【摘要】 微分求积法具有数学概念简单、精度高和计算时间少等优点,是一种不断受到重视的数值方法。目前微分求积法在方法本身的研究已经相当充分和成熟,而应用方面的研究则大多集中在边值问题的求解,本文的研究集中在采用微分求积法求解动力学初值问题方面。先介绍了一种新近提出的逐步积分方法,该方法基于一种特殊的节点分布的微分求积法。然后通过理论分析与几种常用的时间积分方法进行了稳定性、精确性和计算量的比较。最后计算了一个双质点系在强迫力下的瞬态响应。比较结果表明新近提出的逐步积分方法具有无条件稳定、高精度和计算量少的优点。更多还原

【Abstract】 The differential quadradure(DQ) method is a distinct numerical solution technique with advantages of conceptual simplicity,high accuracy and relatively small computing effort.The method itself has been extensively studied and matured.In the aspect of applications,the DQ method has been usually applied to solve boundary value problems.In this thesis,the study was focused on solving initial value problems by using the DQ method.The newly proposed time integration algorithm,based on differential quadrature with a special type of grid points,was introduced first.Through theoretic analysis,the stability,accuracy and computing effort of the DQ based integration algorithm and other commonly used time integration schemes were compared.The transient response of a double-degree-of-freedom system under forced load was computed.The results by different integration schemes were compared each other.It is shown that the DQ based time integration method has the advantages of unconditional stability,high accuracy and relatively small computing effort.更多还原