Abstract
This paper aims at providing a simplified analytical solution for functionally graded beam stress analysis and optimized material gradation on the beam deflection. The power-law (P-FGM) and exponential (E-FGM) material functions were considered for an exact solution of the normal and shear stress distributions across the beam thickness. Optimization of material function on the FGM beam deflection, which is new of its kind, was also investigated considering both simply supported and cantilever beams. It was observed that the non-dimensional normal stress and shear stress are independent of the elastic moduli values of the constituent materials but rather depends on both the ratio of the elastic moduli and the location across the beam thickness in the E-FGM material function model. This observation was first validated from available kinds of literature and through numerical simulation using ABAQUS and extended to the P-FGM stress analysis. The maximum deflection on the FGM beam occurred for a homogenous steel beam while the minimum deflection was observed on the beam with a P-FGM material function. The results of this work demonstrate that if properly designed and optimized, FGMs can provide an alternative material solution in structural applications.
Highlights
Graded materials (FGMs) are a new class of advanced composite materials that possess gradually varying material properties within a given direction
Finite element method for characterizing the dynamic free vibration of a functionally graded beam with material graduation axially or transversely through the thickness based on the power-law function and a finite element method to study the static behavior of Timoshenko Functionally graded materials (FGMs) cantilever beam subjected to a concentrated load at the free end and using power law for varying material properties through-beam thickness was investigated and proposed in [5,6]
The exact free vibration and buckling analysis of tapered beam-column made of FGM material and assumed the P-FGM material variation along with the cross-section’s height and the vibration behavior of composite coupled conical shell structures were presented in [9,10,11]
Summary
Graded materials (FGMs) are a new class of advanced composite materials that possess gradually varying material properties within a given direction. A new beam finite element analysis was developed in [3] and investigated the thermo-elastic behavior of functionally graded beam structures based on first-order shear deformation theory and accounting for varying elastic and thermal properties along with the beam thickness. Finite element method for characterizing the dynamic free vibration of a functionally graded beam with material graduation axially or transversely through the thickness based on the power-law function and a finite element method to study the static behavior of Timoshenko FGM cantilever beam subjected to a concentrated load at the free end and using power law for varying material properties through-beam thickness was investigated and proposed in [5,6]. The static behavior of functionally graded metal-ceramic beams under transverse loading using higher-order shear deformation theory, assuming power-law function to account for material variation through-beam thickness was studied in [7]. Literature on FGM beams under arbitrarily distributed loading, crack growth, and bilayer FGM cantilever beams are available in [21,22,23]
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