Abstract
In this study, we propose a new approach to control the transient response of a shell structure by optimizing the thickness. The free-form optimization method for shells, a parameter-free shape optimization method developed by one of the authors, is extended for the transient response problem of a shell structure. The design objective is to minimize the dynamic compliance or to control the displacement at arbitrary domains and time to the desired values under volume constraint. This problem is directly solved without converting the discrete equivalent static loads, which is often employed in time-dependent optimization problems. The optimum design problem is formulated as a distributed-parameter optimization problem and the sensitivity function for this problem is theoretically derived based on the variational method. With the H 1 gradient method for scalar design variable, we determine the optimum thickness distribution of a shell structure while minimizing the objective functional and maintaining the smoothness of the thickness distribution. Some optimum design examples are demonstrated and the results are discussed.
