薄壳动力分析的三维半显式迭代算法

Three dimensional semi explicit iteration algorithm for dynamic analysis of thin shells

利用三维变分差分方法研究薄壳的动力分析。针对显式迭代格式最大稳定时间步长过小，而隐式迭代格式计算量大且精度不足这一问题，构造了一种半显式迭代格式（即关于厚度方向隐式、而关于其余两个方向显式），它的最大稳定时间步长较显式迭代格式有很大的提高，而计算量并未显著增加。算例的数值结果表明，这种半显式迭代格式具有较高的精度，它的时间步长满足计算薄壳波动问题的要求。

The three dimensional variational difference method was applied to dynamic analysis of thin shells. By explicit schemes, the maximum stability time step is too small and by implicit schemes, the precision is not good because of the computer time. Present paper constructed an effectual semi explicit scheme (i.e. it is implicitial in depth direction and explicitial in other two directions), its maximum stability time step is bigger than that explicit scheme and the computer time does not increase. By examples shown, this semi explicit scheme has the high precision and step satisfies the requirement of analysis of the thin shell problems.