The thesis deals with adaptive finite element modeling of plate structures. The finite element modeling of plates has grown to a mature research topic, which has contributed significantly to the development of the finite element method for structural analysis due to its complexity and inherently specific issues. At present, several validated plate models and corresponding families of working and efficient finite elements are available, offering a sound basis for an engineer to choose from. In our opinion, the main problems in the finite modeling of plates are nowadays related to the adaptive modeling. Adaptive modeling should reach much beyond standard discretization (finite element mesh) error estimates and related mesh (discretization) adaptivity. It should also include model error estimates and model adaptivity, which should provide the most appropriate mathematical model for a specific region of a structure. Thus in this work we study adaptive modeling for the case of plates. The primary goal of the thesis is to provide some answers to the questions related to the key steps in the process of adaptive modeling of plates. Since the adaptivity depends on reliable error estimates, a large part of the thesis is related to the derivation of computational procedures for discretization error estimates as well as model error estimates. A practical comparison of some of the established discretization error estimates is made. Special attention is paid to what is called equilibrated residuum method, which has a potential to be used both for discretization error and model error estimates. It should be emphasized that the model error estimates are quite hard to obtain, in contrast to the discretization error estimates. The concept of model adaptivity for plates is in this work implemented on the basis of equilibrated residuum method and hierarchic family of plate finite element models. The finite elements used in the thesis range from thin plate finite elements to thick plate finite elements. The latter are based on a newly derived higher order plate theory, which includes through the thickness stretching. The model error is estimated by local element-wise compu- tations. As all the finite elements, representing the chosen plate mathematical models, are re-derived in order to share the same interpolation bases, the difference between the local com- putations can be attributed mainly to the model error. This choice of finite elements enables effective computation of the model error estimate and improves the robustness of the adaptive modeling. Thus the discretization error can be computed by an independent procedure. Many numerical examples are provided as an illustration of performance of the derived plate elements, the derived discretization error procedures and the derived modeling error procedure. Since the basic goal of modeling in engineering is to produce an effective model, which will produce the most accurate results with the minimum input data, the need for the adaptive modeling will always be present. In this view, the present work is a contribution to the final goal of the finite element modeling of plate structures: a fully automatic adaptive procedure for the construction of an optimal computational model (an optimal finite element mesh and an optimal choice of a plate model for each element of the mesh) for a given plate structure. viii
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