A non-classical model for first-ordershear deformation circular cylindrical thin shells incorporating microstructure and surface energy effects

A new non-classical model for first-order shear deformation circular cylindrical thin shells is developed by using a modified couple stress theory and a surface elasticity theory. Through a variational formulation based on Hamilton’s principle, the equations of motion and boundary conditions are simultaneously obtained, and the microstructure and surface energy effects are treated in a unified manner. The newly developed non-classical shell model contains one material length-scale parameter to account for the microstructure effect and three surface elastic constants to capture the surface energy effect. The new model includes shell models considering the microstructure effect only or the surface energy effect alone as special cases and recovers the first-order shear deformation circular cylindrical thin shell model based on classical elasticity as a limiting case. In addition, the current shell model reduces to the non-classical model for Mindlin plates incorporating the microstructure and surface energy effects when the thin shell radius tends to infinity. To illustrate the new model, the static bending and free vibration problems of a simply supported circular cylindrical thin shell are analytically solved. The numerical results reveal that the inclusion of the microstructure and surface energy effects leads to reduced shell deflections and rotation angles and increased natural frequencies. The differences are significant when the shell is very thin, but they diminish as the shell thickness increases. These predicted size effects at the micron scale agree with the general trends observed in experiments.