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In this paper, a space-time absolute nodal coordinate formulation cable (SAC) element forming technique based on the Lagrange family of shape functions is proposed. Two distinct SAC elements, each with a distinct spatial shape function, have been generated by this method. Moreover, the external forces such as the bending moment and the air resistance formula have been accounted for. The Lagrange multiplier method, along with the concepts of replacement constraint and supplementary constraint, has been employed to provide a solution for the dynamics of constrained mechanical systems. Additionally, a constraint conversion strategy has been suggested. The solver has been constructed through Hamilton’s law of varying action. The space-time finite element method is used to solve dynamic problems, employing the Newton algorithm and quasi-Newton algorithm. The accuracy and efficiency of the solution has been verified by three simulations and one experiment. The circle-bending static simulation and the double-ended velocity impact dynamic simulation demonstrate the accuracy of the two elements. The correlation between statics and dynamics has been studied for different discretization methods and different solvers’ calculation accuracy and efficiency. Different modeling methods, time steps, order and the application of the quasi-Newton method all have a bearing on the efficiency of the solution. Finally, a comparison with an experiment in the free-pendulum simulation reveals the capability of this model to simulate dynamic problems with air resistance.

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.

In this paper, a tilting system of ground penetrating radar by 5R1C 6-bar linkage mechanism is proposed. The kinematic function of hydraulic cylinder and the output angle is given in explicit format. The quasi-static formulation of the tilting system is proposed to calculate the shaft and revolute force. The simulation of mechanism via ADAMS and an experiment is made to verify the design. The maximum stress is exposed in curved shaft and the worst working condition is the tilt condition. It proves the validity of tilting system that both mechanism and hydraulic system work well in the loading condition and unloading condition.