Buckling of composite plates with a reinforced circular cutout subjected to uniform and non-uniform compression

An semi-analytical solution method is presented for the buckling analysis of plates with a reinforced cutout under both uniform and non-uniform compression loading. The cutout is reinforced on both sides of the plate. The solution for buckling response is achieved in two subsequent steps: pre-buckling response from in-plane stress analysis and the critical buckling load and its mode from a buckling analysis that utilizes the prebuckling stresses. The pre-buckling stresses are obtained based on the principle of minimum potential energy while automatically satisfying the equilibrium equations and compatibility condition. Hence, the strain energy of the plate is directly achieved by boundary integrals only. However, there exist material and thickness discontinuities between the unreinforced and reinforced regions of the plate. Unlike the pre-buckling equilibrium equations, the buckling equations, which are obtained from the Treftz criterion, are highly complex, and the potential functions automatically satisfying these equations do not exist. Hence, the Treftz criterion is applied with the assumed transverse displacement functions utilizing the full domain integration. In both pre-buckling and buckling analyses, the form of the assumed functions (real or complex) does not necessarily satisfy the kinematic boundary conditions. The kinematic boundary conditions are applied by introducing elastic springs along the boundaries, and by enforcing the displacement field to satisfy kinematic boundary conditions through energy minimization.