Abstract
In this paper, a non-parametric, or a node-based shape optimization method was proposed for achieving a desired static deformation of frame structures. For a frame structure composed of arbitrarily curved linear elastic members, the deformation control is one of the important problems in the stiffness design problem, and it also enables to give a function to frame structures. As an objective functional, we introduce the sum of squared error norms to the desired displacements on specified members, and the assumption that each frame member varies in the out-of-plane direction to the centoroidal axis. The shape gradient function and the optimality conditions for this problem were theoretically derived by the Lagrange multiplier method and the material derivative method. An optimal geometry is determined by applying the negative shape gradient function as fictitious external forces to the frame members and analyzing an optimal variation that minimizes the objective functional. With the proposed, an optimal arbitrarily formed frame structure with smoothness can be obtained while minimizing the objective functional. The validity and practical utilities of this method for the static deformation control of frame structures were verified through design examples.
