abaqus_static_fil from Indirect reduced-order modelling: using nonlinear manifolds to conserve kinetic energy

Nonlinear dynamic analysis of complex engineering structures modelled using commercial finite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost by constructing low-dimensional models using a static solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and in-plane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement arises from the fact that, in existing methods, in-plane kinetic energy is assumed to be negligible. For structures such as thin plates and slender beams with fixed/pinned boundary conditions, this is often reasonable, but in structures with free boundary conditions (e.g. cantilever beams), this assumption is violated. Here, we exploit the concept of nonlinear manifolds to show how the in-plane kinetic energy can be accounted for in the reduced dynamics, without requiring any additional information from the FE model. This new insight enables indirect reduction methods to be applied to a far wider range of structures while maintaining accuracy to higher deflection amplitudes. The accuracy of the proposed method is validated using an FE model of a cantilever beam.

采用商用有限元（FE）软件建模的复杂工程结构，其非线性动力学分析往往计算成本高昂。间接降阶建模策略通过从有限元模型中提取静力解数据集构建低维模型，从而降低计算开销。此类方法的适用范围通常存在局限，仅适用于满足如下两类条件的结构：其一，非线性的主要来源为横向模态与面内模态间的准静态耦合（即膜拉伸效应）；其二，面内位移量有限。研究表明，第二项限制条件的根源在于，现有方法默认面内动能可忽略不计。对于固支/铰支边界条件下的薄板、细长梁等结构，该假设通常具备合理性，但对于自由边界条件的结构（如悬臂梁），该假设不再成立。本文依托非线性流形的相关概念，阐明了如何在降阶动力学建模过程中纳入面内动能，且无需额外调用有限元模型获取其他信息。这一创新性见解使得间接降阶方法能够应用于更广泛的结构类型，同时在更大的挠度幅值范围内维持建模精度。本文所提方法的准确性，通过悬臂梁的有限元模型得到了验证。