Influence Of Material Gradation Research Articles

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 and buckling analysis of FGM plates using inverse trigonometric shear deformation theory

PurposeThe purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate.Design/methodology/approachEquilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate.FindingsThe finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied.Originality/valueDevelopment and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.

Co-rotational 3D beam element for nonlinear dynamic analysis of risers manufactured with functionally graded materials (FGMs)

This paper considers a co-rotational beam formulation for beams, which is used for the finite element analysis of flexible risers and pipelines made of functionally graded materials. The influence of material gradation is addressed using an exponential variation of properties throughout the thickness of the pipe. Space discretization of the equilibrium equations is derived based on the Euler–Bernoulli assumptions considering two-node Hermitian beam elements which are referred to a co-rotation coordinate system attached to the element local frame of coordinates. The geometric non-linear effects of the beam are considered under large displacement and rotations, but under small-strain conditions. The deflections of the riser result from forces caused by self-weight, buoyancy, sea currents, waves, the action of floaters, seabed-structure interactions, and ship’s motion. We provide numerical examples and compare our results with the ones available in the literature. In addition, applications related to practical offshore engineering situations are considered to highlight the behavior of functionally graded materials (FGMs) as compared to homogeneous risers.

Design of functionally graded piezocomposites using topology optimization and homogenization – Toward effective energy harvesting materials

In the optimization of a piezocomposite, the objective is to obtain an improvement in its performance characteristics, usually by changing the volume fractions of constituent materials, its properties, shape of inclusions, and mechanical properties of the polymer matrix (in the composite unit cell). Thus, this work proposes a methodology, based on topology optimization and homogenization, to design functionally graded piezocomposite materials that considers important aspects in the design process aiming at energy harvesting applications, such as the influence of piezoelectric polarization directions and the influence of material gradation. The influence of the piezoelectric polarization direction is quantitatively verified using the Discrete Material Optimization (DMO) method, which combines gradients with mathematical programming to solve a discrete optimization problem. The homogenization method is implemented using the graded finite element concept, which takes into account the continuous gradation inside the finite elements. One of the main questions answered in this work is, quantitatively, how the microscopic stresses can be reduced by combining the functionally graded material (FGM) concept with optimization. In addition, the influence of polygonal elements is investigated, quantitatively, when compared to quadrilateral 4-node finite element meshes, which are usually adopted in material design. However, quads exhibit one-node connections and are susceptible to checkerboard patterns in topology optimization applications. To circumvent these problems, Voronoi diagrams are used as an effective means of generating irregular polygonal meshes for piezocomposite design. The present results consist of bi-dimensional unit cells that illustrate the methodology proposed in this work.

Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation

This paper presents a geometric nonlinear analysis formulation for beams of functionally graded cross-sections by means of a Total Lagrangian formulation. The influence of material gradation on the numerical response is investigated in detail. Two examples are given that illustrate the main features of the formulation, in which the behavior of beams of graded cross-sections is compared with homogeneous material beams. A motivation for this work is the potential development of functionally graded risers for the offshore oil exploration industry.