关于动力分析精细积分算法精度的讨论

对动力问题分析的精细积分算法的精度问题进行深入研究，并在此基础上提出对原有的算法的改进策略，改进后的算法可以较好地克服算法精度对积分时间步长的依赖性问题。

DISCUSSION ON THE ACCURACY OF PRECISE INTEGRATION METHOD IN DYNAMIC ANALYSIS

It is well known that analysis of transient dynamic problem is very important in engineering practice. Due to the fact that it will be very difficult to find the analytical solution for a complex engineering problem, numerical methods are widely adopted for the solution of the general problems. Among the existing methods, the finite element method is widely used for its good applicability. To solve the time domain problem with the finite element method, direct time integration method is the most popular one and has been widely adopted in numerical simulation. However, it has been observed that with the time integration method the numerical results sometimes will face large errors or strong oscillation behaviour due to the numerical discretization in time domain. In all the existing time integration methods, Zhong ^ 1] proposed a very special explicit integration scheme, i.e. precise integration method for structural dynamic analysis. The method can not only give precise numerical results, which are almost equal to the results of the exact solution at the integration point, but also persists some advantages such as unconditionally stable, zero-amplitude rate of decay, zero-period specific elongation and non-overstep in the time integration process. However, a disadvantage problem is still left in the method, because the accuracy of the final results will generally depend on the selection of parameter N , which is proposed as a constant, i.e. N=20 , in the original method. In this paper, from the inverse accuracy analysis of the method, it will be observed that the value of N will control the accuracy of the method. It can also be found that the selection of a fixed value of N is not reasonable for implementation of the method. In this paper an improved precise integration algorithm is proposed and applied for the analysis of transient dynamic problems. It can be found that the accuracy of the new improved precise integration method will no longer be controlled by the value of the time step in dynamic integration process, and the new method has an adaptive behaviour.