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.

利用改进的耦合应力理论和表面弹性理论，开发了一种新的非经典一阶剪切变形圆柱薄壳模型。通过基于汉密尔顿原理的变分公式，可以同时获得运动方程和边界条件方程，并统一处理微观结构和表面能效应。新开发的非经典壳模型包含一个用于解释微结构效应的材料长度尺度参数，以及三个用于捕获表面能效应的表面弹性常数。新模型包括仅考虑微观结构效应或仅考虑表面能效应的壳模型作为特殊情况，并基于经典弹性作为极限情况恢复了一阶剪切变形圆柱薄壳模型。此外，当薄壳半径趋于无穷大时，当前的壳模型简化为结合了微观结构和表面能效应的Mindlin板的非经典模型。为了说明新模型，分析了简单支撑的圆柱薄壳的静态弯曲和自由振动问题。数值结果表明，包含微观结构和表面能的作用导致减小的壳挠度和旋转角以及增加的固有频率。当外壳非常薄时，差异很大，但随着外壳厚度增加，差异会减小。这些预测的微米级尺寸效应与实验中观察到的总体趋势一致。