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

(我刊编委高强来稿)

基金项目:

国家自然科学基金 12002347

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

详细信息

作者简介:
沈瑞博(1998—)，男，硕士生(E-mail: 1585807230@qq.com)

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
计量
- 文章访问数: 49
- HTML全文浏览量: 14
- PDF下载量: 25
- 被引次数: 0
出版历程
- 收稿日期: 2025-02-17
- 修回日期: 2026-03-31
- 刊出日期: 2026-05-01

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

SHEN Ruibo^1
,,
LI Jianyu^{1, 2
, ,},
GAO Qiang²,
LI Guangli³

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

(Contributed by GAO Qiang, Member of the Editorial Board of AMM)

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
edited-by

edited-by
注释:

1) (我刊编委高强来稿)

HTML全文

图 1 矩形薄板温度场

Figure 1. The temperature field of the rectangular thin plate

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图 2 矩形薄板网格划分

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. The rectangular thin plate meshing

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图 3 矩形薄板Riks方法温度-位移图

Figure 3. The temperature-displacement diagram of the rectangular thin plate with the Riks method

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图 4 矩形薄板Southwell方法得到临界屈曲温度图

Figure 4. The critical buckling temperature diagram of rectangular thin plates is obtained with the Southwell method

下载: 全尺寸图片幻灯片

图 5 不同厚度板的临界热屈曲温度计算结果

Figure 5. Calculation results of critical thermal buckling temperatures for plates with different thicknesses

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图 6 矩形薄板-本文方法与文献[9]方法的迭代误差比较

Figure 6. For the rectangular thin plate the comparison of iterative errors between the present and that of ref. [9]

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图 7 圆环薄板温度场

Figure 7. The ring plate temperature field

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图 8 圆环薄板网格划分

Figure 8. The ring plate meshing

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图 9 圆环薄板Riks方法温度-位移图

Figure 9. The temperature-displacement diagram of the circular plate with the Riks method

下载: 全尺寸图片幻灯片

图 10 圆环薄板Southwell方法得到临界屈曲温度图

Figure 10. The critical buckling temperature diagram obtained with the Southwell method

下载: 全尺寸图片幻灯片

图 11 不同厚度圆环薄板的临界热屈曲温度计算结果

Figure 11. Calculation results of critical thermal buckling temperature for circular plates with different thicknesses

下载: 全尺寸图片幻灯片

图 12 圆环薄板: 本文方法与文献[9]方法的迭代误差比较

Figure 12. For the circular thin plate the comparison of iterative errors between the present and that of ref. [9]

下载: 全尺寸图片幻灯片

表 1 矩形薄板临界屈曲温度计算结果对比

Table 1. The numerical results comparison of critical buckling temperatures for rectangular thin plates

thickness/m	result of this paper	result^[9]	Riks	linear buckling
0.12	101.553 1	101.798 7	100.782 1	139.181 7
0.22	280.657 1	280.783 2	271.112 4	460.744 9
0.32	489.356 5	490.118 4	499.882 7	952.125 6

下载: 导出CSV

表 2 圆环薄板临界热屈曲温度计算结果对比

Table 2. The numerical results comparison of critical thermal buckling temperatures for ring thin plates

thickness/mm	result of this paper	result^[9]	Riks	linear buckling
1	38.879 4	38.575 59	38.879 4	38.439 95
3	126.281 66	126.973 88	128.328 57	265.477 46
5	260.114 31	259.481 54	261.617 14	641.545 54

下载: 导出CSV

参考文献(27)

