On the size-dependent bending and buckling of the partially covered laminated microplate

Engineering with Computers - Tập 39 - Trang 685-710 - 2022
Guangyang Fu1,2, Zhenjie Zhang3, Yulin Ma1,2, Hongyu Zheng1,2, Qianjian Guo1, Xuye Zhuang1
1Centre for Advanced Laser Manufacturing (CALM), School of Mechanical Engineering, Shandong University of Technology, Zibo, People’s Republic of China
2State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, People’s Republic of China
3School of Mechanical Engineering, Shandong University, Jinan, People’s Republic of China

Tóm tắt

The bending and buckling of the microcomponents show size dependency. The strain gradient elasticity theory is proposed to explain the size dependency. In this paper, we derive the theoretical relations among the modified strain gradient elasticity theory, the modified couple stress theory and the general strain gradient elasticity theory, and clarify the degradation relation. The general theory includes all strain gradients while the modified strain gradient elasticity theory and the modified couple stress theory only contain part of strain gradients. By ignoring the deviatoric part of the strain gradients $$\eta _{ijk}^{'(2)}$$ or the symmetric part of the strain gradients $$\eta _{ijk}^{s}$$ , the general theory is simplified as the modified couple stress theory or the modified strain gradient elasticity theory, respectively. The ability of the general theory and the reduced theories in describing the bending and buckling response of the partially covered laminated microplate is subsequently compared. Results reveal that the general theory predicts smaller bending deflection and axial displacement while larger buckling load than that of the reduced theories. The general theory is more effective in reflecting the size effects. In addition, it is found that the increase of the thickness or radius of the upper elastic layer makes the buckling load increase while the deflection increase firstly and then decrease. There exists the specific radius ratio and thickness ratio to make the clamped-clamped microplate achieve the maximum deflection.

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