The dissertation deals with dynamics of geometrically exact elastic and reinforced concrete planar structures.\ud
The main topic is the treatment of exact (Reissner’s) kinematic equations in problems concerning\ud
dynamics of planar beams. The kinematic equations include axial, bending as well as shear strains. The\ud
dissertation is divided into four themes. The first theme concerns solving the problem of dynamics of\ud
elastic planar beams by taking the strains as the only unknown functions. It turns out that the direct approach\ud
to solving problems, defined in this way, is numerically inefficient as it involves multiple nesting\ud
of integrals. An enhancement of the approach is therefore developed and tested on numerical examples.\ud
In the next theme we discuss the issue of time integration in kinematically exact dynamics. During the\ud
analysis we restrict ourselves to displacement and rotation based finite elements, which is the standard\ud
approach to solving problems in mechanics. The classical approach is presented first followed by the\ud
detailed energy approach. As a part of the analysis of energy conservation based integrators, a new time\ud
integration scheme is developed. It is based on the use of kinematic equations, which are differentiated\ud
with respect to time. Conservational properties of all analysed integration schemes are analytically and\ud
numerically tested. The schemes have been supplemented with numerical dissipation, which can be arbitrarily\ud
turned on or off according to a special algorithm in order to affect the lower modes of response\ud
as little as possible. This is also verified by the numerical examples. The third theme of the dissertation\ud
deals with the optimization of kinematically exact elastic structures. This part of the dissertation\ud
contributes to the development and the application of the sensitivity analysis for the newly developed\ud
time integration scheme. A wide array of problems dealing with optimization of dynamical systems can\ud
be solved. These problems include the optimization of shape and resistance of structures as well as the\ud
loading regimes and the optimal shape of mechanical manipulators. In the final part of the dissertation,\ud
the dynamics of kinematically exact reinforced concrete structures is discussed. A numerical procedure\ud
is developed, verified by the Opensees program and validated by experimental results. The majority of\ud
the numerical procedures presented in the dissertation have been developed in AceGen and AceFEM\ud
computer programs, through the symbolic programming of the finite element computer code and the expression\ud
optimization. These programs have been found to offer a versatile environment for testing and\ud
using finite element based analyses
