一种无条件稳定的结构动力学显式算法

发布时间：2018-07-02 22:11

  本文选题：结构动力学显式算法 + 离散控制理论　； 参考：《力学学报》2015年02期

【摘要】：利用离散控制理论,针对结构动力学方程时间积分提出了一种新的无条件稳定的显式算法.新算法采用CR算法的速度和位移递推格式,同时利用Z变换获得算法对应的传递函数,进而根据极点条件推导了递推格式系数的具体表达式.然后,在其系数中引入了一个控制周期延长率的变量s,从而调节新算法的精度.理论分析表明无条件稳定显式新算法具有二阶精度、零振幅衰减率、无超调和自起步特性,且周期延长率可以用变量s控制,而CR算法只是本文新算法的特例.最后,确定了非线性刚度硬化系统的稳定性界限,并给出了使新算法精度达到较高的变量s的区间.算例分析表明,在此变量区间内取值时,新算法的精度要优于纽马克常平均加速度算法和CR算法.
[Abstract]:Based on the discrete control theory, a new unconditionally stable explicit algorithm is proposed for the time integral of structural dynamic equations. The new algorithm uses the CR algorithm's velocity and displacement recursion scheme and the Z transform to obtain the corresponding transfer function, and then derives the concrete expression of the recursive format coefficient according to the pole condition. In its coefficient, a variable s that controls the extension rate of the control period is introduced to adjust the accuracy of the new algorithm. The theoretical analysis shows that the unconditional stable explicit algorithm has two order precision, zero amplitude attenuation rate, no super harmonic self starting characteristic, and the period extension rate can be controlled by variable s, and the CR algorithm is only a special case of the new algorithm in this paper. Finally, the new algorithm is a special case of the new algorithm. The stability limit of the nonlinear stiffness hardening system is determined and the interval of the new algorithm with a high variable s is given. An example analysis shows that the precision of the new algorithm is better than the Newmark constant average acceleration algorithm and the CR algorithm when the value of the variable is taken in the interval.
【作者单位】： 大连理工大学工程力学系工业装备结构分析国家重点实验室;
【基金】：国家自然科学基金(51478086,11332004) 陕西省科技统筹创新工程重点实验室基金(2013SZS02-K02)资助项目~~
【分类号】：TU311.3
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本文编号：2091071