Optimization of natural frequencies of bidirectional functionally graded beams

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Thermo-elastic optimization of material distribution of functionally graded structures by an isogeometrical approach (2014, methodology): “At the first model problem, we verify the presented results by optimization of a three layered Ni–Al2O3 FGM square plate for which the optimal results of other numerical methods such as finite elements (Cho and Ha, 2002b) and meshless method (Goupee and Vel, 2006b) are available in the literature.”
Semi‐analytical analysis for multi‐directional functionally graded plates: 3‐D elasticity solutions (2009, methodology): “A similar problem was also treated by Goupee and Vel [25] for 2-D FGM beams using the element-free Galerkin method.”