可动边界条件下含有具备二阶导数的二元函数的泛函变分

Variation of a Functional with a Dual Function and of Second Derivative under the Moving Boundary Condition

可动边界条件下含有具备二阶导数的二元函数的泛函变分具有重要的工程应用价值.根据变分原理建立了其泛函表达式,并推导出了该泛函的Euler-Ostrogradskii方程以及相应的横截条件.根据得到的微分方程和横截条件,进一步求解了均布载荷下圆形薄板与基底发生接触时的挠度以及临界载荷.这些分析结果对于工程设计,以及MEMS、生物的毛细黏附等有一定的参考价值.

It＇s of great engineering value for the variation of a functional with a dual function and of second derivative under the moving boundary condition.In this paper,we construct the functional expression according to variational theory,and then derive the Euler-Ostrogradskii equation and the corresponding transversality condition.According to the ordinary equation and the transversity condition,we then solve the deflection and critical load for a circular plate contacting to the substrate under the uniformly distributed load.These analyses can be beneficial to engineering design,MEMS and capillary adhesion of biology.