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本文提出了一种建立广义变分原理的新方法,即首先把应力、应变及位移均看成独立变量,提出一个与弹性力学的全部方程和边界条件等价的“拟广义虚功原理”,然后进一步导出了包含三个独立变量和一个加权函数的两个极其普遍的广义变分原理。到目前为止的各种三变量广义变分原理,均可包含在本文的两个变分原理之中。本文还进一步导出了具有弹性边界的两个三变量分区广义变分原理,这些原理对于建立弹性力学各种新的非协调有限元法,将是十分有用的理论工具。
This paper proposes a new method to establish the generalized variational principle, that is, first consider the stress, strain and displacement as independent variables, and propose a “quasi-generalized virtual work principle” equivalent to all equations and boundary conditions of elasticity mechanics. Then we further derived two extremely generalized generalized variational principles including three independent variables and a weighting function. The three variable generalized variational principles so far can be included in the two variational principles of this paper. In this paper, we also derive two generalized variational principles for three-variable partitions with elastic boundaries. These principles will be very useful theoretical tools for the establishment of a variety of new non-coordinated finite element methods for elastic mechanics.