| Summary: | Because of its extremely high strength-to-weight ratio and specific elastic modulus, carbon fiber reinforced polymer (CFRP) has been widely employed in aerospace, automotive, sports equipment, civil engineering, and so on. Commonly, composite structures made of CFRP are manufactured as plates or shells, which are weak in noise and vibration due to their thin thickness and light weight. Hence, developing new design optimization methods for the enhancement of the vibration behavior of CFRP composite structures, especially in the lower frequencies, is very important and popular among scholars. In the present work, we aim to develop a free-form optimization system and apply it for optimizing the shapes of CFRP plate/shell structures considering the fiber orientation to maximize their fundamental frequencies under the volume constraint. This shape optimization system composed of vibrational eigenvalue analysis, derivation of shape gradient function, velocity analysis, and shape update, is implemented with a finite element method code and in-house program. We employ the method of Lagrange multiplier and the material derivative method to derive the shape gradient function considering the repeat eigenvalues, and adopt the H1 gradient method in the velocity analysis to achieve the “free-form” of CFRP shells. By considering different fiber orientations of CFRP plate/shell structures, we perform two simple numerical design examples using the developed free-form optimization system. The optimal results show that the smooth optimal shapes can be obtained, and the fundamental frequency of CFRP in each design example can be significantly enhanced from 1.73 to 4.60 times as much as its initial value after the free-form optimization.
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