A new concurrent optimization method of structural topologies and continuous fiber orientations for minimum structural compliance under stress constraints

The concurrent optimization of structural topologies and fiber orientations offers an effective way for improving the mechanical performance of fiber-reinforced composite structures. However, its local optimal solution problem under stress constraints remains extremely challenging. To tackle this problem, this paper presents an orientation variable corrected principal stress direction (OVCPSD) method, which is composed by a two-step optimization strategy. In the first step, the fiber orientation for the shear-weak materials is roughly distributed along the principal stress direction, and the principal stress direction of the previous iteration step is used as the initial fiber orientation. In the second step, the principal stress direction is further modified by an orientation variable in a small subinterval. Finally, a new optimization model of structural topologies and fiber orientations for minimum structural compliance under stress constraints is established, and the sensitivities of the objective and constraint functions with respect to both the pseudo-density and orientation variable are derived. Three numerical examples are presented to verify the effectiveness of the OVCPSD method. The complete code is available from the website: https://github.com/TopOpt-lbg/OVCPSD_L-shaped-beam.