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Optimization of structures with repeated eigenvalues. (English) Zbl 0543.73117

Optimization of distributed parameter structures, Vol. I, NATO Adv. Study Inst. Ser., E, Appl. Sci. 49, 219-277 (1981).
[For the entire collection see Zbl 0511.00034.]
Structural optimization problems in which multiple eigenvalues may occur are formulated and analyzed. Several optimal design problems are presented that exhibit a repeated eigenvalue at an optimum design. Finite dimensional structural design problems are first analyzed. Quasi- differentiability of the eigenvalue is proved and useful necessary conditions are derived. Methods and results are then extended to distributed parameter structures, for which response and design are described by functions.

MSC:

74P99 Optimization problems in solid mechanics
74G60 Bifurcation and buckling
74H45 Vibrations in dynamical problems in solid mechanics

Citations:

Zbl 0511.00034