Abstract
The present paper describes an approach for solving a shape optimization problem of maximizing a target eigen furequency of elastic continuum in equilibrium condition after large deformation while maintaining the mass of elastic continuum. The main problem is defined as the eiven value problem for natural vibration in equilibrium condition after large deformation. The negative value of the eigen value for the target natural vibration is chosen as an objective function for minimizing. Mass is used for a constraint function. The Frechet derivative of the objective function with respect to the domain variation, which we call the shape derivative of the objective function, is evaluated using the solutions of the main problem and the adjoint problem. A scheme to solve the shape optimization problem is presented as an iterative algorithm that uses the H^1 gradient method (the traction method) for reshaping in order to keep the smoothness of original boundary. The validity of proposed method is verified with a numerical example.
