Shape Design Optimization of CFRP Composite Structures in Natural Vibration Problem

Abstract

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. In the present work, we aim to develop a free-form optimization system and apply it for optimizing the shapes of CFRP shells considering the fiber orientation to maximize its fundamental frequency 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. We adopt the H¹ gradient method in the velocity analysis to achieve the “free-form” of CFRP shells. We perform two simple numerical examples using the developed free-form optimization system. The optimal results show that the natural vibration behavior of CFRP in each design example can be significantly enhanced after the free-form optimization.