TY - JOUR A1 - Wu, Cheng-Chieh A1 - Völker, Daniel A1 - Weisbrich, S. A1 - Neitzel, F. ED - Holl, H. T1 - The finite volume method in the context of the finite element method N2 - The finite volume method (FVM), like the finite element method (FEM), is a numerical method for determining an approximate solution for partial differential equations. The derivation of the two methods is based on very different considerations, as they have historically evolved from two distinct engineering disciplines, namely solid mechanics and fluid mechanics. This makes FVM difficult to learn for someone familiar with FEM. In this paper we want to show that a slight modification of the FEM procedure leads to an alternative derivation of the FVM. Both numerical methods are starting from the same strong formulation of the problem represented by differential equations, which are only satisfied by their exact solution. For an approximation of the exact solution, the strong formulation must be converted to a so-called weak form. From here on, the two numerical methods differ. By appropriate choice of the trial function and the test function, we can obtain different numerical methods for solving the weak formulation of the problem. While typically in FEM the basis functions of the trial function and test function are identical, in FVM they are chosen differently. In this paper, we show which trial and test function must be chosen to derive the FVM alternatively: The trial function of the FVM is a “shifted” trial function of the FEM, where the nodal points are now located in the middle of an integration interval rather than at the ends. Moreover, the basis functions of the test function are no longer the same as those of the trial function as in the FEM, but are shown to be a constant equal to 1. This is demonstrated by the example of a 1D Poisson equation. KW - Finite Volume Method KW - Finite Element Method KW - Variational Calculation KW - Numerical Methods PY - 2022 U6 - https://doi.org/10.1016/j.matpr.2022.05.460 SN - 2214-7853 VL - 62 SP - 2679 EP - 2683 PB - Elsevier Ltd. CY - Amsterdam AN - OPUS4-55046 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Wu, Cheng-Chieh A1 - Völker, Daniel A1 - Weisbrich, S. A1 - Neitzel, F. ED - Holl, H. T1 - The Finite Volume Method in point of view of Finite Element Method N2 - The best-known discretization methods for solving engineering problems formulated as partial differential equations are finite difference method (FDM), finite element method (FEM) and finite volume method (FVM). While the finite volume method is used in fluid mechanics, the finite element method is predominant in solid state mechanics. At first glance, FVM and FEM are two highly specialized methods. However, both methods can solve problems of both solid mechanics and fluid mechanics well. Since experimental mechanics deals not only with solid state physics but also with fluid mechanics problems, we want to understand FVM in the sense of FEM in this work. In the long term, we want to use the variational calculus to unify many important numerical methods in engineering science into a common framework. In this way, we expect that experiences can be better exchanged between different engineering sciences and thus innovations in the field of experimental mechanics can be advanced. But in this work, we limit ourselves to the understanding of the FVM with the help of the variational calculus already known in FEM. We use a simple 1D Poisson equation to clarify the point. First, we briefly summarize the FVM and FEM. Then we will deal with the actual topic of this paper, as we establish the FEM and the FVM on a common basis by variation formulation. It is shown here that the FVM can be understood in terms of the finite element method with the so-called Galerkin-Petrov approach. T2 - 37th Danubia Adria Symposium on Advances in Experimental Mechanics CY - Linz, Österreich DA - 21.09.2021 KW - Finite element method KW - Finite volume method KW - Variational calculation KW - Simulation KW - Computational physics PY - 2021 SN - 978-3-9504997-0-4 SP - 12 EP - 13 AN - OPUS4-53422 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Wu, Cheng-Chieh A1 - Völker, Daniel A1 - Weisbrich, S. A1 - Neitzel, F. T1 - The Finite