Thin elastic and periodic plates
Thin elastic and periodic plates
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DOI：
10.1002/mma.1670060112
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发表时间：
1984
影响因子：
2.9
通讯作者：
D. Caillerie;J. Nédélec
中科院分区：
文献类型：
--
作者：
D. Caillerie;J. Nédélec
本文研究了弹性周期板的三维模型，当板的厚度e和周期的大小ω都很小时。在所研究的三个极限（e → 0然后ω → 0）、（ω → 0然后e → 0）和最近的极限（e和ω一起→ 0）中，用线性各向异性板的二维一般方程逼近三维弹性力学方程，其中拉伸和弯曲是耦合的。本文指出了两个小参数之比的重要性，实际上二维方程中出现的模量在三个极限中是不同的。在每种情况下，进行收敛性证明。
This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e → 0 then ω → 0), (ω → 0 then e → 0) and lately (e and ω → 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.