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.

薄结构的屈曲和起皱通常会导致非常复杂的响应曲线，标准路径跟踪技术很难遵循这些曲线，特别是对于处于松弛或接近松弛状态的非常薄的膜。最近的许多论文都提到了在处理起皱问题时遇到的数值困难，特别是在路径跟踪程序中，这些作者经常转向伪动态算法。此外，许多皱纹的数值建模会导致非常大的尺寸问题。在本文中，提出了一种基于双泰勒级数的新数值程序，它结合了路径跟踪技术和 Trefftz 方法的离散化：泰勒级数关于载荷参数（渐近数值方法）和空间变量（泰勒无网格方法）。