Optimization of composite structures with continuous spatial variation of fiber angle through Shepard interpolation

In the present paper, we propose a method for the optimization of composite structures with continuous spatial variation of fiber angle. The key idea is to construct a continuous global function interpolating scattered design points to represent the fiber angle arrangement throughout the design domain. To be more specific, the Shepard interpolation method is employed to construct the interpolation function. The angles at scattered design points are taken as the design variables to be optimized. The Shepard interpolation inherently guarantees spatial continuity of fiber angle. In addition, the design freedom of the proposed method can be readily enlarged by increasing the number of design points or the number of design variables to accommodate complex or rapid local variation of fiber angle. Several examples with in-plane load are investigated. In the simple representative numerical examples, the proposed method shows good performance.