The shooting methods to solve 3D nonlinear strings assemblies
Florian Surmont · Applied Ocean Research · 2026
This paper presents a comprehensive framework for solving the statics of three-dimensional nonlinear interconnected strings using shooting methods. The proposed approach is particularly suited for mechanical engineering applications, where strings are subjected to arbitrary external loads and connected through various kinematic joints. The general formulation of the two-point boundary value problem (TPBVP) for strings is derived, considering different types of boundary conditions such as spherical, prismatic, and planar joints, as well as imposed forces and stiffeners. Single and multiple shooting methods are adapted to solve the TPBVP, transforming it into a succession of initial value problems (IVPs). A novel multi-body/multi-shooting method is introduced to efficiently handle string assemblies by combining the multi-body approach with the shooting method. The proposed formalism is validated through several numerical experiments, demonstrating its precision, convergence, and modeling capabilities. The results are compared against semi-analytical catenary solutions, showcasing the method's ability to handle various boundary conditions, nonlinear external loads, and string assemblies with remarkable accuracy. The adaptive step integration scheme used in conjunction with the shooting method optimizes the number of integration points while maintaining high precision. This study provides a novel numerical modeling for string structures providing a versatile and efficient framework for analyzing the statics of 3D nonlinear strings.