The strain coupling problem and model decoupling of ANCF cable/beam element

The cable/beam structure has already been widely applied in civil engineering, aerospace engineering, etc. Among various dynamic modeling methods of cable/beam, the Absolute Nodal Coordinate Formulation (ANCF) is very suitable for the modeling of large deformed cable/beam to describe the large deformation and rotation of flexible bodies. According to the strain analysis of ANCF cable/beam element, the bending deformation will cause uneven distribution of axial strain within the element, which means axial and bending strains are coupled with each other. The strain coupling effect brings unrealistic strain energy to the element, resulting in an increased stiffness and element distortion. It is known from the analysis of strain and strain energy at various bending angles that the larger the bending deformation is, the more serious the distortion is. The axial and bending strains are decoupled by redescribing axial strain based on a new constructed equivalent 1D rod element. Then the generalized elastic force is deduced and the strain-decoupled model of ANCF cable/beam element is obtained. The statics and dynamics simulations of two beam models are conducted and the results indicate that the unrealistic strain is eliminated by the decoupled model, and compared with the original model, the decoupled model shows better convergence and curvature continuity and more accurate under same number of elements. Meanwhile, as the stiffness is reduced by the decoupled model, there is no high frequency vibration in the velocity curve any more by compared with the original model.