只含两个独立变量的扁壳大挠度问题修正的海林格-赖斯内变分泛函

A Modified Hellinger-Reissner Variational Functional Including only Two Independent Variables for Large Displacement of Thin Shallow Shell

本文首先用海林格-赖斯内变分原理建立任意形状扁壳大挠度问题的泛函，然后用修正的变分原理导出适合于有限单元法的变分泛函表达式．泛函中只包含应力函数F和挠度W两个独立交量．其中也导出了在边界上用上述两个变量表示的中面位移的表达式．推导中考虑了边界的曲率，所以适用于任意形状的边界．

The variational functional of the Hellinger-Reissner variational principle for the large displacement problem of a thin shallow shell with all arbitrary shape is first established. Then the functional of the modified principle suitable for the finite clement method is derived. In the functional, only two independent variables, the deflection w and the stress function F are included. The displacement expressions in the middle surface on the boundary of the shell is also derived by means of the previous two variables.