**5. Conclusion**

Taken into consideration the nonlinear thin plate theory for orthotropic material allows, as is presented in exemplary results of calculation, to analyse thin-walled structures composed of flat plates and subjected to static and dynamic load. The nonlinear orthotropic plate theory is the base for the proposed analytical-numerical method which allows to find buckling load with corresponding buckling mode, natural frequencies with corresponding modes and to analyse the postbuckling behaviour – drawing the postbuckling equilibrium paths for plate, segment of girders or columns made of isotropic, orthotropic or even composite materials. As it was shown not only static load can be considered but also dynamic load with intermediate velocity – the dynamic buckling can be analysed using assumed plate theory and the proposed method of solution.

The proposed analytical–numerical method gives almost the same results for eigenvalue problem (buckling loads, natural frequencies with corresponding modes) and similar results for dynamic buckling as the finite element method. However the dimensionless deflection versus dynamic load factor relation obtained with both (proposed and FEM) methods are not identical (especially for higher DLF value). These relations allow to find similar critical value of DLF taking into consideration one of the well-known criterion. The differences in the dimensionless deflection ξ appear because the numerical model in the FEM has more degrees of freedom than the model in the analytical–numerical method, but the results from the ANM are obtained in a significantly faster way than those from the finite element method.