Volume Method in point of view of Finite Element Method N2 - The best-known discretization methods for solving engineering problems formulated as partial differential equations are finite difference method (FDM), finite element method (FEM) and finite volume method (FVM). While the finite volume method is used in fluid mechanics, the finite element method is predominant in solid state mechanics. At first glance, FVM and FEM are two highly specialized methods. However, both methods can solve problems of both solid mechanics and fluid mechanics well. Since experimental mechanics deals not only with solid state physics but also with fluid mechanics problems, we want to understand FVM in the sense of FEM in this work. In the long term, we want to use the variational calculus to unify many important numerical methods in engineering science into a common framework. In this way, we expect that experiences can be better exchanged between different engineering sciences and thus innovations in the field of experimental mechanics can be advanced. But in this work, we limit ourselves to the understanding of the FVM with the help of the variational calculus already known in FEM. We use a simple 1D Poisson equation to clarify the point. First, we briefly summarize the FVM and FEM. Then we will deal with the actual topic of this paper, as we establish the FEM and the FVM on a common basis by variation formulation. It is shown here that the FVM can be understood in terms of the finite element method with the so-called Galerkin-Petrov approach. T2 - 37th Danubia Adria Symposium on Advances in Experimental Mechanics CY - Linz, Austria DA - 21.09.2021 KW - Finite volume method KW - Finite element method KW - Variational calculation KW - Simulation KW - Computational physics PY - 2021 AN - OPUS4-53424 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Wu, Cheng-Chieh A1 - Weisbrich, S. A1 - Burger, M. A1 - Neitzel, F. ED - Zemčík, R. T1 - A four-point bending test apparatus for measurement- and model-based structural analysis N2 - By means of a small-scale truss bridge, the ability of the Measurement- and Model-based Structural Analysis to detect and localise damage was examined in. Although there was no noteworthy difficulty in detecting damage, it turned out that damage localisation responds sensitively to systematic influences, i.e. non-modelled properties of the mechanical model. Therefore, another experiment is being conducted to re-examine the Measurement- and Model-based Structural Analysis. For this purpose, the bending test is carried out as it has been already theoretically respectively numerically discussed in. In this attempt, the systematic influences such as residual stress are kept as low as possible. T2 - 36th Danubia Adria Symposium on Advances in Experimental Mechanics CY - Pilsen, Czech Republic DA - 24.09.2019 KW - Damage detection KW - Adjustment calculation KW - Finite element method KW - Integrated analysis PY - 2020 UR - http://www.sciencedirect.com/science/article/pii/S2214785320326432 U6 - https://doi.org/10.1016/j.matpr.2020.04.028 SN - 2214-7853 VL - 32 IS - 2 SP - 156 EP - 161 PB - Elsevier Ltd. AN - OPUS4-51551 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Wu, Cheng-Chieh A1 - Weisbrich, S. A1 - Neitzel, F. A1 - Kadoke, Daniel A1 - Fischer, Michael A1 - Kohlhoff, Harald ED - Pastramă, Ştefan Dan ED - Constantinescu, Dan Mihai T1 - A Small-Scale Test Bridge for Measurement and Model-based Structural Analysis N2 - The Measurement- and Model-based Structural Analysis (MeMoS) integrates a finite element model into least squares adjustment and thus allows to evaluate a mechanical model and measurements in a combined analysis. To examine the capability to detect and localise damage using this integrated analysis MeMoS, a small-scale truss bridge made of aluminium profiles is built as a test specimen for this purpose. T2 - 35th Danubia Adria Symposium on Advances in Experimental Mechanics CY - Sinaia, Romania DA - 25.09.2018 KW - Structural analysis KW - Damage detection and localisation KW - Finite element method KW - Photogrammetry KW - Adjustment calculation PY - 2019 UR - http://www.sciencedirect.com/science/article/pii/S2214785319304894 U6 - https://doi.org/10.1016/j.matpr.2019.03.130 