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A Review on the Size-Dependent Models of Micro-beam and Micro-plate Based on the Modified Couple Stress Theory

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Abstract

Micro scale experiments demonstrated that the material deformation behaviors of some metals and polymers deformed elasticity are size dependence, and the modified couple stress theory (MCST), which introduce an additional material length scale parameter, could capture the size dependences. The article reviews the available size-dependent models of micro-beam and micro-plate based on the MCST. For the representative micro-beams and micro-plates, the relevant mechanical models of micro-structures for static bending, vibration, buckling and pull-in instability, have been established based on the MCST, and the analytical and numerical solutions have been obtained. The results show that the size effects on the mechanical properties of the micro-structures are obvious and significant. Further possible researches on the size-dependent behaviors of the micro-structures are proposed.

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Acknowledgements

The author would like to acknowledge the support by the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2017RA006 and ZR2017LEE013).

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    Shengli Kong

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Kong, S. A Review on the Size-Dependent Models of Micro-beam and Micro-plate Based on the Modified Couple Stress Theory. Arch Computat Methods Eng 29, 1–31 (2022). https://doi.org/10.1007/s11831-021-09567-w

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