应用数学和力学2026，Vol.47Issue(5)：550-559,10.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
Thermal Buckling Analysis of Thin-Walled Structures With Temperature-Dependent Material Properties Based on Nonlinear Eigenvalue Solutions
摘要
Abstract
Thermal buckling is a common instability phenomenon in thin-walled structures under high-tempera-ture environments.Accurately predicting the critical instability temperature makes an important issue for ther-mal 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 a-nalysis was presented.In this algorithm,the automatic differentiation technique was used to calculate the deriv-ative 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 effi-ciency 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 exam-ples were used to verify the effectiveness and accuracy of the proposed method.关键词
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Key words
thermal buckling/temperature dependence of material parameters/nonlinear eigenvalue/successive linearized approximation algorithm/thin plate分类
数理科学引用本文复制引用
沈瑞博,李建宇,高强,李广利..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[J].应用数学和力学,2026,47(5):550-559,10.基金项目
国家自然科学基金(12002347) （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) （GZ24131）
