子区间法的稳定性和精度
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摘要
子区间法在研究结构动力响应中优势明显,但尚需解决稳定性和精度等问题.文中分析了单步和两步子区间法递推格式的条件稳定性和精度,探讨了其无条件稳定递推格式的构造.在条件稳定区间,精度分析表明,单步和两步子区间法递推格式无周期延长和振幅衰减;对于无条件稳定的递推格式,其计算阻尼很大,无法满足计算精度的要求.
Subinterval method possesses obvious superiority over structural dynamic response analysis,yet its stability and accuracy have not been well solved.This paper analyzes the conditional stability and accuracy analysis of single- and two-step subinterval methods,and discusses the unconditional stable recurrence algorithms.In conditional stable interval,the accuracy analysis shows that there are no period delay and amplitude attenuation in recurrence algorithms of single- and two-step subinterval method,while unconditional stable recurrence algorithms can't satisfy the requirement on calculating accuracy because of its high computational damping.
Subinterval method possesses obvious superiority over structural dynamic response analysis,yet its stability and accuracy have not been well solved.This paper analyzes the conditional stability and accuracy analysis of single- and two-step subinterval methods,and discusses the unconditional stable recurrence algorithms.In conditional stable interval,the accuracy analysis shows that there are no period delay and amplitude attenuation in recurrence algorithms of single- and two-step subinterval method,while unconditional stable recurrence algorithms can't satisfy the requirement on calculating accuracy because of its high computational damping.
引文
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[2] 曹文衔,丁学成.动力分析的混合元子区间法[J].振动工程学报,1993,6(1):73—78.CaoWenxian,DingXuecheng.Themixedelementsubintervalmethodfordynamicanalysis[J].JournalofVibrationEngineering,1993,6(1):73—78.
[3] 巴特KJ,威尔逊EL.有限元分析中的数值方法[M].北京:科学出版社,1985.BatheKJ,WilsonEL.NumericalMethodsinFiniteElementAnalysis[M].Beijing:SciencePress,1985.
[4] 张汝清,殷学纲,董 明.计算结构动力学[M].重庆:重庆大学出版社,1987.ZhangRuqing,YinXuegang,DongMing.ComputationalStructuralDynamics[M].Chongqing:ChongqingUniversityPress,1987.
[5] 石钟慈.样条有限元[J].计算数学,1979(1):50—72.ShiZhongci.Onsplinefiniteelementmethod[J].MathematicaNumericaSinica,1979(1):50—72.
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