The study and application of space-time absolute nodal coordinate formulation quadrilateral cable element

The construction of high-order shape function is a key and difficulty for unstructured grid mesh and sliding boundary problem. In this paper, a construction method of space-time absolute nodal coordinate formulation quadrilateral cable (SACQ) is proposed and the accuracy of SACQ element is studied and verified with 3 different applications. First, the shape function of SACQ is constructed with spatiotemporal reduction coordinate and the action integral of SACQ is composed with Lagrangian function and discrete with perspective transformation. second, numerical convergence region is discussed and determined with Courant number. Furthermore, a space-time nodal dislocation and its relation with Courant number is studied. The simulation and verification are focusing on some realistic problems. Finally, one-sided impact, free-flexible pendulum, taut string with sliding boundary and a deployable guyed mast under impact transverse wave are simulated. In these problems, unstructured grid meshed with SACQ has similar energy convergence and accuracy with structured grid but shows better efficiency.