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

TY - JOUR

T1 - Buckling and wrinkling of thin membranes by using a numerical solver based on multivariate Taylor series

AU - Tian, H.

AU - Potier-Ferry, M.

AU - Abed-Meraim, F.

PY - 2021/11/1

Y1 - 2021/11/1

N2 - 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.

AB - 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.

KW - Wrinkling

KW - Buckling

KW - Trefftz method

KW - Asymptotic Numerical Method

KW - Taylor meshless method

U2 - 10.1016/j.ijsolstr.2021.111165

DO - 10.1016/j.ijsolstr.2021.111165

M3 - 文章

SN - 0020-7683

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

ER -