Abstract
In this paper, we present a solution to shape optimization of plate and shell structures for a natural frequency problem. The weight is minimized under a natural frequency constraint. The designed boundaries are assumed to be movable only to in-plane directions. Optimized structures are discretized by the plane elements based on the Mindlin-Reissner's plate theory. A non-parametric, or a distributed shape optimization problem is formulated and the shape gradient function is theoretically derived using the material derivative method and the Lagrange multiplier method. The traction method, or the shape optimization method developed by authors is applied to obtain the optimal shape in this problem. The validity of this numerical solution to minimize the weight of plate and shell structures is verified through simple and practical examples.
