Morphogenesis of free-form surface structures based on geometrically nonlinear isogeometric analysis

Free-form surface structures have taken the forefront in space structure research owing to their free and flexible expressiveness and aesthetic visual effects. Yet, their irregular shapes and large span of the initial structure often lead to the problem of large displacement, necessitating the incorporation of geometric nonlinearity in the analysis. In this paper, we employ structural optimization design principles to investigate the morphogenesis of free-form surface structures while considering their geometric nonlinearity. Particularly, we explore both single-objective and double-objective shape optimization of free-form surface structures by employing structural strain energy and the first natural frequency as optimization indexes and the vertical coordinates of control points as optimization variables. The effectiveness of the proposed method is finally verified by several examples.