New Fourier expansion for thermal buckling analysis of rectangular thin plates with various edge restraints

For the first time, a modified two-dimensional Fourier series approach is proposed for new thermal buckling analysis of rectangular thin plates under various edge conditions. The solution form of plate deflection is considered to be in terms of a double Fourier Sine series (Navier-form solution) whose derivatives are determined via utilizing the Stoke’s transform technic. The present study exhibits the following significant merits: (a) the method adopted allows one to consider any possible combination of boundary conditions with no necessity to be satisfied in the Fourier series; (b) the given solution procedure is simple and straightforward since the complicated boundary value problem (BVP) of partial differential equation (PDE) can be changed into solving sets of linear algebra equations, which heavily decreases the complicated mathematical manipulations of plate thermal buckling problem; (c) all the results acquired converge rapidly because of using the sum function of series. Greeting agreements between the present analytical solutions with the numerical results provided by FEM testifies the accuracy of the approach proposed. The present results are believed to be severe as new benchmarks for validating other methods and providing better design for plate structures. The influences of the aspect ratio and boundary condition on the thermal buckling behaviors of plates are also investigated and discussed. Furthermore, it is capable to extend the present solution procedure to deal with problems of plates under more complex edge conditions by ways of utilizing other Fourier series.