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本文从最一般的三维有限变形的广义变分原理出发,引入 Kirchhoff-Love 假设,推导了薄板的大挠度方程及其相应的边界条件。本文建议的方法有助于了解薄板大挠度问题的全貌,深入理解Kirchhoff-Love 假设的含义和作用,很容易获得简化理论的边界条件。比之用静力法和建立在简化理论基础上的变分原理来推导薄板的大挠度方程,有一定的优越性。
In this paper, starting from the general generalized variational principle of three-dimensional finite deformation, the Kirchhoff-Love hypothesis is introduced, and the large-deflection equation of the thin plate and its corresponding boundary conditions are deduced. The method proposed in this paper helps us to understand the overall picture of the large deflection of thin plates and to understand in depth the meaning and role of the Kirchhoff-Love hypothesis. It is easy to obtain the boundary conditions of the simplified theory. Compared with the static method and the variational principle based on the simplified theory, the large deflection equation of the thin plate is deduced, which has certain advantages.