本文将牛顿迭代法的思想引入平均加速度法，对方程式以加速度项作为迭代变量进行内嵌一次牛顿迭代处理，推导出了一种新型的线性隐式数值积分方法。然后通过离散控制理论和根轨迹法分析了新算法在求解含非线性恢复力和非线性阻尼力的结构运动方程时维持稳定的条件，并利用一个单自由度剪切型结构，检验了新算法的非线性稳定性。最后通过数值模拟，考察了新算法对于非线性多自由度结构体系的适用性和可靠性。
Abstract
In this paper, the strategy of Newton iteration is introduced into the average acceleration method. A novel linear implicit numerical integration algorithm is derived by embedding once Newton iteration in the method with the acceleration term as the iteration variable. Then, according to discrete control theory and root locus method, the conditions for maintaining stability of the novel algorithm is derived when the novel algorithm is used to solve the structure with nonlinear restoring forces and nonlinear damping forces. Meanwhile, a single-degree-of-freedom shear- type structure is used to exam the stability of the novel algorithm in solving the problem with nonlinear restoring forces and nonlinear damping forces. Finally, the applicability and reliability of the novel algorithm in solving problems of multi-degree-of-freedom structures with nonlinear restoring forces and nonlinear damping forces is proved through numerical simulations.
关键词
非线性结构体系 /
平均加速度法 /
牛顿迭代法 /
动力响应分析
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Key words
nonlinear structures /
the average acceleration method /
Newton iteration method /
dynamic response /
analysis
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参考文献
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