We revisit some existing time-stepping schemes for structural dynamics with the algorithmic dissipation that fall either into the class of generalized-$\alpha$ methods or into the class of energy-decaying (and momentum-conserving) methods. Some of the considered schemes are designed for the second-order and some for the first-order form of the differential equations of motion. We perform a comparison (for linear dynamics) of their accuracy, dissipation, dispersion, as well as of the overshoot. In order to study how these features extend to nonlinear dynamics, we choose numerical tests on shell-like examples. Shell models are a difficult check for dynamic schemes because numerically stiff equations need to be solved as an effect of a large difference between the bending (and shear) and the membrane deformation modes. For the considered schemes we illustrate their ability to decay/dissipate energy, their ability to fully/approximately conserve the angular momentum, and nonlinear order of accuracy by error indicators.

我们用算法耗散重新归纳了一些现有的结构动力学时步方案，这些耗时都属于广义-$\alpha$ methods or into the class of energy-decaying (and momentum-conserving) methods. Some of the considered schemes are designed for the second-order and some for the first-order form of the differential equations of motion. We perform a comparison (for linear dynamics) of their accuracy, dissipation, dispersion, as well as of the overshoot. In order to study how these features extend to nonlinear dynamics, we choose numerical tests on shell-like examples. Shell models are a difficult check for dynamic schemes because numerically stiff equations need to be solved as an effect of a large difference between the bending (and shear) and the membrane deformation modes. For the considered schemes we illustrate their ability to decay/dissipate energy, their ability to fully/approximately conserve the angular momentum, and nonlinear order of accuracy by error indicators.