Bending and Buckling of Functionally Graded Nanoplates Based on the Nonlocal Strain Gradient Theory

WANG Pingyuan; LI Cheng; YAO Linquan

doi:10.21656/1000-0887.410188

Volume 42 Issue 1

Jan. 2021

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WANG Pingyuan, LI Cheng, YAO Linquan. Bending and Buckling of Functionally Graded Nanoplates Based on the Nonlocal Strain Gradient Theory[J]. Applied Mathematics and Mechanics, 2021, 42(1): 15-26. doi: 10.21656/1000-0887.410188

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Bending and Buckling of Functionally Graded Nanoplates Based on the Nonlocal Strain Gradient Theory

doi: 10.21656/1000-0887.410188

¹Department of Vehicle Engineering, School of Rail Transportation, Soochow University, Suzhou, Jiangsu 215131, P.R.China;²MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632, P.R.China

Funds: The National Natural Science Foundation of China（11972240；11572210）

Received Date: 2020-06-22
Rev Recd Date: 2020-07-17
Publish Date: 2021-01-01

Abstract

Abstract

The bending and buckling of functionally graded nanoplates in intelligent devices (e.g., nanorobots) were studied based on the nonlocal strain gradient theory. The motion equations in general cases were derived, and then reduced to bending and buckling in special cases. The effects of the nonlocal scale parameter, the material characteristic scale parameter, the gradient index and the geometric size on the bending deflection and the critical buckling load were acquired and analyzed in detail. The results show that, the maximum bending deflections under different higherorder continuum mechanics theories increase with the gradient index. The deflection goes lower for the square nanoplate. The thicker the nanoplate is, the smaller the bending deflection will be. The maximum deflection increases with the nonlocal scale parameter but decreases with the material characteristic scale parameter. The critical buckling load decreases with the gradient index, and increases with the thickness and the aspect ratio. When the nonlocal scale parameter increases, the critical buckling load will decrease, but will increase with the material characteristic scale parameter. The softening and hardening mechanisms exist in higherorder bending and buckling of the functionally graded nanoplates, and the coupling effect between 2 internal characteristic parameters also occurs. When the nonlocal scale is greater than the material characteristic scale, the nonlocal effect will dominate in the mechanical properties of functionally graded nanoplates, otherwise the strain gradient effect will play a leading role. The analytical solutions also show that, when the nonlocal scale is equal to the material characteristic scale, the results based on the nonlocal strain gradient theory will degenerate into the corresponding classical ones.
- nonlocal strain gradient theory,
- functionally graded nanoplate,
- bending,
- buckling,
- critical load

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References

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