| 引用本文: | 傅博,张付泰,张清凯,陈瑾.一种具有可控数值阻尼的无条件稳定半显式积分算法[J].哈尔滨工业大学学报,2025,57(2):113.DOI:10.11918/202311063 |
| FU Bo,ZHANG Futai,ZHANG Qingkai,CHEN Jin.An unconditionally stable semi-explicit integration algorithm with controllable numerical damping[J].Journal of Harbin Institute of Technology,2025,57(2):113.DOI:10.11918/202311063 |
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| 摘要: |
| 结构模型经过有限元方法空间离散化处理之后,可能引入虚假的高频分量,这部分高频分量会对结构的动力响应求解带来不利影响。为此,需要引入算法的数值阻尼有效地抑制这部分虚假的高频分量。使用半显式算法格式,通过匹配隐式ρ∞-Bathe算法放大矩阵的特征方程系数,提出一种具有可控数值阻尼的无条件稳定半显式积分算法,记为NSE(New Semi-Explicit)-ρ∞算法,新算法通过两个自由参数ρ∞和γ控制算法的数值阻尼,并且无需对结构运动方程进行加权处理。对新算法的稳定性、精度、周期延长和振幅衰减等数值特性进行分析,结果表明,新算法对于线弹性体系和非线性刚度软化体系均为无条件稳定。通过具有代表性的数值算例,将新算法与两种具有可控数值阻尼的无条件稳定显式积分算法进行对比,证明新算法能够更加有效地抑制虚假高频分量。 |
| 关键词: 积分算法 显式 稳定 数值阻尼 结构动力学 |
| DOI：10.11918/202311063 |
| 分类号:TU311.3 |
| 文献标识码:A |
| 基金项目:国家自然科学基金(8,2,52478124)；陕西省高校科协青年人才托举计划(20230406)；长安大学中央高校基本科研业务费专项资金(300102283201);长安大学青年学者学科交叉团队建设项目(300104240923) |
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| An unconditionally stable semi-explicit integration algorithm with controllable numerical damping |
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FU Bo,ZHANG Futai,ZHANG Qingkai,CHEN Jin
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(School of Civil Engineering,Chang′an University, Xi′an 710061, China)
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| Abstract: |
| After the structural model is discretized by the finite element method, it may introduce false high-frequency components that can adversely affect the structural dynamic response of the structure. Therefore, it is necessary to introduce numerical damping into the integration algorithm to effectively suppress these false high-frequency componments. Based on a semi-explicit integration formulation, this paper proposes an unconditionally stable semi-explicit integration algorithm with controllable numerical damping by matching the characteristic equation coefficients of the amplification matrix of the implicit ρ∞-Bathe algorithm. The new semi-explicit (NSE)-ρ∞ algorithm controls the numerical damping of the integration algorithm by two free coefficients ρ∞ and γ, and does not require weighted equation of motion. The numerical characteristics of the new algorithm, such as stability, accuracy, period elongation and amplitude decay, are analyzed. It is found that the new algorithm is unconditionally stable for both linear elastic and nonlinear stiffness softening systems. Through representative numerical examples, the new algorithm is compared with two other unconditionally stable explicit integration algorithms with controllable numerical damping. The analytical results demonstrate that the new algorithm is more effective in suppressing the spurious high-frequency components. |
| Key words: integration algorithm explicit stability numerical damping structural dynamics |
