Green’s operator for a periodic medium with traction-free boundary conditions and computation of the effective properties of thin plates
Green’s operator for a periodic medium with traction-free boundary conditions and computation of the effective properties of thin plates
复制标题
无牵引边界条件周期性介质的格林算子及薄板有效特性的计算
DOI：
10.1016/j.ijsolstr.2008.08.015
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发表时间：
2008
影响因子：
3.6
通讯作者：
G. Bonnet
中科院分区：
文献类型：
--
作者：
Trung‐Kien Nguyen;K. Sab;G. Bonnet
本文提出了一种新的适用于混合周期边界条件和无应力边界条件的绿色算子（Γ-算子）。该解决方案分为一个经典的周期性解决方案和一个补充解决方案，以考虑无应力边界条件。利用快速傅里叶变换、周期薄板理论和单元内应变能的计算，得到了周期单元组成的非均匀薄板的有效性质。数值应用，包括与封闭形式的解决方案和有限元解决方案的比较。
This paper presents a new Green’s operator (Γ-operator) for mixed periodic and stress-free boundary conditions. The solution is split into a classical periodic solution and a complementary solution to account for stress-free boundary conditions. This operator is used to obtain the effective properties of thin heterogeneous plates made of periodic cells, using the Fast Fourier Transform, the periodic thin plate theory and the computation of the strain energy within the cell. Numerical applications are provided, including comparisons with closed-form solutions and finite element solutions.