一种基于离散控制理论的无条件稳定显式算法

基于离散控制理论，结合CR法和RST法提出一种无条件稳定的动力学显式新算法。以算法精度和稳定性为条件，通过离散传递函数推导参数表达式和极点，使得新算法可满足零振幅衰减率和零周期延长率。算法参数α和γ作为传递格式选择参数，当α和γ分别取1时，新算法对应CR法和RST法的位移速度表达式。对新算法的精度和稳定性理论分析表明:新算法可满足无振幅衰减和周期延长，且对于线性系统和非线性刚度软化系统为无条件稳定，对非线性刚度硬化系统为条件稳定，并给出了非线性刚度硬化系统的稳定性范围。算例分析验证了新算法的精度和稳定性，证明提出的新算法是可靠有效的。

An unconditionally stable explicit algorithm based on discrete control theory

Based on discrete control theory, combined with CR method and RST method, an unconditionally stable dynamic explicit algorithm was proposed. Based on the characteristics of the algorithm, the parameter expressions and poles are derived through discrete transfer functions. The new algorithm has zero amplitude decay and higher accuracy. When the algorithm parameters α and γ are equal to 1, the new algorithm corresponds to the displacement velocity expression of the CR method and RST method. Theoretical analysis on the accuracy and stability of the new algorithm showed that the new algorithm can meet the amplitude-free attenuation and period extension, and was unconditionally stable for linear systems and nonlinear stiffness softening systems, and conditionally stable for nonlinear stiffness hardening systems. Stability range of nonlinear stiffness hardening system was given. The example analysis verified the accuracy and stability of the new algorithm, and proved that the proposed new algorithm is reliable and effective.