Form-finding method for the target configuration under dead load of a new type of spatial self-anchored hybrid cable-stayed suspension bridges

General form-finding problems of cable-supported bridges are established based on a design scenario in which rigidly fixed starting control points must be given as necessary design constraints prior to independent analysis of any of its cable subsystems. This article presents a form-finding method to address a new case, in which the starting control point serves as an intermediate, flexibly variable connection, to couple two related cable subsystems in a multi-nonlinear environment for the target configuration under dead load (TCUD) of a novel type of spatial self-anchored hybrid cable-stayed suspension (HCSS) bridge. A two-layer framework is proposed by integrating finite element analysis (FEA) and analytical formulas with optimization algorithms to form a self regulated interactive analysis among subsystems in an iterative manner. The outer layer seeks to achieve self equilibrium of the global system under the control information of the TCUD, while the inner layer optimizes the subsystems in terms of the initial tensions in the main cables, stay-cables, branches and hangers to obtain a rational mechanical state of the bridge. Then, the TCUD and the intermediate starting control points are determined. To achieve computational stability, a high-performance accelerated Steffens-Newton (ASN) differential algorithm is developed for the shape finding of the cable-hanger subsystem, whereas the non-dominated sorting genetic algorithm (NSGA-II) is adopted as a multiobjective optimizer for TCUD optimization of the other subsystems. The proposed framework is applied to a real-scale self-anchored HCSS bridge, and its validity and performance are demonstrated by comparison studies with a non-optimal scheme and in-field test data.