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Homogenization and pre‐integration techniques for multilayer composite and sandwich finite element models
Author(s) -
Laschet G.,
Jeusette J. P.,
Beckers P.
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620270204
Subject(s) - homogenization (climate) , finite element method , composite number , stiffness matrix , numerical integration , stiffness , structural engineering , materials science , mathematics , computer science , mathematical analysis , composite material , engineering , biodiversity , ecology , biology
The multilayer degenerated 3‐D shell element, for which the stiffness matrix is calculated by numerical integration ply by ply, gives accurate results even for moderately thick composite panels, but needs an important linear and non‐linear generation time when the number of plies is high ( N > 10). In order to reduce this time some pre‐integration and homogenization techniques are investigated. Different pre‐integration methods have been reviewed and discussed. Then, two new homogenization methods, based on a series expansion of an equivalent Hooke matrix over the thickness, are presented. Next, simple numerical validation tests of these new methods are discussed, indicating necessary further investigations. Finally, a general discussion about the properties of the pre‐integration and homogenization techniques tends to define their respective application domain.