首页|单步无条件稳定显式结构动力学算法

单步无条件稳定显式结构动力学算法

扫码查看
原文链接
  • 万方数据
  • 维普
在结构动力学分析中,数值积分方法通常被用来高效和准确地求解复杂结构系统在动态负载下的响应.基于量纲分析的原理,提出一种求解结构动力学问题的单步无条件稳定显式算法.首先对所构造的关于位移和速度的函数关系式进行无量纲化处理,然后通过算法精度要求、无条件稳定条件和数值阻尼可控条件确定了其最终递推格式,并根据算法最终递推格式分析得出算法耗散与弥散特性、超调和自启动特性和多自由度系统计算步骤,最后通过数值算例验证了算法的收敛精度、可控数值阻尼和计算效率优势.研究结果表明:对于线性和非线性系统,该算法都兼具显式算法的非迭代特性和隐式算法的无条件稳定特性;该算法能实现真正意义上的自启动并且在速度和位移上均无超调;该算法的数值阻尼由单自由参数控制,数值耗散和弥散对系统低模态响应的影响可以忽略不计,与具有代表性的非迭代显式算法KR-α法相比,该算法在引入数值阻尼滤除虚假高频模态的同时更真实地保留了低阶振型的贡献,从而表现出更好的计算精度;该算法在求解非线性结构动力学问题时相较于常用隐式算法有着显著的计算效率优势,并略优于两求解器非迭代显式算法KR-α法.研究结果很有希望成为求解非线性结构动力学问题的最新且更加有效的显式算法.
A single-step unconditionally stable explicit structural dynamics algorithm
In structural dynamics analysis,numerical integration methods are usually used to efficiently and accurately solve the response of complex structural systems under dynamic loads.Based on the principle of dimensional analysis,a single-step unconditionally stable explicit algorithm for solving structural dynamics problems was proposed.Firstly,the dimensionless processing of the constructed functional relationship between displacement and velocity was carried out.Then,the final recursive format of the algorithm was determined by the accuracy requirements,unconditional stability conditions and numerical damping controllable conditions.According to the final recursive format of the algorithm,the dissipation and dispersion characteristics,overshoot and self-starting characteristics of the algorithm and the calculation steps of the multi-degree-of-freedom system were obtained.Finally,the convergence accuracy,controllable numerical damping and computational efficiency advantages of the algorithm were verified by some examples.The results show that for linear and nonlinear systems,the algorithm has both the non-iterative characteristics of the explicit algorithm and the unconditional stability of the implicit algorithm.The algorithm can realize self-starting in the true sense and has no overshoot in velocity and displacement.The numerical damping of the algorithm is controlled by a single free parameter,and the influence of numerical dissipation and dispersion on the low-mode response of the system can be neglected.Compared with the representative non-iterative explicit KR-α algorithm,the algorithm introduces numerical damping to filter out spurious high-frequency modes while retaining the contribution of low-order modes more realistically,thus showing better calculation accuracy.The algorithm has computational efficiency advantages over the commonly used implicit algorithms in solving nonlinear structural dynamics problems,and is slightly better than the two-solver non-iterative explicit KR-α algorithm.The research results are expected to become the latest and more effective explicit algorithm for solving nonlinear structural dynamics problems.

explicit algorithmnoniterative algorithmunconditional stabilitycontrollable numerical dampingstructural dynamic calculation

李常青、李正藩、蒋丽忠

展开 >

中南大学 土木工程学院,湖南 长沙 410075

高速铁路建造技术国家工程研究中心,湖南 长沙 410075

显式算法 非迭代算法 无条件稳定 可控数值阻尼 结构动力计算

国家自然科学基金中国中铁股份有限公司科技研发计划国家重点研发计划国家重点研发计划

U19342072022-重大-172022YFB23026032022YFC3004304

2024

10.19713/j.cnki.43-1423/u.T20230761

铁道科学与工程学报
中南大学 中国铁道学会

铁道科学与工程学报

CSTPCD北大核心EI
影响因子：0.837
ISSN：1672-7029
年,卷(期)：2024.21(3)
  • 22