Improvement of two-dimensional dynamic modeling of cable based on strain modification

In this paper, based on the nonlinear continuum mechanics and curve theory in differential geometry, we comprehensively consider the nonlinear strain of Perkins’ model and the dynamic curvature of Howell’s model for model establishment. Under the updated Lagrangian formulation, we establish the plane dynamic equations of the cable structure, including dynamic curvature and large strain based on the current configuration. The expression of shear force is simplified using dimensionless parameter analysis, and the nonlinear geometric equation and the relative rotation angle equation are supplemented in the plane dynamic equations to form the modified Howell model. We illustrate the difference between the original and modified Howell model by analyzing the tension and shear coefficients. Moreover, we illustrate the superiority of the modified Howell model in terms of computational accuracy and efficiency through examples.