Exact stress functions implementation in stability analysis of plates with different boundary conditions under uniaxial and biaxial compression

• Analytical solutions for buckling of plates with mixed boundary conditions are given.
• Main contribution is exact elasticity solutions for in-plane stress distributions.
• High accuracy level is proven by comparison with FEM results obtained by ANSYS.
• General program for the stability analysis is in the building process.
• The program will provide an analytical approach to the complex stability problems.

Analytical approach used for critical load determination is based on Ritz energy technique in which two factors are crucial for the accuracy of results. First factor is deflection function. Herein, double Fourier series are used to represent buckled shape of the plates under arbitrary external loads. The second and the most important factor is adoption of adequate realistic stress distribution within plate prior to buckling. Based on the Baker&Pavlović&Tahan and Pavlović&Liu investigations, exact stress distributions were introduced herein. In that way, with the adequate deflection functions and precise stress distribution, Ritz energy method can produce highly accurate results.Through several examples for the plates with different boundary conditions, for which available literature offers very few analytical solutions, accuracy of the presented analytical approach is proved. Results obtained by analytical approach are reaffirmed by numerical finite-element runs.