SANDERS薄壳方程的自共轭性

本文对Sanders薄壳方程的自共轭性作了讨论.证明了以下三点: 1.通常的齐次边界条件是简单自共轭边界条件; 2.在简单自共轭边界条件下,Sanders薄壳方程是自共轭的、其蜕化(元矩)方程也是自共轭的; 3.任何薄壳理论,其满足功的互等定理与具有自共轭性所需条件是相同的: 作为6个变形分量的正定二次型的应变能函数存在. 由于Sanders薄壳理论在任意曲线坐标系中成立,故以上结论亦适用于任意曲线坐标系. 本文的讨论为采用Sanders理论对薄壳进行动力分析提供了理论准备.

ON SELF-CONGUGATION OF SANDERS THIN SHELL EQUATION

In order to exploit Sanders thin shell theory for analysis of thin shell vibration, it is necessary to discuss its self-conjugation. In this paper, following conclusions are proved: 1. Ordinary homogeneous boundary conditions are simple self-conjugate boundary conditions. 2. Under the simple self-conjugate boundary conditions, either Sanders shell equations, or its membrane equations are self-conjugate. 3. For any thin shell theory, in case when the reciprocity principle is satisfied, the seff-conjugation holds true.