El uso de barras de materiales compuestos (FRP) se propone como una alternativa efectiva para las tradicionales estructuras de hormigón armadas con acero que sufren corrosión en ambientes agresivos. La aceptación de estos materiales en el mundo de la construcción está condicionada a la compresión de su comportamiento estructural. Este trabajo estudia el comportamiento adherente entre barras de FRP y hormigón mediante dos programas experimentales. El primero incluye la caracterización de la adherencia entre barras de FRP y hormigón mediante ensayos de pull-out y el segundo estudia el proceso de fisuración de tirantes de hormigón reforzados con barras de GFRP mediante ensayo a tracción directa. El trabajo se concluye con el desarrollo de un modelo numérico para la simulación del comportamiento de elementos de hormigón reforzado bajo cargas de tracción. La flexibilidad del modelo lo convierte en una herramienta flexible para la realización de un estudio paramétrico sobre las variables que influyen en el proceso de fisuración. / The use of Fibre Reinforced Polymers (FRP) as reinforcement in concrete structures is considered to be a possible alternative to steel in those situations where corrosion is present. The full acceptance of FRP reinforcement in concrete construction is contingent on a complete study and comprehension of all aspects of their structural performance. This thesis investigates the bond behaviour between Fibre Reinforced Polymer (FRP) reinforcement and concrete. Two experimental programs were conducted. In the first program the role of the variables which affect the bond behaviour was studied through pull-out test. In the second program, GFRP RC members were tested in tension to study their cracking response. To conclude the thesis, a numerical model was developed to simulate the cracking behaviour of RC tensile members. Since the model was flexible enough to include any "user-defined" bond-slip law and variable materials' properties, a parametric study was conducted to analyze which are the variables that influence the cracking behaviour.

L’objectif de cette thèse est la prise en compte du comportement raidissant en traction sur des poutres en béton armé du à l’adhérence entre les armatures tendues et le béton. Un vaste programme expérimental sur des poutres minces et des poutres épaisses permet de quantifier expérimental le profil de contraintes dans le béton tendu entre deux fissures de flexion. La création d’un nouvel élément fini est ensuite mise en œuvre à partir des observations expérimentales. Les tests conduits sur des tirants ont permis de mettre en évidence à la fois l’existence d’une longueur de transfert et une longueur de totale décohésion qui caractérisent le phénomène d’adhérence entre l’acier le béton entre deux fissures consécutives de flexion. La longueur de transfert correspond à la mise en tension du béton et donc l’établissement de la contribution du béton tendu à la rigidité flexionnelle, ce qui limite la diminution de rigidité de la poutre après fissuration. Les mesures de la flèche en flexion des différentes poutres testées, minces ou épaisses, permettent de caractériser la longueur de transfert et de réaliser l’objectif de la thèse qui est de prendre en compte le béton tendu dans le calcul de la rigidité flexionnelle des poutres en béton armé / The aim of this thesis is to study the stiffening effect of tensile concrete in flexural reinforced concrete beams by controlling the bond between steel and concrete. The process consists of experimentally determining the strain profile in both deep and thin flexural beams. We created a new finite element model for both deep and thin beams in accordance with experimental observations. The experimental tests we conducted on tension members highlight the existence of both transfer length and length with total bond loss characterizing the bond between tensile steel and concrete. The transfer length contributes to the production of a tension stiffening effect, thus limiting the stiffness decrease of the flexural beam. Measuring the beam deflection makes it possible to determine the transfer length, and consequently to achieve the main objective, namely the contribution of tensile concrete to beam stiffness

O presente trabalho é uma contribuição para o esclarecimento e a quantificação das influências na deformabilidade e na capacidade portante de elementos unidimensionais de concreto armado em solicitação plana, decorrentes da não-linearidade física dos materiais concreto e aço, bem como da fissuração e do enrijecimento da armadura tracionada, também na sua fase plástica. Para aplicações práticas determinam-se a rigidez à flexão e a capacidade de rotação plástica dos elementos estruturais, o que permite limitar com mais precisão e coerência a demanda de rotação plástica obtida na análise. De início, descrevem-se os comportamentos não-lineares do concreto e do aço, aplicando-se conceitos da Mecânica da Fratura, bem como a atuação conjunta destes materiais, sob os aspectos de aderência e de fissuração. O núcleo deste trabalho concentra-se na obtenção do diagrama momento-curvatura e dos seus pontos principais, e na subseqüente determinação da capacidade de rotação plástica dos mencionados elementos. Consideram-se as seções geradas a partir da seção duplo T assimétrico, com várias camadas de armadura, sujeitas à flexão composta normal. Com dados deste diagrama e através do modelo da viga equivalente simétrica, posteriormente estendido à viga equivalente assimétrica e às vigas contínuas de pórticos planos, determina-se a capacidade de rotação plástica, considerando-se nesta suas múltiplas influências. Por fim, comparam-se os resultados teóricos e experimentais da capacidade de rotação plástica, e resumem-se as principais conclusões encontradas e os pontos que exigem subseqüente desenvolvimento. / The present study is a contribution to the enlightenment and evaluation of the influences on deformability and load carrying capacity of one-dimensional elements of reinforced concrete subject to in-plane loading, arisen from the constitutive non-linearity of concrete and steel, as well as from the concrete cracking and the tension stiffening of the reinforcement, prior and after yielding. For practical applications, the flexural rigidity and the plastic rotation capacity of structural elements are determined, which makes it possible to limit, more precisely and coherently, the plastic rotation demand coming from the analysis. Firstly, the non-linear behaviors of concrete and steel are described, applying concepts of Fracture Mechanics, and then the joint action of both materials concerning bond and cracking is studied. The core of this study lies on obtaining the bending moment-curvature diagram, specially its main points, and on the subsequent determination of the plastic rotation capacity of the aforementioned elements. The cross-sections generated from an asymmetric double T cross-section are considered, with several layers of reinforcement, acted upon simple or combined bending about one principal axis. With data based on this diagram and through the model of equivalent symmetric beam, later extended to equivalent asymmetric beam and to continuous beams of plane frames, the plastic rotation capacity is determined, considering its multiple influences. Finally, theoretical and experimental results of plastic rotation capacity are compared, and the main conclusions and points in need of subsequent development are summarized.

