A Time-Domain Explicit Integration Algorithm for Fast Overvoltage Computation of High-Voltage Transmission Line

This paper presents a multiple time-step solver based on a time-domain explicit integration algorithm for improving the computational speed of high-voltage transmission line electromagnetic transient (EMT) simulation. For weakly rigid EMT models of high-voltage transmission lines, the previous precise Runge-Kutta integration method with a small time step is adopted; for strongly rigid nonlinear EMT models of high-voltage transmission lines, a an improved precise integration method using a large time step is used for the solver of EMT simulation. Practical simulations for overvoltages of high-voltage transmission line show that multiple time-step EMT solver can be applied to different cases of EMT simulation for transmission line.

Stability Analysis of an Explicit Integration Algorithm with 3D Viscoelastic Artificial Boundary Elements

Viscoelastic artificial boundary elements are one of the most commonly used artificial boundaries when solving dynamic soil-structure interactions or near-field wave propagation problems. However, due to the lack of clear and practical stability criteria for the explicit algorithm that considers the influence of viscoelastic artificial boundary elements, the determination of the stable time increment in such numerical analyses is still a challenge. In this study, we proposed a numerical stability analysis method for the explicit algorithm with a 3D viscoelastic artificial boundary element based on the idea of a subsystem. Through this method, the artificial boundary subsystem that controls the stability of the overall numerical system is determined, and the analytical solution for the stability condition of the explicit integration algorithm with 3D viscoelastic artificial boundary elements is obtained. On this basis, the maximum time increment for solving dynamic problems with viscoelastic artificial boundary elements can be determined.

Explicit Integration Algorithm of the Bounding Surface Model Based on Swell–Shrink Rules for Cyclic Behaviors of Clay

Integration algorithm is a key to ensure the better application of the dynamic constitutive model. As for the bounding surface model based on swell–shrink rules in this paper, an explicit integration algorithm based on sub-stepping and error control scheme has be described in detail. For being adaptable to the constitutive model, several modifications have been made. The modified explicit algorithm includes two procedures: the first procedure is the second-order forward modified Euler scheme with sub-stepping and error control; the second procedure is the stress correction. However, due to the shrink rule of the bounding surface, the second procedure is not needed at the unloading phase. Finally, several numerical simulations have been conducted for assessing the performance of the explicit algorithm, which demonstrates that the corresponding algorithm is stable and accurate, and can simulate the mechanical characteristics of the clay pretty well.

Theory and Implementation of a Two-Step Unconditionally Stable Explicit Integration Algorithm for Vibration Analysis of Structures

Time history analysis is becoming the routine process to quantify the response of the structure under dynamic loads. In this paper, a novel two-step unconditionally stable explicit integration algorithm, named Unconditional Stable Two-Step Explicit Displacement Method (USTEDM), is proposed for vibration analysis of structure. USTEDM is unconditionally stable, requires low memory, produces no overshoot, and is third order accurate. The accuracy and efficiency of USTEDM are presented and compared with other commonly used integration algorithms. The result shows that the proposed algorithm has superior performance and can be used efficiently in solving vibration response of civil engineering structure.