关于Newmark-γ,β法机理的一种解释
首发时间:2010-01-07
摘要:在传统认识上,Newmark-β法和荷载分段插值法被认为是两种完全不同类型的动力数值分析方法。在本文中,研究了这两类方法之间的关系,通过数理推导建立起它们之间的联系。结果发现:Newmark平均常加速度法相当于各时间步距内荷载为二次函数分布模式,但在端点处荷载分布函数不连续,且同真实荷载值不重合;线性加速度法相当于各时间步距内荷载分布模式为三次曲线。这样就从本质上证明了Newmark-β法的机理,给出了另外一种解释,即Newmark-β法本质就是荷载分段插值类型的方法,只不过它没有采用线性插值的方式。
关键词: Newmark-β法 荷载分段插值法 数值机理
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An interpretation of Newmark beta methods in mechanism of numerical analysis
Abstract:In general, Newmark beta methods are considered to be a type of integration method for numerical dynamic analysis, so they are different from methods based on interpolation of excitation or so called piecewise exact method in the mechanism of numerical analysis. In this paper, two special cases of the Newmark beta methods, the constant average acceleration method and linear acceleration method, are selected and researched, and the distribution patterns of excitations over the time step are deduced based on the basic Newmark formulation. It is found that the constant average acceleration method is equivalent to the piecewise exact method that the distribution pattern of the excitation is assumed to be a quadratic function in each time step, and the linear acceleration method the excitation with the pattern of a cubic function. But for the constant average acceleration method, the assumed excitation function is not continuous in the initial point and end of discrete time interval, and do not coincide with the exist excitation of the structure. Thus, the Newmark beta methods are actually a type of methods based on interpolation of excitation, and their numerical mechanism may be explained in another way.
Keywords: Newmark beta methods piecewise exact method numerical mechanism
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