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Multiresolution strategies for the modeling of composite shell structures based on the variable separation method
Author(s) -
Vidal P.,
Gallimard L.,
Polit O.
Publication year - 2018
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.5978
Subject(s) - finite element method , computation , shell (structure) , geometry , displacement field , displacement (psychology) , iterative and incremental development , plane (geometry) , process (computing) , algorithm , transverse plane , polar coordinate system , variable (mathematics) , field (mathematics) , multiresolution analysis , mathematics , mathematical analysis , computer science , structural engineering , engineering , mechanical engineering , artificial intelligence , psychology , discrete wavelet transform , software engineering , wavelet transform , wavelet , pure mathematics , psychotherapist , operating system
Summary We are interested in the layer‐wise modeling of composite cylindrical shell structures based on a variable separation method. The present study is focused on the use of a multiresolution strategy to decrease the computational cost of numerous analyses where some parameters can change. For this purpose, the displacement field is approximated as a sum of separated functions of the in‐plane coordinates and the transverse coordinate. Thus, an iterative process that consists of solving a two‐dimensional (2D) and a one‐dimensional problem successively at each iteration is required. In the thickness direction, a fourth‐order expansion in each layer is considered. For the in‐plane description, a classical finite element method is used. In our framework of a multiresolution process, once a first computation is achieved, the previously built 2D functions can be used. Thus, the following problems to be solved can be limited to a one‐dimensional problem. If needed, only few 2D functions might be built. The approach is assessed through mechanical tests on L‐angle specimens by comparing with a quasi–three‐dimensional layer‐wise approach. It is illustrated by varying the geometry and the stacking sequences of the shell.