Stiffness exerts a significant influence on swimming locomotion of fish. Biological experiments have demonstrated that the stiffness of different body segments in fish is inherently heterogeneous. Although the stiffness variation patterns from head to tail exhibit certain interspecific differences among various fish species, they generally follow a decreasing trend from anterior to posterior. In this study, based on the resistive drag model, we discretized the original model and incorporated improvements such as the distribution function of active bending moments. The analytical model developed herein integrates the stiffness distribution of the fish body into the analysis of its locomotion. Through this model, several typical stiffness distribution patterns were investigated, with a particular focus on sub-topics such as various decreasing distributions and the effects of different segment quantities. The results indicate that a rapidly decreasing stiffness distribution with a low ratio of minimum-to-maximum stiffness yields the optimal swimming performance. This work serves not as a substitute for but rather a supplement to pertinent biological experiments. Simultaneously, it constitutes a foundational study for variable-stiffness distribution robotic fish, informing and guiding future design endeavors.
Ding et al. (2026) studied this question.