A three-dimensional weak formulation for stress, deformation, and free vibration analyses of functionally graded microscale plates based on the consistent couple stress theory. (15th September 2022)

• Record Type: Journal Article
• Authors: Wu, Chih-Ping; Hsu, Chia-Hao
• Is Part Of: Composite structures. Volume 296(2022)
• Publication Date: 2022-09-15
• Subjects: Consistent/modified couple stress theory -- Deformation -- Free vibration -- Functionally graded microscale plates -- Stress -- Three-dimensional analysis; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2022.115829
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: A three-dimensional (3D) weak formulation based on the consistent couple stress theory (CCST) is developed for displacement, stress, and free vibration analyses of simply-supported, power-law-/exponential-type functionally graded (FG) microscale plates. In the formulation, the microscale plate is artificially divided into numerous finite microscale layers, where Fourier functions and Lagrange/Hermite polynomials are used to interpolate the in- and out-of-plane variations in the displacement variables for each individual layer, respectively. Based on the weak formulation, the authors develop layer-wise C 0 quadratic and cubic finite element methods (FEMs), as well as layer-wise C 1 two- and three-node FEMs to address the current issue. The accuracy and convergence of these layer-wise C 0 and C 1 FEMs are validated by comparing their solutions with the 3D exact and the quasi-3D results available in the literature. A 3D weak formulation based on the modified couple stress theory (MCST) is also developed for comparison purposes. The similarity and differences between the results obtained using the CCST- and MCST-based weak formulations are examined and discussed. Some key effects on stress, deformation, and free vibration characteristics of the FG microscale plate are examined, including the material length scale, the material-property gradient index, and the length-to-thickness ratio effects, which are shown to be significant for the FG microscale plate.