Abstract Variable Angle Tow (VAT) composite panels, whereby fibre angle distributions vary continuously in-plane, have more scope for tuning structural properties than traditional straight fibre laminated composite materials. Currently, the geometrically non-linear response of such structures is typically modelled using path-following methods implemented in commercial finite element analysis. However the high computational cost given from both the incremental-iterative procedure and fine mesh required for accurate modelling of the variable trajectory of fibre direction, can be excessively time consuming. Driven by these shortcomings, we use a fast multi-modal Koiter asymptotic method for investigating the nonlinear buckling behaviour of VAT cylindrical panels in compression. In doing so, this paper provides new insight into the multi-modal description and nonlinear buckling mode interactions which are responsible for the highly nonlinear behaviour of cylindrical panels in compression with a particular emphasis on the nonlinear components in the mathematical asymptotic description. As such, through an extensive parametric virtual testing programme we construct, for each panel under investigation, an asymptotic solution projecting the equilibrium equations in the subspace of its first 30 buckling modes. Then, at several points of the resulting equilibrium path, the percentage contribution of each of these modes to the solution is measured. On the basis of the percentage obtained, those modes which give the largest contribution to the solution are identified. The main novelty of this work is that these results are used as a priori information for re-projecting the equilibrium equations into a new modal subspace to which only the buckling modes with the largest participation belong. Moreover, for the first time, we observe that in a multi-modal Koiter-inspired description the modal shapes giving the largest contribution to the asymptotic solution have the same degree of symmetry. In this way, for a generic panel under consideration, we show that it is possible to obtain a more computationally-efficient asymptotic description than current approaches. Finally, the new computed equilibrium paths are compared to benchmark results using the commercial finite element software ABAQUS and the computational advantages given by using a priori information in the asymptotic expansion are commented upon.

中文翻译：

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具有模态相互作用的压缩载荷下变刚度圆柱板的后屈曲行为

摘要 可变角度丝束 (VAT) 复合板，其中纤维角度分布在平面内连续变化，比传统的直纤维层压复合材料具有更大的调整结构性能的空间。目前，此类结构的几何非线性响应通常使用商业有限元分析中实施的路径跟踪方法进行建模。然而，纤维方向可变轨迹的精确建模所需的增量迭代程序和精细网格都给出了高计算成本，可能会非常耗时。由于这些缺点，我们使用快速多模态 Koiter 渐近方法来研究 VAT 圆柱形面板在压缩中的非线性屈曲行为。在这样做，本文提供了对多模态描述和非线性屈曲模态相互作用的新见解，这些相互作用导致圆柱板在压缩中的高度非线性行为，特别强调数学渐近描述中的非线性分量。因此，通过广泛的参数化虚拟测试程序，我们为每个被研究的面板构建了一个渐近解，将平衡方程投影到其前 30 个屈曲模式的子空间中。然后，在生成的平衡路径的几个点，测量这些模式中的每一个对解决方案的贡献百分比。根据获得的百分比，确定对解决方案贡献最大的那些模式。这项工作的主要新颖之处在于，这些结果被用作先验信息，将平衡方程重新投影到一个新的模态子空间中，只有参与度最大的屈曲模式才属于该模态子空间。此外，我们第一次观察到，在多模态 Koiter 启发的描述中，对渐近解贡献最大的模态形状具有相同的对称度。通过这种方式，对于正在考虑的通用面板，我们表明有可能获得比当前方法更具计算效率的渐近描述。最后，将新计算的平衡路径与使用商业有限元软件 ABAQUS 的基准结果进行比较，并评论了在渐近展开中使用先验信息给出的计算优势。