Exact analytical solutions in two dimensional plate-like mechanical metamaterials: State of free deformation in a topological cylinder
Exact analytical solutions in two dimensional plate-like mechanical metamaterials: State of free deformation in a topological cylinder
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二维板状机械超材料中的精确解析解：拓扑圆柱体中的自由变形状态
DOI：
10.1016/j.ijmecsci.2019.105292
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发表时间：
2020
影响因子：
7.3
通讯作者：
Karpov, Eduard G.
中科院分区：
文献类型：
--
作者：
Klein, John T.;Karpov, Eduard G.
当周期性边界条件施加到网格的顶面和底面形成拓扑圆柱时，二维板状网格在静态载荷下的节点位移以精确的解析形式求解。离散傅立叶变换将静力平衡的控制方程转化为一组一维波数相关问题。特征的解决方案，开发每个傅立叶变形模式。逆离散傅立叶变换通过取一维谐波解的线性组合将波数域函数转换回空间域。作为一个例子，点力被分解成一组波数依赖的加载配置文件。单个谐波载荷曲线的位移解的线性组合足以重现点载荷的整体位移解。此属性适用于任何类型的负载。节点位移，表示与解析依赖于节点indicesnandm，商业有限元分析软件的结果相匹配。总之，本文证明了离散晶格的静态响应等效地表示为波数域解的叠加，这类似于声学超材料和声子学中的频域分析。
Nodal displacements for two dimensional plate-like lattices under static loading are solved in exact analytical form, when periodic boundary conditions are applied to the top and bottom surfaces of the lattice forming a topological cylinder. Discrete Fourier transform converts the governing equation of static equilibrium into a set of one dimensional wavenumber dependent problems. Characteristic solutions are developed for each Fourier mode of deformation. Inverse discrete Fourier transform converts the wavenumber domain function back to the spatial domain by taking a linear combination of the one dimensional harmonic solutions. As an example, the point force is decomposed into a set of wavenumber dependent loading profiles. A linear combination of the displacement solutions for the individual harmonic loading profiles is sufficient to reproduce the overall displacement solution for the point load. This property holds for any type of the load. Nodal displacements, expressed with analytical dependence on the nodal indicesnandm, match the results of commercial finite element analysis software. Overall, this paper demonstrates that the static response of discrete lattices is equivalently represented as a superposition of the wavenumber domain solutions, which is analogous to frequency domain analysis in acoustic metamaterials and phononics.
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DOI：
10.1098/rspa.2019.0041
发表时间：
2019-06-01
影响因子：
3.5
作者：
Karpov, Eduard G.;Danso, Larry A.;Klein, John T.
通讯作者：
Klein, John T.
DOI：
--
发表时间：
2000
期刊：
影响因子：
--
作者：
N. Stephen;P. J. Wang
通讯作者：
P. J. Wang
DOI：
10.1016/j.ijmecsci.2018.09.018
发表时间：
2018-11-01
影响因子：
7.3
作者：
Karpov, Eduard G.;Danso, Larry A.
通讯作者：
Danso, Larry A.
影响因子：
56.9
作者：
Frenzel, Tobias;Kadic, Muamer;Wegener, Martin
通讯作者：
Wegener, Martin
DOI：
10.3390/ma11102050
发表时间：
2018-10-20
期刊：
Materials (Basel, Switzerland)
影响因子：
--
作者：
Danso LA;Karpov EG
通讯作者：
Karpov EG