TY - JOUR
T1 - Employing the discrete fourier transform in the analysis of multiscale problems
AU - Ryvkin, Michael
PY - 2008
Y1 - 2008
N2 - The idea of employing the discrete Fourier transform casted as the representative cell method for the solution of multiscale problems is illustrated. Its application in combination with analytical (structural mechanics methods, Wiener-Hopf method, integral transform methods) and numerical (finite element method, higher-order theory) methods is demonstrated. Both cases of 1-D and 2-D translational symmetry are addressed. In particular, the problems for layered, cellular, and perforated materials with and without flaws (cracks) are considered. The method is shown to be a convenient and universal analysis tool. Its numerical efficiency allowed us to solve optimization problems characterized by multiple reanalysis.
AB - The idea of employing the discrete Fourier transform casted as the representative cell method for the solution of multiscale problems is illustrated. Its application in combination with analytical (structural mechanics methods, Wiener-Hopf method, integral transform methods) and numerical (finite element method, higher-order theory) methods is demonstrated. Both cases of 1-D and 2-D translational symmetry are addressed. In particular, the problems for layered, cellular, and perforated materials with and without flaws (cracks) are considered. The method is shown to be a convenient and universal analysis tool. Its numerical efficiency allowed us to solve optimization problems characterized by multiple reanalysis.
KW - Crack
KW - Discrete Fourier transform
KW - Flaw
KW - Periodic microstructure
KW - Representative cell
UR - http://www.scopus.com/inward/record.url?scp=62749188269&partnerID=8YFLogxK
U2 - 10.1615/IntJMultCompEng.v6.i5.40
DO - 10.1615/IntJMultCompEng.v6.i5.40
M3 - מאמר
AN - SCOPUS:62749188269
VL - 6
SP - 435
EP - 449
JO - International Journal for Multiscale Computational Engineering
JF - International Journal for Multiscale Computational Engineering
SN - 1543-1649
IS - 5
ER -