https://orcid.org/0000-0003-2847-9247
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Abstract
People have realized that the mechanical properties of circular nanoplate structures exhibit strong surface effects. In this article, we introduce Gurtin-Murdoch surface theory into von Karman’s plate theory to examine the nonlinear post-buckling behaviors of graded porous circular nano-plates with surface effects, subjected to follower force. The bulk structure is a porous graded material and pores are embedded in the board in both symmetrical and asymmetrical ways along the thickness direction. The post-buckling equilibrium equations governing axi-symmetric deformation of the graded porous circular nanoplate are derived, and then a shooting method combined with analytical continuation is used to numerically solve the control equation. Characteristic curves of the post-buckling equilibrium path and equilibrium configuration relate to the performances were plotted. Finally, a detailed analysis was conducted on the effects of important parameters such as surface elastic modulus, residual surface stress, scale parameters, pore distribution patterns, and even boundary conditions on the buckling and post-buckling of nanocircular plates. Overall, the results show that surface elastic modulus, and residual surface stress play a great role in the analyzing nonlinear post-buckling of circular nanoplate under follower forces. The surface elastic parameters and residual surface stress have important effects on the yield strength and post-buckling behaviors of porous nano-material sturctures. These new findings can provide theoretical basis for the precise design and manufacturing of aerospace nanodevices.
Disclosure statement
No potential conflict of interest was reported by the author(s).