Iterative Form-Finding Method for Overhead Transmission Conductors Based on a Geometric Update Strategy

Overhead transmission conductors are flexible cable structures. Their initial equilibrium configuration is affected by self-weight, tension, boundary constraints, and material deformation, and is required for force analysis, sag calculation, and safety assessment. Existing studies use catenary theory or numerical iterative methods. The direct iterative method is used in conductor form-finding. However, its geometric update ratio is assigned in segments based on empirical thresholds. This may cause unsmooth updates, low efficiency, and numerical instability in sensitive cases. This study investigates a single-span conductor within a nonlinear finite element form-finding framework. The direct iterative method is analyzed in terms of control variables, implementation process, and update-ratio control mode. A continuous error-driven adaptive geometric update strategy is proposed and an adaptive direct iterative method is developed. The two methods are compared under the same finite element model, parameters, loads, constraints, convergence threshold, and maximum iterations. Three factors are selected: element number, nonlinear substep number, and initial strain coefficient. A total of 27 full-factorial cases are calculated. Convergence efficiency, final error, and abnormal case distribution are evaluated. The results show that the proposed method reduces iterations, improves computational efficiency, and enhances numerical stability in sensitive cases without changing the finite element solution framework.