Abstract
In this paper, a parameter-free shape optimization method is presented for designing the optimal free-form of a spatial framed structure. The optimum design problem is formulated as a distributed-parameter shape optimization problem under the assumptions that each member is varied in the out-of-plane direction to the centroidal axis and the cross section is prismatic. Compliance minimization, vibration eigenvalue maximization and displacements control problems are formulated under a volume constraint, and solved as examples of optimal shape design of spatial framed structures. The shape gradient function and the optimality conditions for the problems are then theoretically derived. The optimal free-form is determined by applying the derived shape gradient function to each member as a fictitious distributed force to vary the frame, while minimizing the objective functional. We call this method the H^1 gradient method for frame structures, a gradient method in the Hilbert space. The validity and practical utility of this method are verified through design examples.
