A new beam finite element for the analysis of functionally graded materials

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A new simple shear and normal deformations theory for functionally graded beams (2015, background): “…beam theory is simple to implement and applied for moderately deep FG beams and gives acceptable results but depends on a shear correction factor which is hard to find as it depends on many parameters (Bouremana et al. 2013, Chakraborty et al. 2003, Li 2008, Sina et al. 2009, Wei et al. 2012).”
Hierarchical theories for the free vibration analysis of functionally graded beams (2011, neutral): “[17].”
Modeling and analysis of functionally graded sandwich beams: a review (2019, background): “The Power law (P-FGM) [21], [28], [47–50], [52]–[54], [56], [58]–[63], [66], [67], [71], [74]–[78], [85]–[92], [98]–[103], [109, 110], [113], [115]–[119], [121], [129]–[132], [134–140], [143–146], [149]–[162], [164], [168]–[176], [181]–[184], [186]–[189], [194], [196], [198–209], [211], [213, 214] T”
Free vibration characteristics of a functionally graded beam by finite element method (2011, background): “[5] developed a new beam element to study the thermoelastic behavior of functionally graded beam structures.”