Motion Structural Optimization Strategy for Rhombic Element Based Foldable Structure

Abstract

This research presents a new systematical design approach of foldable structure composed of several rhombic elements by applying genetic algorithm. As structural shapes represented by a foldable structure can be easily and dramatically morphed by manipulating rotational directions and angle of joints, the foldable structure has been used for various elementary structural members and engineering mechanisms. However a systematic design approach determining detail rotational angle and directions of unit cells for arbitrary shaped target areas has not been proposed yet. This research contributes to it by developing a new structural optimization method determining optimal angle and rotation directions to cover arbitrary shaped target areas of interest with aggregated rhombic elements. To achieve this purpose, we present an optimization formulation minimizing the sum of distances between each reference joint of an arbitrary shaped target area and its closest outer joints of foldable structure. To find out the outer joint set of a given foldable structure, an efficient geometric analysis method based on Delaunay triangulation is also developed and implemented. To show the validity and limitations of the present approach, several foldable structure design problems for two-dimensional arbitrary shaped target areas are solved with the present optimization procedure.