三边固支一边自由矩形薄板挠度计算研究

为求解受均布荷载作用下三边固支一边自由矩形薄板的挠度函数,在弹性理论的基础上,建立薄板力学模型。结合三边固支一边自由的边界条件,并采用Rayleigh-Ritz法计算挠度函数中的未知系数k,从而推导挠度函数。最后,通过ANSYS对2个算例进行模拟,得到矩形薄板在z轴方向上的变形云图,并对比理论计算与模拟的结果。结果的一致性为计算三边固支一边自由等复杂边界条件的矩形薄板的挠度提供科学依据。

In order to obtain the deflection function of the rectangular thin plate with three fixed sides and one free side under the uniformly distributed load,the mechanical model for the thin plate was established based on the theory of elasticity.By considering the boundary conditions of three fixed sides and one free side,and employing the Rayleigh-Ritz method,the unknown coefficient k in the deflection function was calculated,thus deriving the deflection function.Finally,two cases were simulated using ANSYS to obtain the deformation contour plot of the rectangular thin plate in the z-axis direction,and the comparison was made between the theoretical calculations and the simulation results.The consistency of the results provides a scientific basis for calculating the deflection of the rectangular thin plate under complex boundary conditions,such as three fixed sides and one free side.