结 构 动 响 应 的 自 启 动 单 解 时 域 积 分 器 优 化

Time integration algorithms are widely used as efficient numerical techniques for analyzing dynamic responses of large-scale structures. Among various integrators，self-starting single-solve time integrators have attracted considerable attention due to their simplicity. Based on analytical techniques for computing the leading terms of amplitude error，phase error，and displacement local truncation error，the paper systematically optimizes three types of self-starting single-solve time integrators with identical second-order accuracy： implicit algorithms， fully explicit algorithms， and explicit algorithms with implicit treatment of velocity. For implicit algorithms， the optimized OSS21* method significantly improves overshooting tendency and high-frequency dissipation compared to the original scheme，demonstrating superior overall performance among the existing second-order self-starting single-solve implicit integrators. For explicit algorithms， the updating velocity scheme in solving equilibrium equations is optimized by minimizing the sum of squared leading terms of amplitude and phase errors，while four sets of optimal algorithmic parameters are determined based on displacement local truncation error analysis. The improved GSSI* algorithm exhibits smaller relative period errors at the same physical damping ratios，with this advantage becoming more pronounced as damping increases. Moreover，under equivalent dissipation levels，it achieves significantly better period accuracy than the original method. Numerical examples validate the theoretical analysis， confirming the optimized integrators’ advantages in accuracy， overshoot， and dissipation performance.