针对石墨烯薄膜微压力传感特性，基于圆薄膜大挠度弹性理论，构建均布载荷-挠度数学模型，求解预应力对挠度变化的影响规律，应用ANSYS静力学非线性和模态分析方法，对弹性模量与层数等薄膜参数引起的挠度特性及振动特性进行数值解析与有限元仿真。结果表明，低载荷条件下预应力对挠度形变作用明显，且在0～3.6 kPa范围内挠度与载荷基本呈线性关系，但随着载荷增加，弹性模量与层数对挠度形变表现出递减效应，不过固有频率与模态特性仍取决于预应力，受薄膜参数影响较小。这种力学特性验证了Beams球壳理论模型的有效性，在线性区间内受预应力影响其解析解与ANSYS仿真解的平均相对误差小于0.49%。

Considering the mechanical behavior analysis of graphene film for micro-pressure sensor, the load-deflection models in graphene film are established based on the large deflection elastic theory of circular film. With regard to the typical load-deflection models, the effects of the film parameters, including elastic modulus and film layer, on deflection deformation and vibration behavior are computed numerically and simulated by using nonlinear statics analysis and mode analysis units with ANSYS software. The results show that the prestressing force has a significant impact on the deflection deformation at low load, and especially there is a linear relation between load and deflection in the pressure range from 0 to 3.6 kPa. However, a decreasing effect on the deflection deformation is produced by the above-mentioned film parameters with the increase of pressure load. Also, the natural frequency and mode shape characteristics mainly depend on the prestressing force instead of these two film parameters. This phenomenon verifies the used validity of spherical shell theoretical model because of the average relative error less than 0.49% between the analytical solution and ANSYS simulation results in the presence of prestressing force in the aforementioned pressure range.