Volume 43 Issue 7
Jul.  2022
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XUE Jianghong, HE Zanhang, XIA Fei, LI Zerong, JIN Fusong, YANG Peng. Size-Dependent Effects of Micro-Nano Mindlin Plates Based on the Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2022, 43(7): 740-751. doi: 10.21656/1000-0887.420171
Citation: XUE Jianghong, HE Zanhang, XIA Fei, LI Zerong, JIN Fusong, YANG Peng. Size-Dependent Effects of Micro-Nano Mindlin Plates Based on the Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2022, 43(7): 740-751. doi: 10.21656/1000-0887.420171

Size-Dependent Effects of Micro-Nano Mindlin Plates Based on the Couple Stress Theory

doi: 10.21656/1000-0887.420171
  • Received Date: 2021-06-22
  • Rev Recd Date: 2021-11-14
  • Publish Date: 2022-07-15
  • A Mindlin plate theory for micro-nano structures was proposed based on the couple stress theory. A length parameter was introduced to consider the size effect, and the constitutive equations for the micro-nano Mindlin plate were derived in view of the transverse shear deformation. The buckling and free vibration governing equations in terms of displacements and the slope functions of the shear deformation micro-nano plate were further deduced with the force equilibrium conditions. The analytical solutions of buckling and free vibration for the shear deformation micro-nano plate were obtained through separation of the displacement and rotation variables in space and time domains. Two scenarios of boundary conditions were analyzed: SSSS (simply supported by 4 edges) and SCSC (2 opposite edges simply supported and other 2 edges clamped). A MATLAB program was developed to compute the critical buckling and natural frequencies with different values of dimensional parameters, aspect ratios and length-to-thickness ratios. The research results, in comparison with those from the ABAQUS finite element analysis and previous literatures, are consistent with the latter ones. The examples show that, the size effects significantly influence the buckling load and the natural frequency.

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