Journal
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
Volume 53, Issue 3, Pages 395-408Publisher
SPRINGER
DOI: 10.1007/s00158-015-1316-y
Keywords
Couple-stress continuum; Topology optimization; Size effects; Fundamental frequency; Multiple eigenvalue
Categories
Funding
- National Natural Science Foundation of China [11002031, 11332004]
- National Basic Research Program (973 Program) of China [2011CB610304]
- Program for Liaoning Excellent Talents in University [LJQ2012040]
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In this paper, the topology optimization formulation of couple-stress continuum is investigated for maximizing the fundamental frequency. A modified bound formulation is used to prevent the order switching and the eigenvalue repeating during the optimization procedure. Also, a modified stiffness interpolation with respect to the element density is employed to avoid the localized mode. Numerical examples are carried out to verify the effectiveness of the present formulation. The results show that the fundamental frequencies increase with the increasing bending modulus but decrease with the increasing inertia of micro-rotation for couple-stress continuum. In addition, the bending modulus contributes dominantly in enlarging the fundamental frequencies. Moreover, the results show that the characteristic length is a factor to determine whether the couple-stress effect is important. The optimal topology and fundamental frequency are both quite different from those of classical continuum when the characteristic length is large and vice versa.
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