Rosenbrock实时积分方法的精度和稳定性分析及其在结构动力学上的应用

Stability and accuracy analysis of Rosenbrock real-time algorithm for structural dynamic problems

Rosenbrock法以其在稳定性和精度方面的优势得到了广泛的应用,但Rosenbrock法大多局限于一阶微分方程的求解,在结构动力学上的应用相对较少。本文针对其在结构动力学问题上的应用,对2级Rosenbrock实时积分方法的精度和稳定性进行了系统地分析。结果表明:该方法对于满足Lipschitz条件的非线性问题,能保持二阶精度;在求解线性无阻尼问题以及带有摆非线性问题时,该方法具有能量衰减的特性;与平均加速度法相比,该方法在求解Bouc-Wen模型的非线性问题时表现出更好的稳定性。本文为采用Rosenbrock法解决复杂的结构动力学问题提供了更有利的理论依据。

Rosenbrock integration method is used extensively in the light of its priorities on stability and accuracy.Nevertheless,its application is mainly limited for solving first order ordinary differential equations while rarely for structural dynamic problems.In respect of its application to structural dynamic problems,this paper rationally studies a 2-stage Rosenbrock method in terms of stability and accuracy.The results obtained indicate that the integrator is second-order accuracy even for nonlinear problems which satisfy the Lipschitz condition;the integrator exhibits energy-decay property for undamped linear problems and nonlinear problems with a pendulum;for nonlinear problems with the Bouc-Wen model,the integrator possesses favorable stability.The theoretical analyses and numerical simulations,on the one hand,efficiently demonstrate the availability of the integrator to complicated structural dynamic problems,on the other hand,provide favorable approaches to investigate performances of other monolithic integrators.