This study presents a multi-objective optimization for a variable-axis stiffness composite laminate to achieve both maximization of its fundamental natural frequency and material-efficient design by minimizing fiber usage. The fiber paths in the placement layers were represented by a third-order polynomial, and their optimal shapes were explored using a multi-objective genetic algorithm (NSGA-II). The two objective functions were the first natural frequency and the total fiber length. The optimization results revealed a trade-off relationship between these two objectives. The optimal fiber paths were found to be shapes extending radially from the fixed boundary of the plate. Furthermore, an inefficient design region was identified where the rate of increase in natural frequency significantly decreases with respect to the increase in fiber length. This suggests that for a material-efficient design, it is crucial to select a design solution that avoids this inefficient region.
OGUSHI et al. (Wed,) studied this question.