The complex buckling behavior of one of the simplest structures, an elastic thin strip under combined stretch and twist loading represents a fascinating example for structural stability analysis. For stretched-twisted strips, in contrast to solely stretched strips, not just the computation of the post-buckling process but also the simulation of the pre-buckling behavior and the determination of the bifurcation loading state requires nonlinearities to be taken into account.

Under twist, not only shear stresses but also membrane normal stresses, with buckling relevant compressive stress contributions, develop. These compressive membrane stresses have components in the longitudinal and – maybe surprisingly – also in the transversal direction, i.e., normal to the long axis of the strip. Depending on the length to width ratio of the strip and on the ratio of the intensity of torque to tension loading, it is either the longitudinal or the transversal compression stress distribution, which is predominantly responsible for the loss of stability of the trivial equilibrium state. This is the reason for the transition from one characteristic of buckling mode shapes to a completely different characteristic of buckling modes in dependence of the loading conditions. Of course, within each of these two characteristics, the buckling modes vary in terms of wave numbers in dependence of the mentioned parameters.

While these kinds of mode transitions has been studied recently elsewhere, the focus of the present paper is, in addition, laid on further mode transitions appearing in the post-buckling domain due to instabilities of equilibrium states either in the form of further bifurcations or snap-through jumps.

Capturing all these effects by numerical simulations requires a well thought out model and a careful control of the computational analysis.

最简单的结构之一的复杂屈曲行为，即在拉伸和扭曲共同作用下的弹性薄带，是结构稳定性分析的一个引人入胜的例子。与单独拉伸的带材相反，对于拉伸扭曲的带材，不仅要进行屈曲后过程的计算，而且还要模拟屈曲前的行为以及确定分叉载荷状态，这需要考虑非线性因素。

在扭曲下，不仅会产生剪切应力，还会产生膜正应力，并伴有屈曲相关的压应力。这些压缩膜应力在纵向上（可能令人惊讶地）在横向上也有分量，即垂直于带材的长轴。取决于条带的长宽比以及扭矩强度与拉力载荷的比值，它是纵向或横向压缩应力分布，这主要是造成平凡平衡态稳定性丧失的原因。这是根据载荷条件从屈曲模式形状的一个特性过渡到屈曲模式的完全不同的特性的原因。当然，在这两个特征中，

尽管最近已经在其他地方研究了这些类型的模式跃迁，但本文的重点还在于，由于平衡态的不稳定性（以进一步的分叉或捕捉形式），在后屈曲域中出现的其他模式跃迁。 -通过跳跃。

要通过数值模拟捕获所有这些影响，就需要一个经过深思熟虑的模型并仔细控制计算分析。