Strength-constrained simultaneous optimization of topology and fiber orientation of fiber-reinforced composite structures for additive manufacturing

Additive manufacturing (AM) enables flexible fabrication of lightweight fiber-reinforced composite (FRC) structures with topological optimized geometries and fiber orientations. However, premature failure may occur if the manufactured FRC structure is not properly designed against stress distribution. The present study develops a strength-constrained optimization algorithm by considering the 3D printed filament embedded with fiber to be orthotropic material. The Tsai–Wu criterion is incorporated in the topological and fiber orientation optimization process. The element density and the fiber angle are formulated as design variables to simultaneously optimize the distribution of matrix and fiber. Meanwhile, both design variables are filtered to prevent checkerboard patterns of matrix elements and to ensure the continuity of fiber angle. A P-norm approach combined with an adaptive normalization scheme is employed to achieve the global strength constraint and reduce the difference between the P-norm value and the actual maximum Tsai–Wu value. Sensitivity analysis of objective function and strength-constraint conditions with respect to design variables is carried out and it serves as a basis for the method of moving asymptotes. Topological optimization of three typical numerical examples under different loading conditions are conducted and the effectiveness of the proposed method is validated. 73.7% decrease in maximum Tsai–Wu value of the optimized L-shaped beam as well as a slight increase (∼0.2%) in compliance are obtained in comparison with the compliance-based design result.