Homogenization of the nonlinear bending theory for plates
Homogenization of the nonlinear bending theory for plates
复制标题
板非线性弯曲理论的均匀化
DOI：
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
H. Olbermann
中科院分区：
文献类型：
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作者：
S. Neukamm;H. Olbermann
我们对板的非线性弯曲理论进行了空间周期齐次化。在$$GAMA$$Γ收敛的意义下，该推导是严格的。与人们自然预期的情况相反，我们的结果表明，极限泛函不是像在非线性板理论中那样简单的变形板的第二基本形式的二次泛函。结果表明，极限泛函判别变形后的板局部形状是否为圆柱体。作为导数，我们利用双尺度收敛研究了与等距浸入相关的第二基本形式序列的振荡行为。这是一个不平凡的任务，因为人们必须处理与非线性微分约束有关的两个尺度的收敛。
We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of $$Gamma $$Γ-convergence. In contrast to what one naturally would expect, our result shows that the limiting functional is not simply a quadratic functional of the second fundamental form of the deformed plate as it is the case in nonlinear plate theory. It turns out that the limiting functional discriminates between whether the deformed plate is locally shaped like a “cylinder” or not. For the derivation we investigate the oscillatory behavior of sequences of second fundamental forms associated with isometric immersions of class $$W^{2,2}$$W2,2, using two-scale convergence. This is a non-trivial task, since one has to treat two-scale convergence in connection with a nonlinear differential constraint.
从 3d 弹性推导均质非线性板理论
DOI：
10.1007/s00526-013-0691-8
发表时间：
2014
影响因子：
2.1
作者：
Peter Hornung;Stefan Neukamm;Igor Velčić
通讯作者：
Igor Velčić