Semi-analytical elasticity solutions for bi-directional functionally graded beams

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Analysis of FGM Beams by Means of Classical and Advanced Theories (2010, methodology): “[49] computed via the method presented by Sankar [33].”
Free vibration characteristics of a functionally graded beam by finite element method (2011, background): “[7].”
Exact frequency equations of free vibration of exponentially functionally graded beams (2013, background): “[4] presented a semi-analytical elasticity solution for static problems of bidirectional functionally graded beams with exponential gradient distribution within the framework of two-dimensional elasticity theory.”
Thermo-elastic optimization of material distribution of functionally graded structures by an isogeometrical approach (2014, methodology): “A semi-analytical elasticity solution for bending and thermal deformations of bidirectional FG beams was introduced by Lü et al. (2008).”