TY - JOUR A1 - Al-Yasiri, Zainab Riyadh Shaker A1 - Mutashar, Hayder Majid A1 - Gürlebeck, Klaus A1 - Lahmer, Tom ED - Shafiullah, GM T1 - Damage Sensitive Signals for the Assessment of the Conditions of Wind Turbine Rotor Blades Using Electromagnetic Waves JF - Infrastructures N2 - One of the most important renewable energy technologies used nowadays are wind power turbines. In this paper, we are interested in identifying the operating status of wind turbines, especially rotor blades, by means of multiphysical models. It is a state-of-the-art technology to test mechanical structures with ultrasonic-based methods. However, due to the density and the required high resolution, the testing is performed with high-frequency waves, which cannot penetrate the structure in depth. Therefore, there is a need to adopt techniques in the fields of multiphysical model-based inversion schemes or data-driven structural health monitoring. Before investing effort in the development of such approaches, further insights and approaches are necessary to make the techniques applicable to structures such as wind power plants (blades). Among the expected developments, further accelerations of the so-called “forward codes” for a more efficient implementation of the wave equation could be envisaged. Here, we employ electromagnetic waves for the early detection of cracks. Because in many practical situations, it is not possible to apply techniques from tomography (characterized by multiple sources and sensor pairs), we focus here on the question of whether the existence of cracks can be determined by using only one source for the sent waves. KW - Windkraftwerk KW - Rotorblatt KW - Elektrostatische Welle KW - MATLAB KW - wind turbine rotor blades KW - electromagnetic waves KW - crack detection KW - Empire XPU 8.01 KW - Matlab KW - OA-Publikationsfonds2022 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220831-47093 UR - https://www.mdpi.com/2412-3811/7/8/104 VL - 2022 IS - Volume 7, Issue 8 (August 2022), article 104 PB - MDPI CY - Basel ER - TY - JOUR A1 - Gürlebeck, Klaus A1 - Legatiuk, Dmitrii A1 - Webber, Kemmar T1 - Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures JF - Mathematics N2 - The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions. KW - Mauerwerk KW - Elastizitätstheorie KW - Mathematische Modellierung KW - quaternionic analysis KW - mathematical modelling KW - operator calculus KW - model comparison KW - micropolar elasticity KW - OA-Publikationsfonds2022 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220721-46726 UR - https://www.mdpi.com/2227-7390/10/10/1670 VL - 2022 IS - Volume 10, issue 10, article 1670 SP - 1 EP - 22 PB - MDPI CY - Basel ER - TY - JOUR A1 - Legatiuk, Anastasiia A1 - Gürlebeck, Klaus A1 - Hommel, Angela T1 - Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice JF - Mathematical Methods in the Applied Sciences N2 - This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp-estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices. KW - diskrete Fourier-Transformation KW - Laplace-Operator KW - discrete fourier transform KW - discrete fundamental solution KW - laplace operator KW - rectangular lattice Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220209-45829 UR - https://onlinelibrary.wiley.com/doi/full/10.1002/mma.7747 VL - 2021 SP - 1 EP - 23 PB - Wiley CY - Chichester ER - TY - JOUR A1 - Kavrakov, Igor A1 - Legatiuk, Dmitrii A1 - Gürlebeck, Klaus A1 - Morgenthal, Guido T1 - A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks JF - Royal Society Open Science N2 - Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary. This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterisation is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications. KW - Brücke KW - Aerodynamik KW - Aeroelastizität KW - bridge KW - abstract modelling KW - category theory KW - bridge aerodynamics KW - bridge aeroelasticity KW - aerodynamic models KW - model complexity KW - OA-Publikationsfonds2019 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20190314-38656 UR - https://royalsocietypublishing.org/doi/10.1098/rsos.181848 IS - Volume 6, Issue 3 ER - TY - JOUR A1 - Gürlebeck, Klaus A1 - Legatiuk, Dmitrii A1 - Nilsson, Henrik A1 - Smarsly, Kay T1 - Conceptual modelling: Towards detecting modelling errors in engineering applications JF - Mathematical Methods in Applied Sciences N2 - Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems. KW - Angewandte Mathematik KW - Angewandte Informatik KW - Ingenieurwissenschaften KW - Modellierung KW - engineering KW - abstraction KW - modelling KW - formal approaches KW - type theory Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20200110-40614 UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.5934 SP - 1 EP - 10 ER - TY - JOUR A1 - Lahmer, Tom A1 - Bock, Sebastian A1 - Hildebrand, Jörg A1 - Gürlebeck, Klaus T1 - Non-destructive identification of residual stresses in steel under thermal loadings JF - Inverse Problems in Science and Engineering N2 - Non-destructive identification of residual stresses in steel under thermal loadings KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 1 EP - 17 ER -