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.

Typical engineering cable structures, such as high-voltage wire and wire rope, usually bring a damping effect which cannot be ignored due to the technological problems of manufacturing. For such problems, especially the damping of cable structures undergoing large displacement and severe deformation, few studies have been reported in the past. In this work, the fractional derivative viscosity model is introduced into the cables described by the absolute nodal coordinate formulation. The computer implementation algorithm of the proposed cable damping model is given based on the three-parameter fractional derivative model. Two numerical examples demonstrate the effectiveness and convergence property of the proposed cable damping model. An experiment is proposed in which a wire is tensioned and released. Configurations are captured by the high-speed camera and compared with the results obtained from the numerical simulation. The agreement of the simulation and experimental results validates the proposed cable damping in application.

This paper, based on the node insertion algorithm for NURBS curves, explicitly defines the method for calculating the node coordinates and weights of subdivided element, without altering the geometric properties and parameter distribution of the RANCF elements. However, the diversity in the definition of RANCF elements can lead to uncontrollable subdivision in parameter space. To address the distortion in the subdivision process of non-uniformly parameterized elements, this paper introduces a distribution density function for the element parameter points and establishes a calculation method for the parameter space subdivision nodes corresponding to the arc length in physical space. This method enables precise subdivision of differently parameterized arc elements in the physical space. Ultimately, guided by numerical computation results, the subdivision criteria for RANCF elements were determined. The results indicate that local refinement in regions with denser parameter point distribution can both ensure computational accuracy and improve computational efficiency.

The construction of rational absolute nodal coordinate formulation (RANCF) elements is usually based on a linear transformation of non-uniform rational B-spline (NURBS) geometry. However, this linear transformation can lead to property transfer issues, which greatly reduce the modeling efficiency, especially for conic sections. To overcome this limitation, we first analyze the geometric constraints of conic sections and derive a unique defining equation in rational parametric form. A corresponding degree-elevation formula is also obtained. Using these results, we propose a direct definition method for RANCF elements that explicitly exploits the analytic properties of conic sections. The method provides fast and accurate expressions for the nodal coordinates and weights, and thus enables efficient modeling of RANCF elements for conic-section configurations. We also mitigate the arbitrariness in element definition by introducing, for the first time, the concept of a mapping factor K, which characterizes the mapping between the physical space and the parameter space. Based on this mapping factor, we establish a parameterization procedure for RANCF conic-section elements. An evaluation criterion for K is further proposed and used to define the optimal mapping factor K_opt, which yields an optimal parameterization and allows the construction of K_opt elements. Numerical examples demonstrate that, in large-deformation analyses of flexible systems, the proposed elements can achieve a given accuracy with fewer elements than conventional approaches.

Crane brakes have limited failure samples, and the braking torque degradation quantity exhibits randomness; thus, traditional prediction methods are unsuitable for reliability prediction of crane brakes. The braking torque is a measurable physical quantity used to characterize braking performance. Therefore, this paper takes the braking torque degradation quantity as the entry point and, based on Bayesian statistical principles, derives a reliability prediction model for the brake. First, using experimental data from the development stage as prior information, the joint prior distribution form of the braking torque degradation quantity parameters was derived, and the hyperparameters in the distribution were determined. Second, by incorporating on-site small samples of experimental data, the corresponding posterior distribution function and the maximum a posteriori estimates values of the parameters are derived. Finally, by incorporating the reliability function of the Weibull distribution, the time for the braking torque degradation quantity to decrease from 0 to the specified threshold at a given confidence level is obtained, enabling the reliability prediction of the brake. The comparison results indicate that the proposed method demonstrates good applicability and accuracy in reliability prediction of crane brakes, providing a theoretical basis for their reliability prediction and maintenance. This study provides an effective approach for reliability prediction of mechanical equipment based on small-sample experimental data.