scholarly journals Improved Control Volume Method for Thermoelastic Analysis of Functionally Graded Solids

2021 ◽  
Vol 01 ◽  
Author(s):  
Bing-Bing Xu ◽  
Yu Liang ◽  
Miao Cui
Keyword(s):  
Control Volume ◽  
Functionally Graded ◽  
High Order ◽  
Shape Functions ◽  
Graded Materials ◽  
Thermoelastic Analysis ◽  
Complex Integration ◽  
Volume Method ◽  
Control Volume Finite Element ◽  
Functionally Graded Structure

Abstract: In this work, an improved control volume finite element method (ICVFEM) is proposed and implemented for thermoelastic analysis in functionally graded materials (FGMs) at steady state. Different from the conventional CVFEM, the sub-control volume used in the proposed method is a circular in the intrinsic coordinate. The advantages of the new integral domain are: (i) the complex integration path can be avoided, (ii) the method is very suitable for many types of elements. High-order shape functions of eight quadrilateral (Q8) elements are used to obtain the unknown variables and their derivatives. Besides, material properties in a functionally graded structure are calculated by the high-order shape functions based on the properties defined at the node. To verify the convergence and accuracy of the proposed method, three numerical examples with analytical solutions are illustrated by using the conventional CVFEM and FEM at the same time.

A high-order control volume finite element method for thermoelastic analysis of functionally graded solids with mixed grids

2018 ◽  
Vol 233 (11) ◽  
pp. 3994-4013
Author(s):  
Qi Liu ◽  
Yan Yu ◽  
Pingjian Ming
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
Control Volume ◽  
Functionally Graded ◽  
High Order ◽  
Shape Functions ◽  
Quadrilateral Element ◽  
Thermoelastic Analysis ◽  
Control Volume Finite Element

In this article, a new two-dimensional control volume finite element method has been developed for thermoelastic analysis in functionally graded materials. A nine-node quadrilateral element and a six-node triangular element are employed to deal with the mixed-grid problem. The unknown variables and material properties are defined at the node. The high-order shape functions of six-node triangular and nine-node quadrilateral element are employed to obtain the unknown variables and their derivatives. In addition, the material properties in functionally graded structure are also modeled by applying the high-order shape functions. The capabilities of the presented method to heat conduction problem, elastic problem, and thermoelastic problem have been validated. First, the defined location of material properties is found to be important for the accuracy of the numerical results. Second, the presented method is proven to be efficient and reliable for the elastic analysis in multi-phase materials. Third, the presented method is capable of high-order mixed grids. The memory and computational costs of the presented method are also compared with other numerical methods.

Thermoelastic analysis of functionally graded solids using a staggered finite volume method

2013 ◽  
Vol 104 ◽  
pp. 134-143 ◽  
Author(s):  
Jing-feng Gong ◽  
Ling-kuan Xuan ◽  
Ping-jian Ming ◽  
Wen-ping Zhang
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Functionally Graded ◽  
Thermoelastic Analysis ◽  
Volume Method

TRANSIENT HEAT CONDUCTION IN FUNCTIONALLY GRADED MATERIALS

2007 ◽  
Vol 04 (04) ◽  
pp. 603-619 ◽  
Author(s):  
S. M. HAMZA-CHERIF ◽  
A. HOUMAT ◽  
A. HADJOUI
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Functionally Graded Materials ◽  
Degrees Of Freedom ◽  
Functionally Graded ◽  
P Element ◽  
Transient Temperature ◽  
Test Problems ◽  
Shape Functions ◽  
Graded Materials

The h-p version of the finite element method (FEM) is considered to determine the transient temperature distribution in functionally graded materials (FGM). The h-p version may be regarded as the marriage of conventional h-version and p-version. The graded Fourier p-element is used to set up the two-dimensional heat conduction equations. The temperature is formulated in terms of linear shape functions used generally in FEM plus a variable number of trigonometric shape functions representing the internal degrees of freedom (DOF). In the graded Fourier p-element, the function of the thermal conductivity is computed exactly within the conductance matrix and thus overcomes the computational errors caused by the space discretization introduced by the FEM. Explicit and easily programmed trigonometric enriched capacitance, conductance matrices and heat load vectors are derived for plates and cylinders by using symbolic computation. The convergence properties of the h-p version proposed and the results of the numbers of test problems are in good agreement with the analytical solutions. Also, the effect of the non-homogeneity of the FGM on the temperature distribution is considered.

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