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Group-theoretic optimization framework for symmetric structures: simple/multiple eigenmode classification and tracking
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DOI：10.1007/s00158-026-04410-x.png)
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Abstract
En 中文
Tracking eigenmodes associated with multiple eigenvalues and optimizing such eigenvalues is challenging. This work presents a group-theoretic framework that integrates results from group representation theory with an effective eigenmode classification algorithm. By systematically assigning eigenmodes to irreducible representations of the underlying group, the proposed method enables robust tracking of both simple and multiple eigenmodes. A partition strategy is also introduced to distinguish group-theoretic multiple eigenvalues from convergent eigenvalues, ensuring reliable mode classification and accurate clustering. The framework considers cluster mean maximization within a bound formulation, naturally accommodating eigenmode crossings and mode order switches while requiring only a limited number of eigenpairs to be computed. Numerical studies on truss structures with all common point-group symmetries—including dihedral, tetrahedral, octahedral, and icosahedral groups—demonstrate accurate eigenmode tracking and consistent optimization performance.
Keywords:
Symmetry
Multiple eigenvalues
Group-theoretic optimization
Eigenmode classification
Eigenfrequency optimization
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