[1]	任青梅. 高超声速飞行器薄壁结构热屈曲行为研究进展[J]. 飞航导弹, 2018(7): 6-12. REN Qingmei. Research progress on thermal buckling behavior of thin-walled structures of hypersonic vehicles[J]. Aerodynamic Missile Journal, 2018(7): 6-12. (in Chinese)
[2]	厄尔·A桑顿. 新一代航空航天热结构与材料[M]. 黄启忠, 译. 北京: 航空工业出版社, 2019. THORNTON EARL A. Aerospace Thermal Structures and Materials for a New Era[M]. Translated by HUANG Qizhong. Beijing: Aviation Industry Press, 2019. (Chinese version))
[3]	李若愚, 王天宏. 薄板热力耦合的屈曲分析[J]. 应用数学和力学, 2020, 41(8): 877-886. doi: 10.21656/1000-0887.400308 LI Ruoyu, WANG Tianhong. Thermo-mechanical buckling analysis of thin plates[J]. Applied Mathematics and Mechanics, 2020, 41(8): 877-886. (in Chinese) doi: 10.21656/1000-0887.400308
[4]	龚雪蓓, 赵伟东, 郭冬梅. 横向非均匀温度场作用的FGM夹层圆板热屈曲分析[J]. 应用数学和力学, 2023, 44(4): 419-430. doi: 10.21656/1000-0887.430094 GONG Xuebei, ZHAO Weidong, GUO Dongmei. Thermal buckling analysis of FGM sandwich circular plates under transverse nonuniform temperature field actions[J]. Applied Mathematics and Mechanics, 2023, 44(4): 419-430. (in Chinese) doi: 10.21656/1000-0887.430094
[5]	REN Y, HUO R, ZHOU D. Thermo-mechanical buckling analysis of non-uniformly heated rectangular plates with temperature-dependent material properties[J]. Thin-Walled Structures, 2023, 186: 110653.
[6]	BIRMAN V. Thermal buckling and postbuckling of columns accounting for temperature effect on material properties[J]. Journal of Thermal Stresses, 2022, 45(12): 1043-1056. doi: 10.1080/01495739.2022.2118198
[7]	郭兆璞, 陈浩然. 复合材料层合板非线性热屈曲分析[J]. 大连理工大学学报, 1995, 35(4): 463-467. GUO Zhaopu, CHEN Haoran. Thermal buckling analysis o flaminated composite plates with temperature-dependent material properties[J]. Journal of Dalian University of Technology, 1995, 35(4): 463-467. (in Chinese)
[8]	邓可顺, 张亚辉. 考虑材料性质参数随温度变化的热屈曲试探解法[J]. 大连理工大学学报, 1999, 39(3): 358-362. DENG Keshun, ZHANG Yahui. Trial and error method of thermal buckling for complex structures[J]. Journal of Dalian University of Technology, 1999, 39(3): 358-362. (in Chinese)
[9]	WILLIAM L. Thermal and mechanical buckling analysis of hypersonic aircraft hat-stiffened panels with varying face sheet geometry and fiber orientation: 4770[R]. NASA Technical Memorandum, 1996.
[10]	HUANG H, RAO D. Thermal buckling of functionally graded cylindrical shells with temperature-dependent elastoplastic properties[J]. Continuum Mechanics and Thermodynamics, 2020, 32(5): 1403-1415. doi: 10.1007/s00161-019-00854-3
[11]	JOUEID N, ZGHAL S, CHRIGUI M, et al. Thermoelastic buckling analysis of plates and shells of temperature and porosity dependent functionally graded materials[J]. Mechanics of Time-Dependent Materials, 2024, 28(3): 817-859. doi: 10.1007/s11043-023-09644-6
[12]	TRABELSI S, FRIKHA A, ZGHAL S, et al. A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells[J]. Engineering Structures, 2019, 178: 444-459. doi: 10.1016/j.engstruct.2018.10.047
[13]	HAJLAOUI A, CHEBBI E, DAMMAK F. Three-dimensional thermal buckling analysis of functionally graded material structures using a modified FSDT-based solid-shell element[J]. International Journal of Pressure Vessels and Piping, 2021, 194: 104547.
[14]	AVEY M, FANTUZZI N, SOFIYEV A. On the solution of thermal buckling problem of moderately thick laminated conical shells containing carbon nanotube originating layers[J]. Materials, 2022, 15(21): 7427. doi: 10.3390/ma15217427
[15]	KAREEM M G, AL-RAHEEM S K, SADIQ S E, et al. Review of research on the vibration and buckling of functionally graded spherical shells[J]. International Journal of Science and Research Archive, 2024, 13(2): 2170-2186. doi: 10.30574/ijsra.2024.13.2.2327
[16]	ALJADANI M H. The porosity effect on the buckling analysis of functionally graded plates under thermal environment using a Quasi-3D theory[J]. Scientific Reports, 2024, 14: 30216.
[17]	GUO H, Z · UR K K, OUYANG X. New insights into the nonlinear stability of nanocomposite cylindrical panels under aero-thermal loads[J]. Composite Structures, 2023, 303: 116231.
[18]	李畅, 万志强, 王晓喆, 等. 热载荷环境下金属-陶瓷功能梯度板屈曲特性[J]. 北京航空航天大学学报, 2025, 51(12): 4196-4206. LI Chang, WAN Zhiqiang, WANG Xiaozhe, et al. Buckling characteristics of metal-ceramic functionally graded plates in thermal loading environments[J]. Journal of Beijing University of Aeronautics and Astronautics, 2025, 51(12): 4196-4206. (in Chinese)
[19]	WANG Z, HAN Q, NASH D H, et al. Thermal buckling of cylindrical shell with temperature-dependent material properties: conventional theoretical solution and new numerical method[J]. Mechanics Research Communications, 2018, 92: 74-80.
[20]	CHAKRABORTY S, DEY T. Non-linear stability analysis of CNT reinforced composite cylindrical shell panel subjected to thermomechanical loading[J]. Composite Structures, 2021, 255: 112995. doi: 10.1016/j.compstruct.2020.112995
[21]	杨坤. 高压捕获翼板的热屈曲分析研究[D]. 天津: 天津科技大学, 2023. YANG Kun. Research on thermal buckling analysis of high-pressure capturing wing plate[D]. Tianjin: Tianjin University of Science & Technology, 2023. (in Chinese)
[22]	TIMOSHENKO S P, GERE J M. Theory of Elastic Stability[M]. Courier Corporation, 2012.
[23]	GVTTEL S, TISSEUR F. The nonlinear eigenvalue problem[J]. Acta Numerica, 2017, 26: 1-94.
[24]	陈小平. 非线性特征值问题的数值方法及其应用[D]. 南京: 南京航空航天大学, 2016. CHEN Xiaoping. Numerical methods for nonlinear eigenvalue problems and their applications[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016. (in Chinese)
[25]	TANG Z, SAAD Y. A rational-Chebyshev projection method for nonlinear eigenvalue problems[J]. Numerical Linear Algebra With Applications, 2024, 31(6): e2563.
[26]	BRENNAN M C, EMBREE M, GUGERCIN S. Contour integral methods for nonlinear eigenvalue problems: a systems theoretic approach[J]. SIAM Review, 2023, 65(2): 439-470.
[27]	BAYDINA G, PEARLMUTTER B A, RADUL A A, et al. Automatic differentiation in machine learning: a survey[PP/OL]. (2018-02-05)[2026-03-31]. https://arxiv.org/abs/1502.05767.