An eigen-based theory for structure-dependent integration methods is constructed and it can provide the fundamental basis for the successful development of this type of integration methods. It is proved that a structure-dependent integration method can simultaneously combine unconditional stability and explicit formulation since it is proposed to accurately integrate low-frequency modes while no instability is guaranteed for high-frequency modes. In general, it is promising for solving inertial problems, where the total response is dominated by low-frequency modes. In addition, it can be explicitly and implicitly implemented for time integration although an explicit implementation is of practical significance since it can save many computational efforts due to the combination of unconditional stability and explicit formulation. A typical procedure to develop structure-dependent integration methods is constructed. In general, a coupled equation of motion for a multiple degree of freedom system can be decomposed into a set of uncoupled modal equations of motion by means of an eigen-decomposition technique. Next, an eigen-dependent integration method is developed to solve each modal equation of motion. Consequently, all the eigen-dependent integration methods are combined to form a structure-dependent integration method by employing a reverse procedure of the eigen-decomposition technique.

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非线性动态分析的结构相关积分方法的基于特征的理论

构建了基于特征的结构依赖积分方法理论，为此类积分方法的成功发展提供了基础。证明了结构相关的积分方法可以同时结合无条件稳定性和显式公式，因为它提出了精确积分低频模式，同时保证高频模式不不稳定。一般来说，它很有希望解决惯性问题，其中总响应由低频模式主导。此外，它可以显式和隐式地实现时间积分，尽管显式实现具有实际意义，因为由于无条件稳定性和显式公式的结合，它可以节省许多计算工作。构建了开发依赖于结构的集成方法的典型过程。一般来说，多自由度系统的耦合运动方程可以通过特征分解技术分解为一组非耦合模态运动方程。接下来，开发了一种与特征相关的积分方法来求解每个模态运动方程。因此，通过采用本征分解技术的逆过程，将所有与本征相关的积分方法结合起来形成一种与结构相关的积分方法。开发了一种与特征相关的积分方法来求解每个模态运动方程。因此，通过采用本征分解技术的逆过程，将所有与本征相关的积分方法结合起来形成一种与结构相关的积分方法。开发了一种与特征相关的积分方法来求解每个模态运动方程。因此，通过采用本征分解技术的逆过程，将所有与本征相关的积分方法结合起来形成一种与结构相关的积分方法。