Journal
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
Volume 167, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijmecsci.2019.105292
Keywords
Mechanical metamaterials; Lattice mechanics; 2D Plate-like lattices; Analytical displacement solutions; Periodic boundary conditions; Discrete Fourier transform
Categories
Funding
- CCDEVCOM Army Research Laboratory [W911NF-18-2-0297]
Ask authors/readers for more resources
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 indices n and m, 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available