刚架弹性屈曲问题基于改进傅里叶级数法的研究

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中图分类号：0343.9 文献标志码：A 文章编号：1000-4939（2025）03-0590-08

Abstract：To establish the general solution method for frame buckling problems with diffrent elastic boundaryconditions，buckling load of rigid frame with elastic brace is studied.First，thedisplacement function expressionof the frame is established based on the Improved Fourier Series Method，and then the buckling characteristic equation is obtained by using the minimum potential energy principle，and the buckling load of the frame is obtained by solving the matrix eigenvalue.Linear springs and rotational springs are set up at the support and the joint of beam and column.Diferent boundary condition and connection condition in the frame is simulated by adjusting the stifness value of spring.Through numerical analysis，the buckling loadsof rigid frames with and without lateral displacement under arbitrary elastic boundary are studied.The obtained results are compared with the analytical solutions to verify the ffectiveness of the proposed method and the generality for different boundary conditions.Then the buckling mode of rigid frames is given.The proposed Improved Fourier Series Method can provide effective preliminary assessment for the buckling of rigid frame with different elastic boundary conditions.

Key words：the Improved Fourier Series Method； rigid frame；principle of minimum potential energy buckling load

随着工程技术的发展，刚架作为一种基本结构被广泛应用于建筑等结构[1]，其稳定性问题一直是工程领域中学者所关注的重要课题之一。（剩余10997字）