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.
KoizumiMNiinoM. Overview of FGM research in Japan. MRS Bull1995; 20: 19–20.
2.
BuyukkayaE. Thermal analysis of functionally graded coating AlSi alloy and steel pistons. Surf Coat Technol2008; 202: 3856–3865.
3.
ZhaoB. Thermal stress analysis of ceramic-coated diesel engine pistons based on the wavelet finite-element method. J Eng Mech2012; 138: 143–149.
4.
ThiemeMet al.Titanium powder sintering for preparation of a porous functionally graded material destined for orthopaedic implants. J Mater Sci Mater Med2001; 12: 225–231.
5.
SukMJChoiSIKimJSet al.Fabrication of a porous material with a porosity gradient by a pulsed electric current sintering process. Met Mater Int2003; 9: 599–603.
6.
HidekiSKatsumiKHitoshiO. Application feasibility of permittivity graded FGM (functionally graded materials) for gas-insulated equipment. Electr Eng Jpn2010; 165: 39–45.
7.
KatoKKurimotoMShumiyaHet al.Application of functionally graded material for solid insulator in gaseous insulation system. Dielectr Electr Insul IEEE Trans2006; 13: 362–372.
OotaoYAkaiTTanigawaY. Three-dimensional transient thermal stress analysis of a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction. J Therm Stress1995; 18: 497–512.
10.
OotaoYTanigawaY. Three-dimensional transient thermal stresses of functionally graded rectangular plate due to partial heating. J Therm Stress1999; 22: 35–55.
11.
VelSS. Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J2002; 40: 1421–1433.
12.
AbaliBEVöllmeckeCWoodwardBet al.Numerical modeling of functionally graded materials using a variational formulation. Continuum Mech Thermodyn2012; 24: 377–390.
13.
KarVRMahapatraTRPandaSK. Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels. Compos Struct2017; 160: 1236–1247.
14.
SantareMHLambrosJ. Use of graded finite elements to model the behavior of nonhomogeneous materials. J Appl Mech2000; 67: 819–822.
15.
KimJHPaulinoGH. Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. ASME J Appl Mech2002; 69: 502–514.
16.
AboudiJPinderaMJArnoldSM. Higher-order theory for functionally graded materials. Compos Part B: Eng1999; 33: 777–832.
17.
BansalYPinderaMJ. Efficient reformulation of the thermoelastic higher-order theory for functionally graded materials. J Therm Stresses2003; 26: 1055–1092.
18.
ZhongYBansalYPinderaMJ. Efficient reformulation of the thermal high reorder theory for FGMs with locally variable thermal conductivity. Int J Comput Eng Sci2004; 5: 795–831.
19.
Bansal Y. Finite-volume direct averaging micromechanics of heterogeneous media. PhD Thesis. University of Virginia, USA, 2005.
20.
BansalYPinderaMJ. Finite-volume direct averaging micromechanics of heterogeneous materials with elastic-plastic phases. Int J Plast2006; 22: 775–825.
21.
CavalcanteMAAMarquesSPCPinderaMJ. Computational aspects of the parametric finite-volume theory for functionally graded materials. Comput Mater Sci2008; 44: 422–438.
22.
CavalcanteMAAMarquesSPCPinderaMJ. Parametric formulation of the finite-volume theory for functionally graded materials-part II: numerical results. ASME. J Appl Mech2007; 74: 946–957.
23.
GoldbergRKHopkinsDA. Thermal analysis of a functionally graded material subject to a thermal gradient using the boundary element method. Compos Methods Appl Mech Eng1995; 5: 793–806.
24.
SutradharSPaulinoGHGrayLJ. Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method. Eng Anal Bound Elem2002; 26: 119–132.
25.
CharoensukJVessakosolP. A high order control volume finite element procedure for transient heat conduction analysis of functionally graded materials. Heat Mass Transf2010; 46: 1261–1276.
26.
CharoensukJVessakosolP. Numerical solutions for functionally graded solids under thermal and mechanical loads using a high-order control volume finite element method. Appl Therm Eng2011; 31: 213–222.
27.
GongJXuanLMingPet al.An unstructured finite-volume method for transient heat conduction analysis of multilayer functionally graded materials with mixed grids. Numer Heat Transf B Fundam2013; 63: 222–247.
28.
GongJXuanLMingPet al.Thermoelastic analysis of functionally graded solids using a staggered finite volume method. Compos Struct2013; 104: 134–143.
29.
GongJXuanLMingPet al.Application of the staggered cell-vertex finite volume method to thermoelastic analysis in heterogeneous materials. J Therm Stresses2014; 37: 506–531.
30.
RawMJSchneiderGEHassanijV. A nine noded quadratic control volume based finite element for heat conduction. J Spacecraft1985; 22: 523–529.
31.
WangXC. Finite element method, Beijing: Tsinghua University Press, 2003.
32.
JabbariMSohrabpourSElsamiMR. Mechanical and thermal stresses in a functionally graded hollow cylinder due to radically symmetric loads. Int J Press Vessel Pip2002; 79: 493–497.
