Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory. We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution.

中文翻译：

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使用三维有限元对几何非线性平面结构的动力学进行非侵入式降阶建模

非侵入式方法自二十年来一直用于推导几何非线性结构的降阶模型，特别强调所谓的刚度评估程序 (STEP)，它依赖于有限元中规定位移的静态应用语境。我们表明，当将这种方法应用于 3D 元素时，观察到模态扩展的收敛特别慢，因为非线性耦合发生在涉及 3D 厚度变形的非常高的频率模式中。关注平面结构的情况，我们首先通过计算结构的所有模式来证明收敛解可以通过使用静态凝聚或范式理论来展示。然后我们证明静态模态导数提供了相同的解决方案，但计算量更少。最后，