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

Gong, Junbo; Xuan, Liang; Ming, Pingjian; Zhang, Wenping

doi:10.1016/j.compstruct.2013.04.018

Cited by 15 publications

(14 citation statements)

References 39 publications

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“…Consequent on this, researchers have been continually motivated to use various techniques and methodologies to deal with this exciting material in order to enhance its state-of-the-art. There are now excellent books [1][2][3][4] Foremost amongst these are the applications of direct analytical procedure using the governing differential equations of motion [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], finite element [20][21][22], Rayleigh-Ritz [23], finite volume [24][25][26], differential quadrature [27], differential transformation [27,28] and transfer function [29,30] methods. Recently the dynamic stiffness method (DSM) has also been proposed [31,32].…”

Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

Banerjee

Ananthapuvirajah

2018

Journal of Sound and Vibration

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The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions.

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Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

Banerjee

Ananthapuvirajah

2018

Journal of Sound and Vibration

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“…In Charoensuk and Vessakosol 25 and Gong et al., 28 the material properties can be defined at the cell center or at the node. For material properties defined at the node, 25 the material properties at the integration point along the face of the control volume in an element is approximated by the high-order shape function, and for material properties defined at the cell center, 28 the material properties at the integration point is approximated by the material properties of the cell center. However, the authors find that the defined location of material properties have a great effect on the accuracy of numerical solution especially for highly graded material with coarse mesh.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Several numerical approaches have been used to investigate FGMs, including the FEM, 5 high-order model, 2 boundary element method (BEM), 23,24 and finite volume method (FVM). 25–28…”

Section: Introductionmentioning

confidence: 99%

“…Gong et al. 28 developed a cell vertex finite volume method (CV-FVM), or also known as CV-FEM, based on the staggered grid technique for thermoelastic analysis in FGMs. The Q4 and three-node triangular (T3) elements were employed to deal with the mixed-grid problems.…”

Section: Introductionmentioning

confidence: 99%

“…The material properties are defined at the node of Q9 or T6 element, and the grading material properties at the integration point along the face of the control volume are modeled by the high-order shape functions of nodal values of material properties. For the purpose of providing accuracy and continuous stress distribution in the thermoelastic field, taking a similar approach as in Gong et al., 28 the presented method calculates stresses on the element node, and then takes a weighted average of those node stresses. The remaining sections of this paper are organized as follows.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Liu

Ming

2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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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.

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A penalty-based cell vertex finite volume method for two-dimensional contact problems

Xuan,

Yan,

Gong

et al. 2024

Comput Mech

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

Cited by 15 publications

References 39 publications

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

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

A penalty-based cell vertex finite volume method for two-dimensional contact problems

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