The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered, as the thickness h of the shell tends to zero. Given the appropriate scalings of the applied force and of the initial data in terms of h, it’s verified that three-dimesional solutions of the nonlinear elastodynamic equations converge to solutions of the time-dependent von KMorármMorán equations or dynamic linear equations for shell of arbitrary geometry.

中文翻译：

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时间相关的VonKármánShell方程作为三维非线性弹性的极限

考虑了薄壳中三维非线性弹性动力学解的渐近行为，因为壳的厚度h趋于零。给定施加力和初始数据的适当缩放比例，以h表示，这证明了非线性弹性动力学方程的三维解都可以收敛到随时间变化的vonKMorármMorán方程或任意线性壳的动态线性方程的解。