Open Access

ARTICLE

Analytical and FE Modeling of FG Beams Based on A Refined Shear Deformable Beam Theory for Static and Dynamic Analyses of FG BeamsWith Thermoelastic Coupling

by Cong Xie¹, Guangyu Shi¹

1 Department of Mechanics, Tianjin University, Tianjin, China
2 Corresponding author. E-mail: shi_guangyu@163.com

Computer Modeling in Engineering & Sciences 2015, 108(6), 397-427. https://doi.org/10.3970/cmes.2015.108.397

Abstract

The static and dynamic thermoelastic analyses of the beams made of functionally graded materials (FGMs) are presented in this paper. Based on the refined third-order shear deformation beam theory proposed by the senior author and the variational principle, the governing equations of FG beams are deduced. The influence of temperature on Young’s modulus and coefficients of thermal expansion is taken into account when FG beams are subjected to thermal loading. The resulting governing equations are a system of the eighth-order differential equations in terms of displacement variables, and the thermoelastic coupling is included in the equations. An accurate and reliable two-noded beam element is developed for the bending and free vibration analysis of FG beams by employing the refined thirdorder shear deformation beam theory and the quasi-conforming element technique. Several typical examples of FG beams are solved using the present FG beam element to show the effects of the material distribution and thermal loading on the defections, stresses and natural frequencies of FG beams. The accuracy of both the analytical solutions and numerical results given by the proposed models are validated against the results reported in the literature or the 2D finite element results solved by the authors. The results show that the present models are capable of yielding not only accurate displacements but also accurate stresses and higher-order frequencies of free vibration for the FG beams with thermoelastic coupling.

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