In this work, we present a new 2D Reduced model capable of taking into account the coupling between local instabilities and global buckling which occur in sandwich structures. To establish this model, we use a multi-scale approach based on the technique of Fourier series with slowly varying coefficients which allows transforming a 2D sandwich model into 2D Reduced model, of which only the envelope of instability is numerically evaluated. It is like the Ginzburg–Landau envelope equation, but it provides the post buckling behavior and takes into account the coupling between global and local instabilities. The proposed model is validated by comparison with the 2D Complete model and the analytical solution.

The non-linear system is solved by the Asymptotic Numerical Method (ANM), which is an efficient, robust and accurate continuation method for solving non-linear systems.

在这项工作中，我们提出了一个新的2D简化模型，该模型能够考虑三明治结构中发生的局部不稳定性和整体屈曲之间的耦合。为了建立这个模型，我们使用基于傅立叶级数的技术的多尺度方法，该方法具有缓慢变化的系数，该方法允许将2D三明治模型转换为2D简化模型，其中仅对不稳定性的包络进行数值评估。它类似于Ginzburg-Landau包络方程，但是它提供了屈曲后的行为，并考虑了全局和局部不稳定性之间的耦合。通过与2D Complete模型和解析解决方案进行比较，对所提出的模型进行了验证。

非线性系统通过渐近数值方法（ANM）进行求解，这是一种有效，鲁棒且准确的连续方法，用于求解非线性系统。