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

SHEN Ruibo; LI Jianyu; GAO Qiang; LI Guangli

doi:10.21656/1000-0887.460027

Volume 47 Issue 5

May 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(5): 550-559

SHEN Ruibo, LI Jianyu, GAO Qiang, LI Guangli. Thermal Buckling Analysis of Thin-Walled Structures With Temperature-Dependent Material Properties Based on Nonlinear Eigenvalue Solutions[J]. Applied Mathematics and Mechanics, 2026, 47(5): 550-559. doi: 10.21656/1000-0887.460027

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

doi: 10.21656/1000-0887.460027

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

Received Date: 2025-02-17
Rev Recd Date: 2026-03-31
Publish Date: 2026-05-01

Abstract

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

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

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References(27)

References

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