SN - 2214-7853 VL - 12 IS - 2 SP - 319 EP - 328 PB - Elsevier Ltd. AN - OPUS4-48053 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Kowitz, Astrid A1 - Wu, Cheng-Chieh A1 - Helmerich, Rosemarie A1 - Hille, Falk A1 - Kadoke, Daniel A1 - Gründer, Klaus-Peter A1 - Hauser, S. A1 - Schwarzinger, H. ED - Bland, S. T1 - Impact on a micro-reinforced UHPC: Experimental studies versus numerical modeling N2 - Within the presented research project, experimental and numerical investigations were performed to develop a thin-shelled, modular, mobile element system made of a micro-reinforced ultra-high-performance ductile concrete (DUCON®). Material parameters were experimentally determined to adapt the material model within the numerical analysis applying the Drucker-Prager relationship. Afterwards, for validation of the numerical models, quasi-static and high-velocity impact tests were performed on plate-like structures. Finally, a suitable geometry of transportable barrier elements will be designed, which provides a maximum of resistance against impact by a minimum of weight and a maximum of mobility. KW - UHPC KW - Impact KW - DUCON® KW - Quasi-static and dynamic tests KW - Micro-reinforcement KW - Ductility KW - Mobile elements KW - Numerical modeling KW - Stereo photogrammetry KW - Compressive strength KW - E-modulus PY - 2019 UR - https://www.sciencedirect.com/science/article/pii/S2214785319305115?dgcid=author U6 - https://doi.org/10.1016/j.matpr.2019.03.152 SN - 2214-7853 VL - 12 IS - 2 SP - 474 EP - 483 PB - Elsevier Ltd CY - Amsterdam AN - OPUS4-48181 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - THES A1 - Wu, Cheng-Chieh T1 - The measurement- and model-based structural analysis for damage detection N2 - Die vorliegende Arbeit soll einen Beitrag zur Überwachung von Ingenieurbauwerken leisten. Die Detektion von Schäden an Bauwerken basiert auf der Auswertung von räumlich und zeitlich verteilten Hybridmessungen. Die erfassten Daten können rein geometrisch oder physikalisch ausgewertet werden. Letzteres ist vorzuziehen, da die Schadensursache mittels geometrisch-physikalischer Gesetze ermittelt werden kann, um rechtzeitig eingreifen und die weitere Nutzung der Bauwerke sicherstellen zu können. Aus diesem Grund werden die kontinuumsmechanischen Feldgleichungen in Verbindung mit der Finite-Elemente-Methode und Hybridmessungen durch die Ausgleichungsrechnung zu einer einzigen Auswertemethode kombiniert. Dabei ergeben sich zwei Aufgabenstellungen. Die erste Aufgabe beschäftigt sich mit der Beziehung zwischen der Finite-Elemente-Methode und der Ausgleichungsrechnung. Die Finite-Elemente-Methode löst bestimmte Problemklassen, die durch ein System elliptischer partieller Differentialgleichungen beschrieben werden. Während die Methode der kleinsten Quadrate eine weitere Klasse von Problemen löst, die als ein überdeterminiertes Gleichungssystem formuliert ist. Die auffallende Ähnlichkeit zwischen den beiden Methoden ist seit vielen Jahrzehnten bekannt. Es bleibt jedoch ungeklärt, warum diese Ähnlichkeit besteht. Der Beitrag soll dies klären, indem die Variationsrechnung im Hinblick auf ihr methodisches Vorgehen untersucht wird. Obwohl das bekannte Gauß-Markov-Modell innerhalb der Methode der kleinsten Quadrate und die Finite-Elemente-Methode inhärent unterschiedliche Problemklassen lösen, wird gezeigt, dass beide Methoden durch die gleichen methodischen Schritte der Variationsrechnung abgeleitet werden können. Aus methodischer Sicht bedeutet dies, dass beide Methoden nicht nur ähnlich, sondern sogar gleich sind. Außerdem wird darauf hingewiesen, wo eine mögliche Querverbindung zu anderen Methoden besteht. Die zweite Aufgabenstellung stellt eine Messungs- und Modellbasierte Strukturanalyse (MeMoS) durch die Integration der Finite-Elemente-Methode in die Ausgleichungsrechnung vor. In numerischen Untersuchungen wird gezeigt, wie diese integrierte Analyse zur Parameteridentifikation sowohl einfacher als auch beliebig geformter Strukturbauteile eingesetzt werden kann. Darauf aufbauend wird untersucht, mit welchen Beobachtungstypen, mit welcher Genauigkeit und an welcher Stelle der Struktur diese Messungen durchgeführt werden müssen, um die Materialparameter möglichst genau zu bestimmen. Dies