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本文根据文献〔1〕中的前两个定理,证明了Newmark法当且仅当2β≥γ≥1/2时对带有阻尼项的线性结构动力学方程组形成的积分格式是无条件稳定的,同时也完整地研究了此法的条件稳定问题。接着进一步讨论了包括弹塑性和非线性弹性情形在内的结构动力分析中的相应问题,指出文献〔1〕中的第三个定理也适用于非线性弹性情形;此外,对阶梯法应用于非线性弹性情形时间能发生的不稳定现象作了一定的分析,并介绍了一个减少不稳定性出现的可能性的方法。
According to the first two theorems in [1], this paper proves that Newmark method is unconditionally stable for the integral format formed by the linear structural dynamic equations with damping term if and only if 2β≥γ≥1/2. At the same time, the conditional stability of this method has also been thoroughly studied. Then we discuss the corresponding problems in structural dynamic analysis including elasto-plasticity and nonlinear elasticity, and point out that the third theorem in [1] also applies to nonlinear elasticity; The instability of the linear elasticity situation can be analyzed in a certain amount of time, and a method to reduce the possibility of instability is introduced.