Systematic occurrence of repeated eigenvalues in structural optimization

DOI10.1007/BF00934087zbMath0471.49022OpenAlexW2025006892MaRDI QIDQ1157561

E. J. jun. Haug, Kyung Kook Choi

Publication date: 1982

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00934087

zbMATH Keywords

numerical methodsstructural optimizationbucklingnecessary conditions of optimalityrepeated eigenvaluesdirectional derivativesconstraints on natural frequencyvibration optimization problem

Mathematics Subject Classification ID

Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Spectral theory; eigenvalue problems on manifolds (58C40) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30) Numerical methods in optimal control (49M99)

Related Items (13)

Multiple eigenvalues in optimization problems ⋮ Structural design for desired eigenfrequencies and mode shapes using topology optimization ⋮ Geometry optimization of a slender cantilever beam subjected to lateral buckling ⋮ Large deformations and stability in topology optimization ⋮ Unnamed Item ⋮ Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints ⋮ Sensitivities of eigenvalues and eigenvectors of problems nonlinear in the eigenparameter ⋮ Structural optimization for specified nonlinear buckling load factor. ⋮ Review of options for structural design sensitivity analysis. I: Linear systems ⋮ Eulerian shape design sensitivity analysis and optimization with a fixed grid ⋮ Bimodal optimal design of vibrating plates using theory and methods of nondifferentiable optimization ⋮ Bimodal solutions in eigenvalue optimization problems ⋮ Sufficient conditions for an extremum in eigenvalue optimization problems

Cites Work

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• On single and bimodal optimum buckling loads of clamped columns
• Strongest Columns and Isoperimetric Inequalities for Eigenvalues
• On the optimal design of a vibrating beam
• Problems of Optimal Structural Design

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