Asymptotic analysis of perforated plates and membranes. Part 2: Static and dynamic problems for large holes
Asymptotic analysis of perforated plates and membranes. Part 2: Static and dynamic problems for large holes
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穿孔板和膜的渐近分析第 2 部分：大孔的静态和动态问题
DOI：
10.1016/j.ijsolstr.2011.10.004
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发表时间：
2012
影响因子：
3.6
通讯作者：
Kalamkarov A.L.
中科院分区：
文献类型：
--
作者：
Andrianov I.V;Danishevs’kyy V.V;Kalamkarov A.L.
将奇异摄动技术与多尺度渐近均匀化方法相结合，求解了周期穿孔弹性板膜的静力和动力问题。考虑了穿孔板的弯曲和振动问题。利用渐近齐次化方法，将原边值问题归结为两类问题的组合。第一类是具有周期连续条件的递归单位元问题系统。第二个问题是整个区域的齐次化边值问题，其特征是由单位元问题的解得到的恒定有效系数。本文考虑大开孔孔板，用奇异摄动法求解相应的单胞问题。利用两点Padé逼近法对小孔和大孔的极限解进行了匹配，得到了任意尺寸孔板的有效刚度的解析表达式。
Static and dynamic problems for the elastic plates and membranes periodically perforated by holes of different shapes are solved using the combination of the singular perturbation technique and the multi-scale asymptotic homogenization method. The problems of bending and vibration of perforated plates are considered. Using the asymptotic homogenization method the original boundary-value problems are reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. In the present paper the perforated plates with large holes are considered, and the singular perturbation method is used to solve the pertinent unit cell problems. Matching of limiting solutions for small and large holes using the two-point Padé approximants is also accomplished, and the analytical expressions for the effective stiffnesses of perforated plates with holes of arbitrary sizes are obtained.