Journal
COMPOSITE STRUCTURES
Volume 170, Issue -, Pages 135-145Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.compstruct.2017.03.007
Keywords
Free-form optimization; Fundamental frequency maximization; Gradient method; Orthotropic shell; Repeated eigenvalues
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Funding
- Research Center of Smart and Tough Machines at Toyota Technological Institute
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In this study, a free-form optimization method is proposed that maximizes the fundamental frequencies of the orthotropic shells to avoid vibrational resonance. The negative fundamental vibrational eigenvalue is employed as the objective function, which is minimized by subjecting to the governing equation of the natural frequency analysis and area constraint. In the free-form optimization process, the natural frequency analysis of the orthotropic shells is performed to calculate the shape gradient function. The shape gradient function is then applied to the velocity analysis for determining the optimal shape variation. The repeated eigenvalues are considered by converting the fundamental eigenvalue to a summation form of the repeated eigenvalues. The proposed optimization method is validated using three examples of the orthotropic shells. The numerical results show that the optimized shapes of the orthotropic shells are smooth, and their fundamental frequencies are significantly enhanced using the proposed free-form optimization method. (C) 2017 Elsevier Ltd. All rights reserved.
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