求解结构动响应的两种有渐进消去特性的算法  

TWO L-STABLE ALGORITHMS FOR SOLVING STRUCTURAL DYNAMIC RESPONSES

作　　者：于开平[1] 李静[2] 杨利芳[1] 邹经湘[1] 

机构地区：[1]哈尔滨工业大学航天科学与力学系,哈尔滨150001 [2]中国航天科工集团二院二部,北京100088

出　　处：《工程力学》2004年第4期101-105,共5页Engineering Mechanics

基　　金：黑龙江省博士后基金项目;哈工大校基金资助项目(HIT.2002.02)

摘　　要：介绍了Rosenbrock方法用于结构动力响应求解步骤,提出了一个新的单步Houbolt直接积分类方法,给出了这两种算法的理论分析,理论分析结果表明这两种算法都是有二阶精度、无条件稳定的单步方法,而且两种方法都有很强的稳定性(即L-稳定)、良好的超调特性,Rosenbrock方法还有好的耗散特性和弥散特性,而且算法步骤还很容易用于非线性问题。最后,对推荐的两种算法通过仿真大系统的两自由度问题、弹性杆的冲击问题和弹簧摆的非线性问题进行了数值分析,验证了理论分析结果,数值分析结果表明所推荐的两种方法适合于刚性、非线性结构动力学问题的分析。The two L-stable algorithms are presented to solve the structural dynamics response. One is the Rosenbrock method and the other is a single-step Houbolt direct integral scheme. A finite difference analysis shows that both are capable of asymptotically annihilating the high-frequency modes and are two-order accurate, unconditionally stable and devoid of overshoot phenomenon. The comparison between the algorithms and the classical ones is made. The Rosenbrock method has a good property of dissipation and dispersion, and is easily implemented when it is used in solving nonlinear structural dynamic problems. The performance of the proposed algorithms are numerically validated by analyzing some examples including a simulated two degree-of-freedom system representing a large structure, elastic bar impact system and nonlinear spring pendulum system.

关 键 词：L-稳定 结构动力学 算法 超调 非线性 

分 类 号：O327[理学—一般力学与力学基础]