Deformační metoda v nelineární mechanice

Abstract

Non-linear analysis of structures has been studied for many years. It still remains to be an important area of research. The thesis is focused on use of displacement method in non-linear solution. It deals with the geometrically, structurally and physically non-linear solutions. The considerable part is devoted to determination of steel arc reinforcement deformation state. The aim of the works is defined in the first chapter. It is elaboration of procedure for non-linear analysis of planar bar structures; the displacement method is utilized. The second chapter discusses the importance of including the geometrical and physical non-linearity into the static analysis of structures. The third chapter reviews approaches that are used in technical standards for non-linear solutions and it also reviews current knowledge in the field and it outlines some of the currently used methods of solution. The principle of displacement method is summarized in the fourth chapter. A geometrically non-linear solution is defined in the fifth chapter. The application of unit moments principle for the finite deformation computation is described. This principle is applied to non-linear solution of planar bar structures subsequently. Further the geometrically non-linear solution of steel arc reinforcement is introduced. The sixth chapter describes the structurally non-linear analysis. The numerical solution of a beam on elastic foundation is presented. Physically non-linear solution is shown in the seventh chapter. At first it deals with determination of the bending stiffness EI in dependence on the bending moment. In consequence it deals with determination of the stiffness EI in dependence on the relative rotation d. Further the geometrically and physically non-linear solution of steel arc reinforcements is introduced. This solution is further extended by inclusion of the influence of passive forces. The eighth chapter summarizes results of the work. Conclusions and recommendations for future development of the field are formulated subsequently.