A comparison between two methods to derive reduced-order models (ROM) for geometrically nonlinear structures is proposed. The implicit condensation and expansion (ICE) method relies on a series of applied static loadings. From this set, a stress manifold is constructed for building the ROM. On the other hand, nonlinear normal modes rely on invariant manifold theory in order to keep the key property of invariance for the reduced subspaces. When the model coefficients are fully known, the ICE method reduces to a static condensation. However, in the framework of finite element discretization, getting all these coefficients is generally too computationally expensive. The stress manifold is shown to tend to the invariant manifold only when a slow/fast decomposition between master and slave coordinates can be assumed. Another key problem in using the ICE method is related to the fitting procedure when a large number of modes need to be taken into account. A simplified procedure, relying on normal form theory and identification of only resonant monomial terms in the nonlinear stiffness, is proposed and contrasted with the current method. All the findings are illustrated on beams and plates examples.

提出了两种方法的比较，用于导出几何非线性结构的降阶模型（ROM）。隐式压缩和膨胀（ICE）方法依赖于一系列施加的静态载荷。从这个组中，构造了一个压力歧管以构建ROM。另一方面，非线性法线模式依赖不变流形理论，以保持不变性的关键性质。当模型系数完全已知时，ICE方法将减少为静态冷凝。但是，在有限元离散化的框架中，获取所有这些系数通常在计算上过于昂贵。仅当可以假定主坐标和从坐标之间的缓慢/快速分解时，应力流形才趋向于不变流形。当需要考虑大量模式时，使用ICE方法的另一个关键问题与拟合过程有关。提出了一种简化程序，该程序依赖于范式理论并仅识别非线性刚度中的谐振单项项，并与当前方法进行了对比。所有的发现都在梁和板的例子中说明。