Objectives  A rectangular plate buckling study is of great theoretical and practical importance. To study the axial compression buckling behavior of the rectangular plate structure commonly used in engineering under arbitrary elastic boundary conditions, we present a method for calculating buckling loads caused by elastic instability based on the minimum potential principle.

  Methods  Rotating restrained springs and lateral restrained springs are respectively arranged on the four boundaries of the plate model. The geometric expression of the displacement function is established based on the improved Fourier series method（IFSM）. The derivative function of the displacement function on the plate boundaries may have discontinuous issues, which can be solved by introducing auxiliary functions on the basis of the classical Fourier series. The potential energy function of the rectangular plate system is established, and by using the minimum potential energy method, the linear equations of the unknown Fourier coefficient are obtained, then the buckling characteristic parameters such as the critical load of the rectangular plate are solved.

  Results  The reasonable values of spring stiffness under different boundary conditions are given, and the obtained results are consistent with the exact solution and finite element software. The method is proved to be correct and convergent.

  Conclusions  The contents of this paper have a certain reference value for the related structural analysis of ships.