Incompatible Deformations of Elastic Plates

S. Lychev
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Abstract

This article considers the methods for mathematical modeling of incompatible finite deformations of elastic plates by using the principles of the differential geometry theory underlying continuously distributed defects. Equilibrium equations were derived by asymptotic expansions of the finite strain measures with respect to two small parameters. One parameter defines the order of smallness of displacements from the reference shape (self-stressed state), while the other specifies the thickness. Asymptotic orders were different for the deflections and displacements in the plate plane, as well as for their derivatives. They were selected in such a way that, with additional assumptions on the possibility of ignoring certain terms in the resulting expressions and the compatibility of deformations, the equations could be reduced to the system of F¨oppl–von Ka´rm´an equations.
弹性板的不相容变形
本文利用连续分布缺陷所依据的微分几何理论原理,研究了弹性板不相容有限变形的数学建模方法。平衡方程是通过有限应变度量与两个小参数的渐近展开得到的。其中一个参数定义了从参考形状(自应力状态)出发的位移小阶,另一个参数则定义了厚度。板平面上的挠度和位移及其导数的渐近阶数各不相同。选择这些阶数的方式是,在对结果表达式中忽略某些项的可能性和变形兼容性进行额外假设的情况下,可以将方程简化为 F¨oppl-von Ka´rm´an 方程系统。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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