薄板弯曲理论中一个新的广义变分原理及其交替max,min性质

本文在薄板弯曲的经典理论中提出一个以挠度、横向剪应变、曲率、弯矩、横向剪力、边界上的未知反力为自变函数的新的变分原理,在对自变函数预加不严厉的约束后,新泛函具有一连串交替max,min的性质。

A NEW GENERALIZED VARIATIONAL PRINCIPLE AND ITS max,min PROPERTY IN THIN PLATE THEORY

A new generalized variational principle in classical thin plate theory is proposed with deflection, transverse shear deformation, curvature, internal moment, transverse shearing force and unknown boundary reaction as argument functions. By applying slight restrictions to the argument functions, the new functional possesses the property of consecutive alternate max min.