dient der Ermittlung eines optimalen und wirtschaftlichen Messaufbaus. Mit dieser integrierten Analyse kann auch ein Ersatzmodell einer geometrisch komplexen Struktur ermittelt werden. Die Frage der Erkennung und Lokalisierung von Schäden innerhalb einer Struktur wird mit Hilfe dieser Strukturanalyse behandelt. Die Messungs- und Modellbasierte Strukturanalyse wird mit zwei verschiedenen Testaufbauten, einer Aluminium-Modellbrücke und einem Biegebalken, validiert. N2 - The present work is intended to make a contribution to the monitoring of civil engineering structures. The detection of damage to structures is based on the evaluation of spatially and temporally distributed hybrid measurements. The acquired data can be evaluated purely geometrically or physically. It is preferable to do the latter, since the cause of damage can be determined by means of geometrical-physical laws in order to be able to intervene in time and ensure the further use of the structures. For this reason, the continuum mechanical field equations in conjunction with the finite element method and hybrid measurements are combined into a single evaluation method by the adjustment calculation. This results in two challenges. The first task deals with the relationship between the finite element method and the method of least squares. The finite element method solves certain problem classes, which are described by a system of elliptical partial differential equations. Whereas the method of least squares solves another class of problems, which is formulated as an overdetermined system of equations. The striking similarity between both methods is known since many decades. However, it remains unresolved why this resemblance exists. The contribution is to clarify this by examining the variational calculus, especially with regard to its methodological procedure. Although the well-known Gauss-Markov model within the method of least squares and the finite element method solve inherently different problem classes, it is shown that both methods can be derived by following the same methodological steps of the variational calculus. From a methodical viewpoint, this implies that both methods are not only similar, but actually the same. In addition, it is pointed out where a possible cross-connection to other methods exists. The second task introduces a Measurement- and Model-based Structural Analysis (MeMoS) by integrating the finite element method into the adjustment calculation. It is shown in numerical examinations how this integrated analysis can be used for parameter identification of simple as well as arbitrarily shaped structural components. Based on this, it is examined with which observation types, with which precision and at which location of the structure these measurements must be carried out in order to determine the material parameters as precisely as possible. This serves to determine an optimal and economic measurement set-up. With this integrated analysis, a substitute model of a geometrically complex structure can also be determined. The issue of the detection and localisation of damage within a structure is studied by means of this structural analysis. The Measurement and Model-based Structural Analysis is validated using two different test setups, an aluminum model bridge and a bending beam. T3 - BAM Dissertationsreihe - 166 KW - Ausgleichungsrechnung KW - Finite-Elemente-Methode KW - Integrierte Analyse KW - Kontinuumsmechanik KW - Schadenserkennung KW - Variationsrechnung KW - Adjustment calculation KW - Continuum mechanics KW - Damage detection KW - Finite element method KW - Integrated analysis KW - Variational calculus PY - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-501977 SN - 1613-4249 VL - 166 SP - 1 EP - 184 PB - Bundesanstalt für Materialforschung und -prüfung (BAM) CY - Berlin AN - OPUS4-50197 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - THES A1 - Wu, Cheng-Chieh T1 - The measurement- and model-based structural analysis for damage detection T1 - Schadensfrüherkennung mittels messungs- und modellbasierter Strukturanalyse N2 - The present work is intended to make a contribution to the monitoring of civil engineering structures. The detection of damage to structures is based on the