**Author details**

246 Nonlinearity, Bifurcation and Chaos – Theory and Applications

pulse loading *Tp* = *T3* = 1.6 ms [56]

**5. Conclusion** 

multimodal analysis are presented in Figure 18, correspondingly.

FEM

AN m=3, m=1, m=1', m=1''

**Figure 18.** Buckling modes for the channel cross-section column

Good agreement between the results obtained with ANM and FEM is possible because the interactive dynamic buckling problem has been solved in the analytical-numerical method. Four modes have been taken into account. The buckling stress and the natural frequency obtained with the analytical-numerical method for all the modes assumed in the multimodal analysis are listed in Table 7. The buckling modes taken into consideration in the

**Figure 17.** Dimensionless edge deflection vs. the *DLF* for channel columns subjected to rectangular

0.5 1 1.5 2 2.5 3 3.5

*DLF*

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 Tomasz Kubiak *Department of Strength of Materials, Lodz University of Technology, Poland* 
