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.

基于具有三个独立长度尺度参数的应变梯度弹性理论，建立了尺寸相关的球形微壳模型。根据汉密尔顿原理导出控制方程，边界条件和初始条件。解决了静态弯曲和自由振动的问题。展示了一些静态弯曲和自由振动的数值结果，以基于尺寸相关模型研究力学行为。结果表明，应变梯度弹性效应将使球形微壳变硬，特别是当厚度与长度尺度参数相同时。考虑应变梯度弹性效应时，球形微壳中心的挠度并不总是减小，与圆形平板的情况不同。分别研究了三个长度尺度参数对异常的影响。另外，当厚度接近长度比例参数时，发现第一固有频率显着增加。