Abstract
This paper presents a non-parametric, or a node-based, shape optimization method for designing the optimal geometry of a 3-D frame structure composed of arbitrarily curved linear elastic members. A design problem dealt with maximizing the natural frequency of a specified mode is formulated as a distributed-parameter shape optimization problem. Under the assumption of that each member varies in the normal direction to its centroidal axis, the shape gradient function and the optimality conditions are theoretically derived by the Lagrange multiplier method and the material derivative method. The optimal free-form geometry is determined by applying the derived shape gradient function as the factious external forces to the members to minimize the objective functional, which is called the free-form optimization method for frame structures, a gradient method in a Hilbert space, proposed by one of the authors. The effectiveness and validity of the proposed method is verified through several design problems.
