Semi-analytical solutions for the compressed thin plate with large displacements

The thin plane plates are largely used in practice as single elements or as components of the thin-walled members. When subjected to compression, they exhibit a large post-critical strength reserve. Various analytical solutions of the uniformly compressed simply supported plate with large deflections were reported almost a century ago, mainly solving the fundamental equations of the flat thin plates or using classic energy methods. Owing to several disadvantages, these solutions were not introduced in the design codes of thin-walled structures, instead the semi-empirical Winter formula is nowadays largely used. This study presents a new semi-analytical solution based on classic energy methods. The main innovation is brought by the considered displacement field which is far more accurate than the ones used by the previous formulations. The advantages over the Winter formula are the improved accuracy and the consideration of the initial geometric imperfections. The advantages over the numerical simulations are the very small number of degrees of freedom and consequently the speed of the geometric nonlinear analysis in the elastic domain. The proposed solutions are validated against numerical solutions and experimental data.