Lagrangian approach for optimizing fiber bundle placements of CFRP shell structures

Abstract

We present a non-parametric shape and topology optimization method for fiber bundle placement and orientation design aimed at controlling the rigidity of CFRP shell structures. Since the fiber bundles are modeled by the beam element, the placement and the orientation of the fiber bundles can be explicitly obtained while moving the positions. In order to achieve the target displacement at an arbitrarily specified position, we considered the problem of minimizing the squared error under the length constraint of the fiber bundles, and formulated it as a distributed-parameter optimization problem. Using the derived shape gradient function and the density gradient function, the optimum placement and the orientation of the fiber bundles are determined simultaneously by the H1 gradient method for vector and scalar variables. The effectiveness of the proposed method is confirmed by numerical examples.