Secondary abstract: |
In dissertation we present the numerical method for analysis of the ductility, bearing capacity and post- critical behaviour of materially nonlinear space structures. We focus specially in analyzing the influence of different material and geometrical imperfections on the bearing capacity of beam structures. Im- perfections include the study of cracks, delaminations of beams and columns and the contact problem between the lamina. Theoretical background of the presented disertation can be devided in four parts. In first part, the modified arc-length method was implemented on adapted to spatial beam element based on strain measures. This procedure allows us to trace load-deflection paths with spatial beam finite ele- ments, which proved to be very efficient at handling materially nonlinear structures. The efficiency and the robustness of the formulation was preserved by properly considering the nonlinearities of the config- uration space of three dimensional of rotations and the related rotational deformations. The second part includes the determination of critical points. Here we deal with both, classification of the critical points and switching of the branches at the bifurcation points. Therefore, we are able to analyze the phenomena such as in-plane and out-of-plane buckling of straight and curved planar beams, torsional buckling of spatial beams and the combination of these phenomena. Buckling failure of bearing elements is even more substantial in case of structures with initial imperfections. Our numerical formulation allows us to take into consideration an arbitrary nonlinear material model, as well as other imperfections, such as delaminations. Delaminations in structures are modeled in third part of dissertation as the separate elements for which the proper boundary conditions must be considered. We also derive the analytical solutions for buckling loads of planar beams with multiple delaminations. The results show that ana- litical solutions which take shear into consideration are in total agreement with our numerical results. In the last part of the dissertation the contact problem at delamination is resolved using spatial springs between delaminated elements. Nonlinear constitutive law for springs is assumed to describe the contact of the laminae. Different constitutive models can be used for each local direction at the cross-sections. An arbitrary constitutive spring model allows us to solve the problem of overlapping of delaminated layers and to model spatial composite structures. Each chapter includes several numerical examples, which confirm, that all of the algorthms were built in our spatial formulation efficiently. Many examples are verified with respect to the relevant problems taken from literature, but we also show results of our own examples which include demanding geometrical and material nonlinearities. In this manner, we conclude the dissertation with three extensive numerical studies: optimal lateral support positioning and lateral buckling capacity of curved timber arches, bearing capacity of reinforced concrete beams with additional steel-plate reinforcement with possible delaminations and analysis of nailed composite timber beam. |