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In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it’s also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material.

Turbomachinery plays an important role in many cases of energy generation or conversion. Therefore, turbomachinery is a promising approaching point for optimization in order to increase the efficiency of energy use. In recent years, the use of automated optimization strategies in combination with numerical simulation has become increasingly popular in many fields of engineering. The complex interactions between fluid and solid mechanics encountered in turbomachines on the one hand and the high computational expense needed to calculate the performance on the other hand, have, however, prevented a widespread use of these techniques in this field of engineering. The objective of this work was the development of a strategy for efficient metamodel based optimization of centrifugal compressor impellers. In this context, the main focus is the reduction of the required numerical expense. The central idea followed in this research was the incorporation of preliminary information acquired from low-fidelity computation methods and empirical correlations into the sampling process to identify promising regions of the parameter space. This information was then used to concentrate the numerically expensive high-fidelity computations of the fluid dynamic and structure mechanic performance of the impeller in these regions while still maintaining a good coverage of the whole parameter space. The development of the optimization strategy can be divided into three main tasks. Firstly, the available preliminary information had to be researched and rated. This research identified loss models based on one dimensional flow physics and empirical correlations as the best suited method to predict the aerodynamic performance. The loss models were calibrated using available performance data to obtain a high prediction quality. As no sufficiently exact models for the prediction of the mechanical loading of the impellercould be identified, a metamodel based on finite element computations was chosen for this estimation. The second task was the development of a sampling method which concentrates samples in regions of the parameter space where high quality designs are predicted by the preliminary information while maintaining a good overall coverage. As available methods like rejection sampling or Markov-chain Monte-Carlo methods did not meet the requirements in terms of sample distribution and input correlation, a new multi-fidelity sampling method called “Filtered Sampling“has been developed. The last task was the development of an automated computational workflow. This workflow encompasses geometry parametrization, geometry generation, grid generation and computation of the aerodynamic performance and the structure mechanic loading. Special emphasis was put into the development of a geometry parametrization strategy based on fluid mechanic considerations to prevent the generation of physically inexpedient designs. Finally, the optimization strategy, which utilizes the previously developed tools, was successfully employed to carry out three optimization tasks. The efficiency of the method was proven by the first and second testcase where an existing compressor design was optimized by the presented method. The results were comparable to optimizations which did not take preliminary information into account, while the required computational expense cloud be halved. In the third testcase, the method was applied to generate a new impeller design. In contrast to the previous examples, this optimization featuredlargervariationsoftheimpellerdesigns. Therefore, theapplicability of the method to parameter spaces with significantly varying designs could be proven, too.

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.