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This dissertation is devoted to the theoretical development and experimental laboratory verification of a new damage localization method: The state projection estimation error (SP2E). This method is based on the subspace identification of mechanical structures, Krein space based H-infinity estimation and oblique projections. To explain method SP2E, several theories are discussed and laboratory experiments have been conducted and analysed.
A fundamental approach of structural dynamics is outlined first by explaining mechanical systems based on first principles. Following that, a fundamentally different approach, subspace identification, is comprehensively explained. While both theories, first principle and subspace identification based mechanical systems, may be seen as widespread methods, barely known and new techniques follow up. Therefore, the indefinite quadratic estimation theory is explained. Based on a Popov function approach, this leads to the Krein space based H-infinity theory. Subsequently, a new method for damage identification, namely SP2E, is proposed. Here, the introduction of a difference process, the analysis by its average process power and the application of oblique projections is discussed in depth.
Finally, the new method is verified in laboratory experiments. Therefore, the identification of a laboratory structure at Leipzig University of Applied Sciences is elaborated. Then structural alterations are experimentally applied, which were localized by SP2E afterwards. In the end four experimental sensitivity studies are shown and discussed. For each measurement series the structural alteration was increased, which was successfully tracked by SP2E. The experimental results are plausible and in accordance with the developed theories. By repeating these experiments, the applicability of SP2E for damage localization is experimentally proven.
This paper presents a novel numerical procedure based on the framework of isogeometric analysis for static, free vibration, and buckling analysis of laminated composite plates using the first-order shear deformation theory. The isogeometric approach utilizes non-uniform rational B-splines to implement for the quadratic, cubic, and quartic elements. Shear locking problem still exists in the stiffness formulation, and hence, it can be significantly alleviated by a stabilization technique. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones.
A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.