A second-order accurate single-step time integration method for nonlinear structural dynamics is developed. The method combines algorithmic dissipation of higher modes and conservation of linear and angular momentum and is composed of two phases. In the first phase, a solution point is computed by a basic integration scheme, the generalized-α method being adopted due to its higher level of high-frequency dissipation. In the second phase, a correction is hypothesized as a linear combination of the solution in the basic step and the gradient of vector components of the incremental linear and angular momentum. By solving a system composed of six linear equations, the searched for corrected solution in the time step is then provided. The novelty in the presented integration scheme lies in the way of imposing the conservation of linear and angular momentum. In fact, this imposition is carried out as a correction of the computed solution point in the time step and not through an enlarged system of equations of motion. To perform tests on plane and spatial motion of three-dimensional structural models, a small strains — finite rotations corotational formulation is also described.

中文翻译：

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一种非线性结构动力学的耗散动量守恒时间积分算法

提出了一种非线性结构动力学的二阶精确单步时间积分方法。该方法结合了更高模式的算法耗散和线性和角动量守恒，并由两个阶段组成。在第一阶段，通过基本积分方案计算解点，即广义-α由于其较高的高频耗散水平而被采用。在第二阶段，将修正假设为基本步骤中的解与增量线性和角动量的矢量分量梯度的线性组合。通过求解一个由六个线性方程组成的系统，然后提供在时间步中搜索到的校正解。所提出的积分方案的新颖之处在于强加线性和角动量守恒的方式。事实上，这种强制是作为时间步中计算的解点的校正来执行的，而不是通过运动方程组的扩大系统来执行的。为了对三维结构模型的平面和空间运动进行测试，还描述了小应变-有限旋转共旋转公式。