Shape optimization of a fish-like hyperelastic body vibrating with a swimming mode

Abstract

In this study, a formulation of the inverse problem to identify the shape of a hyperelastic body in which the vibration mode is similar to the swimming mode of a fish is presented. This research aims to demonstrate the possibility of creating a fish robot that swims with a vibration mode in the water when excited with a vibration generator embedded in the body. Before this study, Chancharoen et al. attempted to formulate an inverse problem as a shape optimization problem for a linear elastic body without considering water. In this study, a cost function was defined by the squared error norm of the vibration mode and the ideal swimming mode. The result of a numerical example confirmed that the approach decreased the cost function, but the obtained vibration model was different from the ideal one. In contrast, in this study, a hyperelastic body is used to approach the actual movement of a fish. Using this replacement, the finite deformation theory is employed to formulate the periodic vibration of the hyperelastic body. The cost function is formulated using the squared error norm of the finite deformation in the cycle. Its shape derivative is evaluated using the solutions of the periodic vibration problem and its adjoint problem with respect to the cost function. To solve the shape optimization problem, an iterative scheme based on the H¹ gradient method for domain variation problems is used. The effectiveness of this approach is illustrated through numerical examples using finite-element models.