In the JLCS annual meetings 2017 and 2018, the speaker reported that some vector fields have invariant tori arranged similarly to double-twist cylinders in cholesteric blue phases and discussed this similarity by using cubic magnetic groups. In this talk, the same approach is applied to hexagonal cases and two vector fields are derived. The arrangement of their invariant tori is observed to vary according to the ratio of the magnitude of <001> twist to that of <210>.
In this research, we study on updating method for the orientation of anisotropic material in topology optimization. In the topology optimization of anisotropic materials, the material distribution and the orientation of the fiber are treated as design variables. In this research, we focus on the optimization of the orientation. First, we express the orientation as a vector field, and define elastic coefficient tensor of an anisotropic material. In the previous research, the upper limit was set for the nom of the orientation vector field, which results in restriction on updating the orientation. Thus, there is a possibility of falling into a local solution. Therefore, in this research, we formulate the optimization problem with constraint on the orientation vector field based on the augmented Lagrangian method. Finally, we present a numerical example for the stiffness maximization problem of the linear anisotropic elastic material, and confirm the validity of the proposed method.