure central to insect flight. In the thorax, flight muscles are surrounded by a thin layer of cuticle. The structure, composition, and material properties of this chitinous structure may influence the efficiency of the thorax in flight. However, these properties, as well as their variation throughout anatomical regions of the thorax or between insect taxa, are not known. In this work, we provide a multi-faceted assessment of thorax cuticle for fliers with asynchronous (honey bee; Apis mellifera) and synchronous (hawkmoth; Manduca sexta) muscles. We investigated cuticle structure using histology, material composition through confocal laser scanning microscopy, and modulus gradation with nanoindentation. Our results suggest that cuticle properties of the thorax are highly dependent on anatomical region and species. Modulus gradation, but not mean modulus, differed between the two types of fliers. In some regions, A. mellifera had a positive linear modulus gradient from cuticle interior to exterior of about 2 GPa. In M. sexta, the modulus gradients were variable and were not well represented by linear fits with respect to cuticle thickness. We utilized finite element modeling to assess how measured modulus gradients influenced maximum stress in cuticle. Stress was reduced when cuticle with a linear gradient was compressed from the high modulus side. These results support the protective role of the A. mellifera thorax cuticle. Our multi-faceted assessment advances our understanding of thorax cuticle structural and material heterogeneity and the potential benefit of material gradation to flying insects.

Closed-form expressions for bending and buckling of functionally graded nanobeams by the Laplace transform

This paper presents analytical solutions for bending and buckling of nonlocal functionally graded (FG) Euler–Bernoulli (EB) nanobeams. Material gradation along the thickness direction could be defined by a power function (P-FG), a sigmoidal function (S-FG), and an exponential function (E-FG). Laplace transform is applied to the differential form of the equation of motion of the nonlocal elasticity theory. Closed-form expressions for bending deflection and critical buckling load of FG nanobeams are derived. Effects of material gradations as well as the nonlocal parameter are examined. It is found that bending displacements and critical buckling loads could be controlled by an appropriate choice of material distribution parameter for P-FG nanobeams. The presented results also demonstrate the influences of factors such as the choice of material gradation, power-law index, and nonlocal parameter on bending and buckling behavior.

Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories

Investigation on the influence of beam theory and partial foundation support on natural frequencies play an important role in design of structures. In this paper, fundamental frequencies of a bidirectional functionally graded sandwich (BFGSW) beam partially supported by an elastic foundation are evaluated using various beam theories. The core of the sandwich beam is homogeneous while its two face sheets are made from three distinct materials with material properties varying in both the length and thickness directions by power gradation laws. The finite element method is employed to derive equation of motion and to compute the frequencies of the beam. The effects of the material gradation, the foundation parameters and the span to height ratio on the frequencies are studied in detail and highlighted. The difference of the frequencies obtained by different beam theories is also examined and discussed. The numerical results of the paper are useful in designing BFGSW beams with desired fundamantal frequencies.

Dependency of critical damping on various parameters of tapered bidirectional graded circular plates rested on Hetenyi medium

In industrial machinery and automobiles the critical damping plates are used as shock absorbers to dampen system and return rest position, in the shortest period of time. The paper is focused on the effects of various parameters on critical damping of a complicated system including a tapered bidirectional graded circular plate subjected to radially variable in-plane pre-load and rested on visco-Hetenyi elastic medium with semi-rigid restraint. By employing a Chebyshev-Ritz method, dependency of critical damping is investigated for the first time on various parameters including bidirectional arbitrary material gradation, variable in-plane pre-load, Hetenyi elastic medium parameters, tapering, semi-rigid restraint and Poisson’s ratio. For the Chebyshev-Ritz method developed here, the proper scale factor and orthogonal shifted Chebyshev polynomials of the first kind without auxiliary function requirement are used. The conventional rule of mixture and Mori-Tanaka homogenization scheme are used to model transverse gradation. The characteristic equation is calculated by vanishing determinant of the total potential energy Hessian. An equivalent ABAQUS model is introduced to eliminate necessity of complicated modeling of original structure.

Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support

This study presents dynamic responses of a composite thick beam with a functionally graded porous layer under dynamic sine pulse load. The boundary conditions of the composite beam are considered as viscoelastic supports. Three layers are considered, and face sheet layers have porous functionally graded materials in which the distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric distribution, X distribution, and ◊ distribution). The layered composite thick beam is modeled as a two-dimensional plane stress problem. The equation of motion is obtained by Lagrange’s equations. In formation of the problem, the finite element method is used with a 12-node 2D plane element. In the solution process of the dynamic problem, a numerical time integration method of the Newmark method is used. In numerical analyses, influences of stiffness and damping coefficients of viscoelastic supports, material gradation index, porosity parameter, and porosity models on the dynamic response of thick functionally graded porous beam are investigated under the pulse load.

Non-Linear Stability of the Step-Variable In-Plane Functionally Graded Plates Subjected to Linear Approaches of the Edges

The analysis of gradations through the thickness in structures are commonly used. It usually refers to the problems of the stability of functionally graded (FG) structures. In this work, rectangular in-plane FG plates built of a material gradation along the transversal direction were assumed. Five-strip FG plates with four cases that were based on the boundary conditions on longitudinal edges and simply supported on transverse loaded edges were considered. The non-linear stability problems of the FG plates that were subjected to linear approaches of the transverse edges for several types of loads were solved. The estimations were executed with two methods: an analytical-numerical way based on Koiter’s theory and finite element method (FEM).

Bi-Directional Functionally Graded Nanotubes: Fluid Conveying Dynamics

In the paper, a novel model of fluid-conveying nanotubes made of bi-directional functionally graded materials is presented for investigating the dynamic behaviors and stability. For the first time, the material properties of the nanotubes along both radical and axial directions are under consideration. Based on Euler–Bernoulli beam and Eringen’s nonlocal elasticity theories, the governing equation of the nanotubes and associated boundary conditions are developed using Hamilton’s principle. Differential quadrature method (DQM) is applied for discretizing the equation to determine the numerical solutions of the nanotubes with different boundary conditions. Numerical examples are presented to examine the effects of the material gradation, nonlocal parameter, and mode order on the dynamics and stability. It is shown that the two-directional materials distribution can significantly change the critical flow velocity, fundamental frequencies and stability. Comparing with traditional one-directional distribution, such 2D is more flexible to tune overall dynamic behaviors, this may provide new avenues for smart pipes.