evaluation of spatially and temporally distributed hybrid measurements. The acquired data can be evaluated purely geometrically or physically. It is preferable to do the latter, since the cause of damage can be determined by means of geometrical-physical laws in order to be able to intervene in time and ensure the further use of the structures. For this reason, the continuum mechanical field equations in conjunction with the finite element method and hybrid measurements are combined into a single evaluation method by the adjustment calculation. This results in two challenges. The first task deals with the relationship between the finite element method and the method of least squares. The finite element method solves certain problem classes, which are described by a system of elliptical partial differential equations. Whereas the method of least squares solves another class of problems, which is formulated as an overdetermined system of equations. The striking similarity between both methods is known since many decades. However, it remains unresolved why this resemblance exists. The contribution is to clarify this by examining the variational calculus, especially with regard to its methodological procedure. Although the well-known Gauss-Markov model within the method of least squares and the finite element method solve inherently different problem classes, it is shown that both methods can be derived by following the same methodological steps of the variational calculus. From a methodical viewpoint, this implies that both methods are not only similar, but actually the same. In addition, it is pointed out where a possible cross-connection to other methods exists. The second task introduces a Measurement- and Model-based Structural Analysis (MeMoS) by integrating the finite element method into the adjustment calculation. It is shown in numerical examinations how this integrated analysis can be used for parameter identification of simple as well as arbitrarily shaped structural components. Based on this, it is examined with which observation types, with which precision and at which location of the structure these measurements must be carried out in order to determine the material parameters as precisely as possible. This serves to determine an optimal and economic measurement set-up. With this integrated analysis, a substitute model of a geometrically complex structure can also be determined. The issue of the detection and localisation of damage within a structure is studied by means of this structural analysis. The Measurement and Model-based Structural Analysis is validated using two different test setups, an aluminum model bridge and a bending beam. N2 - Die vorliegende Arbeit soll einen Beitrag zur Überwachung von Ingenieurbauwerken leisten. Die Detektion von Schäden an Bauwerken basiert auf der Auswertung von räumlich und zeitlich verteilten Hybridmessungen. Die erfassten Daten können rein geometrisch oder physikalisch ausgewertet werden. Letzteres ist vorzuziehen, da die Schadensursache mittels geometrisch-physikalischer Gesetze ermittelt werden kann, um rechtzeitig eingreifen und die weitere Nutzung der Bauwerke sicherstellen zu können. Aus diesem Grund werden die kontinuumsmechanischen Feldgleichungen in Verbindung mit der Finite-Elemente-Methode und Hybridmessungen durch die Ausgleichungsrechnung zu einer einzigen Auswertemethode kombiniert. Dabei ergeben sich zwei Aufgabenstellungen. Die erste Aufgabe beschäftigt sich mit der Beziehung zwischen der Finite-Elemente-Methode und der Ausgleichungsrechnung. Die Finite-Elemente-Methode löst bestimmte Problemklassen, die durch ein System elliptischer partieller Differentialgleichungen beschrieben werden. Während die Methode der kleinsten Quadrate eine weitere Klasse von Problemen löst, die als ein überdeterminiertes Gleichungssystem formuliert ist. Die auffallende Ähnlichkeit zwischen den beiden Methoden ist seit vielen Jahrzehnten bekannt. Es bleibt jedoch ungeklärt, warum diese Ähnlichkeit besteht. Der Beitrag soll dies klären, indem die Variationsrechnung im Hinblick auf ihr methodisches Vorgehen untersucht wird. Obwohl das bekannte Gauß-Markov-Modell innerhalb der Methode der kleinsten Quadrate und die Finite-Elemente-Methode inhärent