Volume 42 Issue 12
Dec.  2021
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LU Jianwei, BAO Siyuan, SHEN Feng. Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1229-1237. doi: 10.21656/1000-0887.410373
 Citation: LU Jianwei, BAO Siyuan, SHEN Feng. Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1229-1237.

# Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method

##### doi: 10.21656/1000-0887.410373
• Accepted Date: 2021-07-31
• Rev Recd Date: 2021-07-30
• Available Online: 2021-11-25
• Publish Date: 2021-12-01
• The elastic buckling of stepped columns with variable cross sections was studied. Firstly, based on the improved Fourier series method, the displacement function of the column was established in the local coordinate system, then the linear equations for buckling loads were obtained with the constrained variational principle of potential energy. The problem was transformed into a matrix eigenvalue problem and the buckling load was obtained from solution of the matrix eigenvalues. Finally, the parameter values in the method were discussed through numerical examples, and the obtained results were compared with the finite element results and previous literature results so as to verify the accuracy of the method. In the presented model the translational and rotational springs were arranged at the 2 ends and the setback cross sections. The method can determine the buckling loads of stepped columns with various elastic boundary conditions accurately in engineering design.

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