Nonlinear three-dimensional stability characteristics of geometrically imperfect nanoshells under axial compression and surface residual stress

Abstract

Through reduction of thickness value in nanostructures, the features of surface elasticity become more prominent due to having a high surface-to-volume ratio. The main aim of this research work was to examine the surface residual stress effect on the three-dimensional nonlinear stability characteristics of geometrically perfect and imperfect cylindrical shells at nanoscale under axial compression. To do so, an unconventional three-dimensional shell model was established via combination of the three-dimensional shell formulations and the Gurtin–Murdoch theory of elasticity. The silicon material is selected as a case study, which is the most utilized material in the design of micro-electromechanically systems. Then, the moving Kriging meshfree approach was applied to take numerically into account the surface free energy effects and the initial geometrical imperfection in the three-dimensional nonlinear stability curves. Accordingly, the considered cylindrical shell domain was discretized via a set of nodes together using the quadratic polynomial type of basis shape functions and an appropriate correlation function. It was found that the surface stress effects lead to an increase the critical axial buckling load of a perfect silicon nanoshell about 82.4%82.4 \% for the shell thickness of 2nm2{\rm{nm}}, about 32.4%32.4 \% for the shell thickness of 5nm5{\rm{nm}}, about 15.8%15.8 \% for the shell thickness of 10nm10{\rm{nm}}, and about 7.5%7.5 \% for the shell thickness of 20nm20{\rm{nm}}. These enhancements in the value of the critical axial buckling load for a geometrically imperfect silicon nanoshell become about 92.9%92.9 \% for the shell thickness of 2nm2{\rm{nm}}, about 36.5%36.5 \% for the shell thickness of 5nm5{\rm{nm}}, about 17.7%17.7 \% for the shell thickness of 10nm10{\rm{nm}}, and about 8.8%8.8 \% for the shell thickness of 20nm20{\rm{nm}}.

Keywords

• nanostructures
• 3d elasticity
• nonlinear buckling
• surface residual stress
• meshfree numerical technique