Imperfection sensitivity of the size-dependent nonlinear instability of axially loaded FGM nanopanels in thermal environments. (English) Zbl 1380.74095
Summary: The nonlinear buckling of thin shell-type structures is sensitive to the initial geometric imperfection. In this study, the imperfection sensitivity of the nonlinear instability of cylindrical nanopanels made of functionally graded material (FGM) is addressed including surface elasticity, aiming to present a background for axial postbuckling behavior of imperfect FGM nanopanels. The material properties are supposed to be graded across the panel thickness in accordance with a simple power law function of the volume fractions of the silicon and aluminum constituents with considering the physical neutral plane position. The non-classical governing differential equations are constructed and then they are deduced to boundary layer-type ones. Afterward, a perturbation-based solution methodology is employed to extract explicit expressions for the size-dependent postbuckling equilibrium paths of FGM nanopanels with and without initial geometric imperfection and corresponding to various panel
thicknesses, geometrical parameters, temperature changes and material property gradient indexes. It is displayed that through reduction of the surface elasticity effects for thicker FGM nanopanels, the influence of the initial geometric imperfection on the minimum load of the postbuckling regime increases. This pattern is more significant for FGM nanopanels with a lower value of the material gradient index.
MSC:
| 74M25 | Micromechanics of solids |
| 74G60 | Bifurcation and buckling |
| 74K25 | Shells |
| 74F05 | Thermal effects in solid mechanics |
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