This article is focused on analysis of influence of functionally graded material parameters in the problem of longitudinal rod deformations. This analysis is based on exact and asymptotic solutions. Accuracy rating of the proposed asymptotic method of calculating deformations in constructions made of functionally graded material is also given.
HaugEChoiKKokovV. Design sensitivity analysis of structurals systems, New York, NY: Academic Press, 1986.
2.
ChoiKKKimN-H. Structural sensitivity analysis and optimization, New York, NY: Springer, 2010.
3.
KimJ-HPaulinoGH. Isoperimetric graded finite elements for non-homogeneous isotropic and orthotropic materials. J Appl Mech2002; 69(4): 502–514.
4.
YasMNShakeriMKhanjaniM. Layer-wise finite-element analysis of a functionally graded hollow thick cylinder with a piezoelectric ring. Proc IMechE Part C: J Mechanical Engineering Science2011; 225(5): 1045–1060.
5.
NaeiMHMasoumiAShamekhiA. Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method. Proc IMechE Part C: J Mechanical Engineering Science2007; 221(11): 1241–1247.
6.
UedaSGasikM. Thermo-elasto-plastic analysis of W-Cu functionally graded materials subjected to a uniform heat flow by micromechanical model. J Therm Stresses2000; 23: 395–409.
YinHMSunLZPaulinoGH. Micromechanics-based elastic model for functionally graded materials with particle interactions. Acta Mater2006; 52: 3535–3543.
9.
ShenH-S. Functionally graded materials: nonlinear analysis of plates and shells, Boca Raton, FL: CRC Press, 2009, New York, NY: Taylor & Francis Group.
10.
AkbarzadehAHHosseini ZadSKEslamiMR, et al.Mechanical behaviour of functionally graded plates under static and dynamic loading. Proc IMechE Part C: J Mechanical Engineering Science2011; 225(2): 326–333.
11.
KhazaeinejadPNajafizadehMM. Mechanical buckling of cylindrical shells with varying material properties. Proc IMechE Part C: J Mechanical Engineering Science2010; 224(8): 1551–1557.
12.
NajafizadehMMMahdavianMKhazaeinejadP. Superposition buckling analysis of rectangular plates composed of functionally graded materials subjected to non-uniform distributed in-plane loading. Proc IMechE Part C: J Mechanical Engineering Science2010; 224(11): 2299–2307.
13.
MohammadiMSaidiARJomehzadehE. A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges. Proc IMechE Part C: J Mechanical Engineering Science2010; 224(9): 1831–1841.
14.
AnthoineA. Second-order homogenization of functionally graded materials. Int J Solids Struct2010; 47: 1477–1489.
15.
NematollahiMAHematiyanMRFaridM. A two-stage inverse method for the evaluation of volume fraction distributions in 2D and 3D functionally graded materials. Proc IMechE Part C: J Mechanical Engineering Science2011; 225(7): 1550–1564.
16.
ManevitchLIAndrianovIVOshmyanVO. Mechanics of periodically heterogeneous structures, Berlin: Springer, 2002.
17.
BolshakovVIAndrianovIVDanishevs’kyyVV. Asymptotic methods for calculation of composite materials with microstructure, Dnipropetrovs'k: Porogi, 2008, (in Russian).
18.
AndrianovIVAwrejcewiczJDiskovskyA. Homogenization of quasi-periodic structures. Trans ASME J Vib Acoust2006; 128(4): 532–534.
19.
AndrianovIVAwrejcewiczJDiskovskyA. Design of the non-homogeneous quasi-regular structures. In: BolshakovVIWeichertD (eds) Advanced problems in mechanics of heterogeneous media and thin-walled structures. Dnipropetrovs’k: ENEM, 2010, pp.7–18.