Topology optimization of continuous fiber-reinforced composites using Shepard interpolation and its design variable reduction

In the design optimization of fiber-reinforced composites, spatial material discontinuity is considered intractable within the manufacturing reality imposed by advanced technologies. This paper presents a topological optimization framework based on truss-like material to design composite structures with continuous fiber. Specifically, the fiber morphology at the scattered design points, which controls the orientation and volume fraction, is taken as design variables. Using the Shepard interpolant scheme, the fiber morphology at any given computational point is interpolated by scattered design variables within a certain circular influence domain. The employed interpolation inherently ensures the spatial continuity and range-restricted of the physical field in an element-independent manner. Since separating the design variable field and analysis mesh on two independent sets of points, this method is well suited for using a sparse design variable field. The computational savings are compelling due to the reduced number of design variables without significantly restricting the design freedom. Numerical instability such as checkerboard and mesh dependencies vanished as no intermediate densities are suppressed in optimization. The continuous fiber-reinforced composites (CFRCs) in the form of truss-like continua are ready to be manufactured with the aid of a simple post-processing. Several numerical examples are investigated to demonstrate the feasibility and effectiveness of the proposed formulation and numerical techniques.