| 陈安全,吴俊力,伏梨莹,彭涛.非线性分析中基于节点位移的正交迭代策略[J].计算力学学报,2026,43(2):236~243 |
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| 非线性分析中基于节点位移的正交迭代策略 |
| Orthogonal iteration strategy based on node displacement in nonlinear analysis |
| 投稿时间：2025-04-02 修订日期：2025-06-02 |
| DOI：10.7511/jslx20250402002 |
| 中文关键词: 非线性分析 增量-迭代法 正交迭代 N+1维空间理论 平衡路径追踪技术 |
| 英文关键词:nonlinear analysis increment-iteration method orthogonal iteration N+1 dimensional space theory equilibrium path-following techniques |
| 基金项目:国家自然科学基金(52078082);内江市基础研究与应用基础研究(NJJH202316);内江师范学院科研资助项目(2023ZD03);内江师范学院大学生创新创业训练计划(X2024077)资助项目. |
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| 中文摘要: |
| 追踪结构非线性屈曲荷载及后屈曲路径常采用增量-迭代方法,但现有的方法对初始参数的设置很敏感,在较大时可能导致数值发散。为增大初始参数的设置范围及数值稳定性,基于增量-迭代的N+1维空间理论,建立了荷载增量因子统一表达形式,同时基于结构全部和部分节点的平动自由度及转动自由度,开发了6种基于节点位移的正交迭代方案用于结构非线性路径追踪。在设置统一初始参数情况下,通过典型数值案例将建立的方案与以往常用的路径追踪技术进行比较,结果表明基于结构全部或部分节点位移的正交迭代策略在高度复杂的结构非线性行为场景中能以更大的增量步长保持数值稳定,具有很好的求解效率,可供实际结构分析选用。 |
| 英文摘要: |
| The incremental-iterative method is commonly employed to track the nonlinear buckling load and post-buckling path of a structure.However,existing methods exhibit significant sensitivity to the initial parameter settings,which may result in numerical divergence when these parameters are improperly specified.To enhance the setting range and numerical stability of the initial parameters in path-following technique,a unified expression for the load increment factor was formulated based on the N+1 dimensional space theory of increment-iteration.Additionally,six orthogonal iterative schemes were developed for nonlinear equilibrium path-following by utilizing the translational and rotational degrees of freedom of all or selected structural nodes.Under unified initial parameter settings,the proposed scheme was compared with conventional path-following techniques using typical numerical examples.The results indicate that the orthogonal iterative strategy based on the displacements of all or selected structural nodes can maintain numerical stability with larger step sizes in highly complex nonlinear scenarios,demonstrating excellent solution efficiency.This approach is thus suitable for practical structural analysis. |
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