unterschiedliche Problemklassen lösen, wird gezeigt, dass beide Methoden durch die gleichen methodischen Schritte der Variationsrechnung abgeleitet werden können. Aus methodischer Sicht bedeutet dies, dass beide Methoden nicht nur ähnlich, sondern sogar gleich sind. Außerdem wird darauf hingewiesen, wo eine mögliche Querverbindung zu anderen Methoden besteht. Die zweite Aufgabenstellung stellt eine Messungs- und Modellbasierte Strukturanalyse (MeMoS) durch die Integration der Finite-Elemente-Methode in die Ausgleichungsrechnung vor. In numerischen Untersuchungen wird gezeigt, wie diese integrierte Analyse zur Parameteridentifikation sowohl einfacher als auch beliebig geformter Strukturbauteile eingesetzt werden kann. Darauf aufbauend wird untersucht, mit welchen Beobachtungstypen, mit welcher Genauigkeit und an welcher Stelle der Struktur diese Messungen durchgeführt werden müssen, um die Materialparameter möglichst genau zu bestimmen. Dies dient der Ermittlung eines optimalen und wirtschaftlichen Messaufbaus. Mit dieser integrierten Analyse kann auch ein Ersatzmodell einer geometrisch komplexen Struktur ermittelt werden. Die Frage der Erkennung und Lokalisierung von Schäden innerhalb einer Struktur wird mit Hilfe dieser Strukturanalyse behandelt. Die Messungs- und Modellbasierte Strukturanalyse wird mit zwei verschiedenen Testaufbauten, einer Aluminium-Modellbrücke und einem Biegebalken, validiert. KW - Damage detection KW - Continuum mechanics KW - Adjustment calculation KW - Finite element method KW - Variational calculus KW - Integrated analysis KW - Schadenserkennung KW - Kontinuumsmechanik KW - Ausgleichungsrechnung KW - Finite-Elemente-Methode KW - Variationsrechnung KW - Integrierte Analyse PY - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2019100201583156925935 SP - 1 EP - 169 PB - Technische Universität Berlin CY - Berlin AN - OPUS4-49288 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Wu, Cheng-Chieh A1 - Weisbrich, S. A1 - Burger, M. A1 - Neitzel, F. T1 - A Four-Point Bending Test Apparatus for Measurement- and Model-based Structural Analysis N2 - By means of a small-scale truss bridge, the ability of the Measurement- and Model-based Structural Analysis to detect and localize damage was examined. Although there was no noteworthy difficulty in detecting damage, it turned out that damage localization responds sensitively to systematic influences, i.e. non-modelled properties of the mechanical model. Therefore, another experiment is being conducted to re-examine the Measurement- and Model-based Structural Analysis. For this purpose, the bending test is carried out as it has been already theoretically respectively numerically discussed. In this attempt, the systematic influences such as residual stress are kept as low as possible. T2 - 36th Danubia Adria Symposium on Advances in Experimental Mechanics CY - Pilsen, Czech Republic DA - 24.09.2019 KW - Damage detection KW - Adjustment calculation KW - Finite element method PY - 2019 SN - 978-80-261-0876-4 SP - 63 EP - 64 CY - Pilsen, Czech Republic AN - OPUS4-49290 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Wu, Cheng-Chieh A1 - Weisbrich, S. A1 - Burger, M. A1 - Neitzel, F. T1 - A Four-Point Bending Test Apparatus for Measurement- and Model-based Structural Analysis N2 - By means of a small-scale truss bridge, the ability of the Measurement- and Model-based Structural Analysis to detect and localize damage was examined. Although there was no noteworthy difficulty in detecting damage, it turned out that damage localization responds sensitively to systematic influences, i.e. non-modelled properties of the mechanical model. Therefore, another experiment is being conducted to re-examine the Measurement- and Model-based Structural Analysis. For this purpose, the bending test is carried out as it has been already theoretically respectively numerically discussed. In this attempt, the systematic influences such as residual stress are kept as low as possible. T2 - 36th Danubia Adria Symposium on Advances in Experimental Mechanics CY - Pilsen, Czech Republic DA - 24.09.2019 KW - Damage detection KW - Adjustment calculation KW - Finite element method PY - 2019 AN - OPUS4-49291 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -