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Buckling and wrinkling of thin membranes by using a numerical solver based on multivariate Taylor series

Article dans une revue avec comité de lecture
Author
TIAN, Haitao
POTIER-FERRY, Michel
243747 Labex DAMAS
ccABED-MERAIM, Farid
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]

URI
http://hdl.handle.net/10985/20655
DOI
10.1016/j.ijsolstr.2021.111165
Date
2021
Journal
International Journal of Solids and Structures

Abstract

Buckling and wrinkling of thin structures often lead to very complex response curves that are hard to follow by standard path-following techniques, especially for very thin membranes in a slack or nearly slack state. Many recent papers mention numerical difficulties encountered in the treatment of wrinkling problems, especially with path-following procedures and often these authors switch to pseudo-dynamic algorithms. Moreover, the numerical modeling of many wrinkles leads to very large size problems. In this paper, a new numerical procedure based on a double Taylor series is presented, that combines path-following techniques and discretization by a Trefftz method: Taylor series with respect to a load parameter (Asymptotic Numerical Method) and with respect to space variables (Taylor Meshless Method). The procedure is assessed on buckling benchmarks and on the difficult problem of a sheared rectangular membrane.

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