Analytical or Semi-analytical Solutions of Functionally Graded Material Structures

2021 ◽  
Author(s):  
Zheng Zhong ◽  
Guojun Nie
Keyword(s):  
Functionally Graded Material ◽  
Analytical Solutions ◽  
Functionally Graded ◽  
Graded Material

Analytical Solutions Using a Higher-Order Refined Theory for the Static Analysis of Functionally Graded Material Plates

2013 ◽  
Vol 705 ◽  
pp. 30-35
Author(s):  
K. Swaminathan ◽  
D.T. Naveenkumar
Keyword(s):  
Shear Deformation ◽  
Static Analysis ◽  
Functionally Graded Material ◽  
Analytical Solutions ◽  
Degrees Of Freedom ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Simply Supported ◽  
Graded Material

Analytical formulations and solutions to the static analysis of simply supported Functionally Graded Material (FGM) plates hitherto not reported in the literature based on a higher-order refined shear deformation theory with nine degrees-of-freedom already reported in the literature are presented. This computational model incorporates the plate deformations which account for the effect of transverse shear deformation. The transverse displacement is assumed to be constant throughout the thickness. In addition, another higher order theory with five degrees-of-freedom and the first order theory already reported in the literature are also considered for comparison. The governing equations of equilibrium using all the computational models are derived using the Principle of Minimum Potential Energy (PMPE) and the analytical solutions are obtained in closed-form using Naviers solution technique. A simply supported plate with SS-1 boundary conditions subjected to transverse loading is considered for all the problems under investigation. The varying parameters considered are the side-to-thickness ratio, power law function, edge ratio and the degree of anisotropy. Correctness of the formulation and the solution method is first established and then extensive numerical results using all the models are presented which will serve as a bench mark for future investigations.

scholarly journals Nonlinear Transient Thermal Modeling and Analysis of a Convective-Radiative Fin with Functionally Graded Material in a Magnetic Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
M. G. Sobamowo ◽  
G. A. Oguntala ◽  
A. A. Yinusa
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Thermal Performance ◽  
Functionally Graded Material ◽  
Analytical Solutions ◽  
Functionally Graded ◽  
Approximate Analytical Solutions ◽  
Graded Material ◽  
Nonlinear Transient ◽  
Transient Thermal

Nonlinear transient thermal analysis of a convective-radiative fin with functionally graded materials (FGMs) under the influence of magnetic field is presented in this study. The developed nonlinear thermal models of linear, quadratic, and exponential variation of thermal conductivity are solved approximately and analytically using the differential transformation method (DTM). In order to verify the accuracies of the nonlinear solutions, exact analytical solutions are also developed with the aids of Bessel, Legendre, and modified Bessel functions. Good agreements are established between the exact and the approximate analytical solutions. In the parametric studies, effects of heat enhancement capacity of fin with functionally graded material as compared to fin with homogeneous material are investigated. Also, influence of the Lorentz force and radiative heat transfer on the thermal performance of the fin are analyzed. From the results, it is shown that increase in radiative and magnetic field parameters as well as the in-homogeneity index improve the thermal performance of the fin. Also, the transient responses reveal that the FGM fin with quadratic-law and exponential-law function shows the slowest and fasted thermal responses, respectively. This study will provide a very good platform for the design and optimization of an improved heat transfer enhancement in thermal systems, where the surrounding fluid is influenced by a magnetic field.

Material optimization of a cemented tibia tray using functionally graded material

2016 ◽  
Vol 58 (3) ◽  
pp. 260-268 ◽  
Author(s):  
Hassan S. Hedia ◽  
Saad M. Aldousari ◽  
Noha Fouda
Keyword(s):  
Functionally Graded Material ◽  
Functionally Graded ◽  
Material Optimization ◽  
Graded Material

Structural integrity and mechanical properties of the functionally graded material based on 316L/IN718 processed by DED technology

2021 ◽  
Vol 811 ◽  
pp. 141038
Author(s):  
Daniel Melzer ◽  
Jan Džugan ◽  
Martina Koukolíková ◽  
Sylwia Rzepa ◽  
Jaroslav Vavřík
Keyword(s):  
Mechanical Properties ◽  
Functionally Graded Material ◽  
Structural Integrity ◽  
Functionally Graded ◽  
Graded Material

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

2021 ◽  
pp. 146442072098817
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plate ◽  
Dynamic Stiffness Matrix ◽  
Graded Material

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

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