A size-dependent spherical microshell model based on strain gradient elasticity theory

Based on the strain gradient elasticity theory with three independent length scale parameters, a size-dependent spherical microshell model is established. The governing equations, boundary conditions and initial conditions are derived by Hamilton's principle. Both the static bending and free vibration problems are solved. Some numerical results of the static bending and the free vibration are exhibited to investigate the mechanical behaviors based on the size-dependent model. It is demonstrated that the strain gradient elastic effect will stiffen the spherical microshell especially when the thickness is in the same order with the length scale parameter. When the strain gradient elastic effect is considered, the deflection at the center of the spherical microshelldoes not always decrease, which is different from the case in the flat circular plate. Effects of the three length scale parameters on the anomaly are separately investigated. In addition, the first natural frequency is found to significantly increase when the thickness approaches the length scale parameter.