Abstract
The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential function distribution along the thickness direction of the FG beam. The results shown in the numerical examples indicate that the mixed LW HSDT solutions for elastic and thermal field variables are in excellent agreement with the accurate solutions available in the literature. A parametric study related to various effects on the coupled thermo-mechanical behavior of FG beams is carried out, including the aspect ratio, the material-property gradient index, and different boundary conditions.
Highlights
Graded (FG) structures are emerging composite structures, for which material properties can be designed to gradually and smoothly vary through their physical domains
Using Hamilton’s principle and Reddy’s refined shear deformation theory (RSDT), Trinh et al [14] developed a state space method for vibration and buckling analyses of Functionally graded (FG) beams under various boundary conditions when subjected to thermo-mechanical loads
The authors develop the strong formulation of a mixed LW higher-order shear deformation theory (HSDT) for a static analysis of FG beams under various boundary conditions subjected to thermo-mechanical loads, where the material properties of the FG beam are considered to be thickness dependent
Summary
Graded (FG) structures are emerging composite structures, for which material properties can be designed to gradually and smoothly vary through their physical domains. Using Hamilton’s principle and Reddy’s refined shear deformation theory (RSDT), Trinh et al [14] developed a state space method for vibration and buckling analyses of FG beams under various boundary conditions when subjected to thermo-mechanical loads. Based on Carrera’s unified formulation (CUF) [17], Giunta et al [18] derived several ESLT-type beam theories to examine the coupled thermo-mechanical behavior of FG beams subjected to thermal loads. Vo et al [28,29] and Nguyen et al [30] developed a quasi-3D theory for the bending, free vibration, and buckling analyses of sandwiched FG beams, where both the shear deformation and thickness stretching effects were accounted for in the formulation by expanding the in-plane and out-of-plane displacement variables as a hyperbolic function distribution through the thickness direction of the beam. Some effects on the coupled thermo-mechanical behavior of FG beams are conducted, including the aspect ratio, the material-property gradient index, and different boundary conditions
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