Accurate buckling loads of plates with different boundary conditions under arbitrary edge compression

• Analytical solutions for buckling of plates with mixed boundary conditions are given.
• Main contribution is exact elasticity solutions for in-plane stress distributions.
• For the first time, stress solutions for rotated configuration are developed.
• The essence of this paper is presentation of numerous, very complex examples.
• High accuracy level is proven by comparison with FEM results obtained by ANSYS.

Analytical procedure for critical load determination of plates with different boundary conditions under arbitrary in-plane compression loads is presented. Ritz energy technique with implemented exact stress distributions within plates and deflection functions in form of double Fourier series which satisfy all boundary conditions, term by term, provides results of high accuracy.The essence and value of this paper are in presentation of numerous examples and data which were used during the convergence and preciseness control of each part of very complex analytical procedure for critical load determination.Hence, through numerous examples of plates with wide range of aspect ratios and different boundary conditions under some classical as well as some not so classical compressive loads, applicability and accuracy of the presented analytical approach are proved. Results here obtained are reaffirmed by numerical finite element runs and also compared with still very few, until now, existing analytical solutions.