A three-dimensional weak formulation for stress, deformation, and free vibration analyses of functionally graded microscale plates based on the consistent couple stress theory

Chih Ping Wu, Chia Hao Hsu

研究成果: Article同行評審

摘要

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 C0 quadratic and cubic finite element methods (FEMs), as well as layer-wise C1 two- and three-node FEMs to address the current issue. The accuracy and convergence of these layer-wise C0 and C1 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.

原文English
文章編號115829
期刊Composite Structures
296
DOIs
出版狀態Published - 2022 9月 15

All Science Journal Classification (ASJC) codes

  • 陶瓷和複合材料
  • 土木與結構工程

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