挠度函数对均布荷载椭圆薄板挠度曲线的影响分析

Analysis of the Influence of Deflection Function on the Deflection Curve of Elliptical Thin Plate under Uniform Load

半逆解法是解决弹性薄板问题的重要方法之一,其基本步骤为先设置符合实际的挠度函数,使其满足边界条件和弹性曲面的微分方程,然后求出薄板位移和内力的精确解或近似解.就椭圆半球形式的挠度曲线函数进行了变化,将椭圆函数中的2次幂变为可变的实数k次幂后进行了计算分析.得出参数变为k后假设的挠度函数依然能满足边界条件和弹性曲面微分方程,并计算了最大挠度,作出了长轴和短轴的挠度曲线.结果表明,随着参数k的增加,最大挠度以双曲线模式逐渐减小并趋近于零,并用矿山开采沉陷方面的研究成果进行了实例对比分析,说明在半逆解法中选择符合实际的挠度函数非常重要.

The semi inverse method is one of the important methods to solve the elastic thin plate problem.The basic step is to first set the deflection function that conforms to the actual situation,make it meet the boundary conditions and the differential equation of the elastic surface,and then get the accurate or approximate solution of the displacement and internal force of the thin plate.In this paper,the deflection curve function in the form of elliptical hemisphere is changed,and the square is changed into a variable real number.It is concluded that the parameters of the deflection function can still meet the boundary conditions and the differential equation of elastic surface after being changed,and the maximum deflection is calculated,and the deflection curves of the long axis and the short axis are made.The results show that with the increase of the parameters,the maximum deflection decreases gradually in hyperbolic mode and approaches to zero.The comparative analysis of the case calculation is carried out by using the research results of mining subsidence,which shows that it is very important to select the deflection function that conforms to the actual situation in the semi inverse solution.