Elimination of Spurious Modes in Reduced‐Order‐Modeling‐Based Topology Optimization of Geometrically Nonlinear Structures

In geometrically nonlinear topology optimization, elements with low pseudo‐densities, subjected to compression from neighboring stiffer regions, can lead to complications, such as “inside‐out” elements in 2D structures or spurious local buckling in shells and plates. The former typically causes computational divergence, while the latter, though not always divergent, could significantly increase the analysis iterations required for convergence, resulting in significantly higher computational costs. To enhance efficiency, reduced‐order modeling (ROM) could be used, as it employs a small number of generalized variables to approximate the behavior governed by the numerous degrees of freedom (DOFs) in the full‐order model (FOM). However, the presence of spurious buckling can severely compromise ROM efficiency, even requiring more analysis iterations compared to methods relying on FOMs. To address the analysis convergence difficulties caused by spurious buckling in ROMs, two types of approaches are investigated. The first and simplest approach involves removing spurious modes from the ROM basis. The second approach focuses on eliminating spurious modes directly from the underlying physics, which can be extended to standard FOM‐based analyses. The above strategies are primarily evaluated using shell models, providing a detailed analysis of their effectiveness. The objective of this paper is not to propose a complete or definitive solution to spurious modes. Rather, the goal is to highlight and compare the strengths and limitations of different methodologies, and to provide insight into their behavior when applied to the problems considered.