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Steel and Composite Structures Volume 51, Number 2, April 25 2024 , pages 103-116 DOI: https://doi.org/10.12989/scs.2024.51.2.103 |
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A unified consistent couple stress beam theory for functionally graded microscale beams |
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Chih-Ping Wu and Zhen Huang
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| Abstract | ||
| Based on the consistent couple stress theory (CCST), we develop a unified formulation for analyzing the static bending and free vibration behaviors of functionally graded (FG) microscale beams (MBs). The strong forms of the CCSTbased Euler-Bernoulli, Timoshenko, and Reddy beam theories, as well as the CCST-based sinusoidal, exponential, and hyperbolic shear deformation beam theories, can be obtained by assigning some specific shape functions of the shear deformations varying through the thickness direction of the FGMBs in the unified formulation. The above theories are thus included as special cases of the unified CCST. A comparative study between the results obtained using a variety of CCST-based beam theories and those obtained using their modified couple stress theory-based counterparts is carried out. The impacts of some essential factors on the deformation, stress, and natural frequency parameters of the FGMBs are examined, including the material length-scale parameter, the aspect ratio, and the material-property gradient index. | ||
| Key Words | ||
| consistent couple stress theory; deformation; microscale beams; modified couple stress theory; unified shear deformation theory; vibration | ||
| Address | ||
| Chih-Ping Wu and Zhen Huang:Department of Civil Engineering, National Cheng Kung University, 1 University Road, Tainan 70101, Taiwan | ||