基于非线性特征值解算的材料参数温度相关薄壁结构热屈曲分析方法

沈瑞博; 李建宇; 高强; 李广利

doi:10.21656/1000-0887.460027

基于非线性特征值解算的材料参数温度相关薄壁结构热屈曲分析方法

doi: 10.21656/1000-0887.460027

沈瑞博¹,
李建宇^1,2, ,,
高强²,
李广利³

1. 天津科技大学机械工程学院，天津 300457;
2. 大连理工大学工业装备结构分析优化与CAE软件全国重点实验室，辽宁大连 116023;
3. 中国科学院力学研究所高温气动国家重点实验室，北京 100190

基金项目:

工业装备结构分析优化与CAE软件全国重点实验室开放基金（GZ24131）

国家自然科学基金（12002347）

详细信息

作者简介:
沈瑞博（1998—），男，硕士生(E-mail: 1585807230@qq.com)；李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).

通讯作者:
李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).

中图分类号: O342
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出版历程
- 收稿日期: 2025-02-17
- 修回日期: 2026-03-31
- 网络出版日期: 2026-06-04
- 刊出日期: 2026-05-01

Thermal Buckling Analysis of Thin-Walled Structures With Temperature-Dependent Material Properties Based on Nonlinear Eigenvalue Solutions

1. College of Mechanical Engineering, Tianjin University of Science & Technology, Tianjin 300457, P.R. China;
2. State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R. China;
3. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, P.R. China

Funds:

The National Science Foundation of China(12002347)

摘要

摘要: 热屈曲是薄壁类结构在高温环境下常见的失稳现象，准确预测临界失稳温度是热屈曲分析的重要内容.高温环境下材料参数的温度相关性导致临界热屈曲分析呈现不可忽略的非线性特征，关于该问题的解算目前仍以精度和效率不高的试验误差类启发式算法为主.本文从非线性特征值问题的角度研究其高效解算方法.首先，基于热屈曲分析的力学原理，将材料参数温度相关的热屈曲分析表征为一个非线性特征值解算的问题.其次，给出了求解热屈曲分析非线性特征值问题的一种逐次线性化方法，该算法中采用自动微分技术计算迭代过程中所需的刚度矩阵和几何刚度矩阵的导数信息；与已有的迭代类算法相比，所提算法在不提高计算复杂度的基础上显著提高了算法效率.最后，具体针对非均匀温度场作用下的薄板结构，给出其非线性特征值热屈曲分析的有限元方程及逐次线性化特征值解算方法，并以数值算例验证了所提方法的有效性与准确性.
- 热屈曲 /
- 材料参数温度相关 /
- 非线性特征值 /
- 逐次线性化算法 /
- 薄板
Abstract: Thermal buckling is a common instability phenomenon in thin-walled structures under high-temperature environments. Accurately predicting the critical instability temperature makes an important issue for thermal buckling analysis. The temperature dependence of material parameters in high-temperature environments leads to non-negligible nonlinear characteristics in critical thermal buckling analysis. Currently, the solutions to this problem are mainly based on heuristic algorithms of experimental error types, which have low accuracy and efficiency. An efficient solution method was studied from the perspective of nonlinear eigenvalue problems. Firstly, based on the mechanical principles of thermal buckling analysis, the thermal buckling analysis with temperature-dependent material parameters was characterized as a problem of solving nonlinear eigenvalues. Secondly, a successive linearization method for solving the nonlinear eigenvalue problem in thermal buckling analysis was presented. In this algorithm, the automatic differentiation technique was used to calculate the derivative information of the stiffness matrix and geometric stiffness matrix required during the iterative process. Compared with existing iterative algorithms, the proposed algorithm significantly improves the algorithm efficiency without increasing the computational complexity. Finally, specifically for the thin plate structure under the action of a non-uniform temperature field, the finite element equations for its nonlinear eigenvalue thermal buckling analysis and the successive linearization eigenvalue solution method were given, and numerical examples were used to verify the effectiveness and accuracy of the proposed method.
- thermal buckling /
- temperature dependence of material parameters /
- nonlinear eigenvalue /
- successive linearized approximation algorithm /
- thin plate

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参考文献(27)

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基于非线性特征值解算的材料参数温度相关薄壁结构热屈曲分析方法

doi: 10.21656/1000-0887.460027

作者简介:
沈瑞博（1998—），男，硕士生(E-mail: 1585807230@qq.com)；李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).

通讯作者:
李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).

计量

Thermal Buckling Analysis of Thin-Walled Structures With Temperature-Dependent Material Properties Based on Nonlinear Eigenvalue Solutions

计量

目录

留言板

基于非线性特征值解算的材料参数温度相关薄壁结构热屈曲分析方法

doi: 10.21656/1000-0887.460027

作者简介: 沈瑞博（1998—），男，硕士生(E-mail: 1585807230@qq.com)；李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).

通讯作者: 李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).

计量

出版历程

Thermal Buckling Analysis of Thin-Walled Structures With Temperature-Dependent Material Properties Based on Nonlinear Eigenvalue Solutions

计量

出版历程

目录

作者简介:
沈瑞博（1998—），男，硕士生(E-mail: 1585807230@qq.com)；李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).

通讯作者:
李建宇（1978—），男，教授，博士(通信作者. E-mail: lijianyu@tust.edu.cn).