The Study and Application of Quadrilateral Space-Time Absolute Nodal Coordinate Formulation Cable Element

The construction of a high-order shape function is a key and difficulty for unstructured grid mesh and sliding boundary problems. In this paper, a construction method of space-time absolute nodal coordinate formulation quadrilateral cable (SACQ) is proposed, and the accuracy of the SACQ element is studied and verified with three different applications. First, the shape function of SACQ is constructed with spatiotemporal reduction coordinates, and the action integral of SACQ is composed with the Lagrangian function and discrete with perspective transformation. Second, the numerical convergence region is discussed and determined with the Courant number. Furthermore, a space-time nodal dislocation and its relation with the Courant number are studied. The simulation and verification are focusing on some realistic problems. Finally, a one-sided impact, a free-flexible pendulum, a taut string with a sliding boundary and a deployable guyed mast under an impact transverse wave are simulated. In these problems, an unstructured grid meshed with SACQ has similar energy convergence and accuracy to a structured grid but shows better efficiency.