Approximate buckling analysis of the CCFF orthotropic plates subjected to in-plane bending

• The buckling problem for the CCFF orthotropic plate under in-plane bending is solved.
• The Kantorovich procedure is employed to derive governing equations.
• An analytical solution is obtained based on the generalised Galerkin method.
• The effectiveness of the approach is demonstrated using particular examples.
• The results are verified using the finite-element analysis.

An analytical solution of the buckling problem formulated for a rectangular orthotropic plate with two opposite edges clamped and another two edges free of load and support (CCFF) loaded by linearly distributed in-plane loads is presented. The Kantorovich procedure is employed to derive a governing equation and boundary conditions for the buckling problem which is subsequently solved using the generalised Galerkin method. The plate deflection is approximated by certain combinations of beam functions. The analytical formula for the critical load has been obtained and verified by comparison with a finite-element solution. Applications of this formula to the solutions of design problems have been demonstrated for the CCFF plates with various elastic characteristics and geometric parameters.