Computational Modeling of Functionally Graded Beams: A Novel Approach
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Date
2022
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Abstract
Aim: A novel computational approach is propounded to model the material gradation of a functionally graded Euler–Bernoulli beam using Ansys Workbench, the finite element method-based software. Novelty: Contrary to layer-by-layer modeling approaches to express functional material gradation for different structures in the literature, the new approach states a continuous variation of the material gradation obeying gradation laws (e.g., power-law). Method: The new approach is applied to the computational free vibration analyses of functionally graded beams. Three types of functionally graded beams are investigated: (1) One-directional beam with a uniform cross section. (2) One-directional beam with a non-uniform cross section. (3) Bi-directional beam with a uniform cross section. Power-law and exponential-law types mathematical expressions are used in modeling the material gradation of functionally graded beams. Results: The finite element results of free vibration analyses for each beam are obtained. The results are compared with the analytical results from the literature [Lee and Lee, Int J Mech Sci 122:1–17; Sinir et al., Compos Part B Eng 148:123–131; Karamanli, Anadolu Univ J Sci Technol A Appl Sci Eng https://doi.org/10.18038/aubtda.361095; Simsek, Compos Struct 133:968–978] to present the accuracy of the novel approach. Several support conditions are investigated. The effects of the gradient indices (power-law and exponential-law indices) on the natural frequencies of the beams are discussed. © 2022, Krishtel eMaging Solutions Private Limited.