Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints

M. Ohsaki, K. Fujisawa, N. Katoh, Y. Kanno

Research output: Contribution to journalArticlepeer-review

62 Citations (Scopus)


Topology optimization problem of trusses for specified eigenvalue of vibration is formulated as Semi-Definite Programming (SDP), and an algorithm is presented based on the Semi-Definite Programming Algorithm (SDPA) which utilizes extensively the sparseness of the matrices. Since the sensitivity coefficients of the eigenvalues with respect to the design variables are not needed, the SDPA is especially useful for the case where the optimal design has multiple fundamental eigenvalues. Global and local modes are defined and a procedure is presented for generating optimal topology from the practical point of view. It is shown in the examples, that SDPA has advantage over existing methods in view of computational efficiency and accuracy of the solutions, and an optimal topology with five-fold fundamental eigenvalue is found without any difficulty.

Original languageEnglish
Pages (from-to)203-217
Number of pages15
JournalComputer Methods in Applied Mechanics and Engineering
Issue number1-2
Publication statusPublished - Nov 15 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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