The Aveston Copper and Kelly (ACK) Method has been routinely used in estimating the efficiency of the bond between the textile and cementitious matrix. This method however has a limited applicability due to the simplifying assumptions such as perfect bond. A numerical model for simulation of tensile behavior of reinforced cement-based composites is presented to capture the inefficiency of the bond mechanisms. In this approach the role of interface properties which are instrumental in the simulation of the tensile response is investigated. The model simulates the tension stiffening effect of cracked matrix, and evolution of crack spacing in tensile members. Independent experimental results obtained from literature are used to verify the model and develop composite tensile stress strain response using alkali resistant (AR) glass textile reinforced concrete. The composite stress strain response is then used with a bilinear representation of the composite obtained from the tensile stiffening model. The closed form and simplified equations for representation of flexural response are obtained and used for both back-calculation and also design. A method based on the average moment-curvature relationship in the structural design and analysis of one way and two way flexural elements using yield line analysis approaches is proposed. This comprehensive approach directly shows the interrelation of fundamental materials characterization techniques with simplified design equations for further utilization of textile reinforced concrete materials.

Gelžbetonis yra kompozitinė medžiaga, kurios komponentai yra betonas ir plieninė armatūra. Kaip žinoma, betono stipris tempiant yra 1020 kartų mažesnis nei stipris gniuždant. Atrodytų, kad tempiamojo betono įtaka, atlaikant įrąžas skerspjūvyje, yra nereikšminga. Iš tiesų, nustatant lenkiamųjų elementų stiprumą normaliniame pjūvyje, tempiamo betono įtempių galima nevertinti. Kita vertus, skaičiuojant įlinkius, neįvertinus tempiamojo betono įtakos, gali būti daroma didesnė nei 100 % paklaida. Adekvatus supleišėjusio tempiamojo betono įtakos įvertinimas, nustatant trumpalaike apkrova veikiamų gelžbetoninių elementų deformacijas, yra bene svarbiausia ir sudėtingiausia problema. Plyšio vietoje betonas negali atlaikyti tempimo įtempių, todėl visą įrąžą atlaiko armatūra. Kadangi plyšyje ir gretimuose pjūviuose armatūra praslysta betono atžvilgiu, kontakto zonoje atsiranda tangentiniai įtempiai. Šie įtempiai perduodami betonui, todėl jis atlaiko tempimo įtempius. Armatūros ir betono sąveika ruožuose tarp plyšių standina gelžbetoninį elementą. Supleišėjusio betono gebėjimas atlaikyti tempimo įtempius vadinama tempimo sustandėjimu (angl. tension stiffening). Šis efektas dažniausiai modeliuojamas supleišėjusio betono įtempių ir deformacijų diagrama, taikant vidutinių plyšių koncepciją. Tuomet neatsižvelgiama į diskrečius plyšius, o supleišėjęs betonas traktuojamas kaip ortotropinė medžiaga su pakitusiomis savybėmis. Dauguma tempimo sustandėjimo modelių įvertina betono įtempių... [toliau žr. visą tekstą] / Modelling behaviour of cracked tensile concrete is a complicated issue. Due to bond with reinforcement, the cracked concrete between cracks carries a certain amount of tensile force normal to the cracked plane. Concrete adheres to rein-forcement bars and contributes to overall stiffness of the structure. The phe-nomenon, called tension-stiffening, has significant influence on the results of short-term deformational analysis. Assumption of a tension-stiffening law has great influence on numerical results of load – deflection behaviour of reinforced concrete members subjected to short – term loading. Under wrong assumption of this law, errors in calculated deflections, particularly for lightly members, may exceed 100 %. Most known tension-stiffening relationships relate average stresses to average strains. However, some experimental and theoretical investi-gations have shown that tension-stiffening may be affected by other parameters. The scientific supervisor of the thesis has proposed a tension-stiffening model depending on reinforcement ratio. This model has been developed using experi-mental data reported in the literature. Besides, concrete shrinkage effect was not taken into account. The main objective of this PhD dissertation is to propose a tension-stiffening law for bending RC members subjected to short-term loading with eliminated concrete shrinkage effect.

Application of refined ultimate state theories and use of high strength materials have resulted in longer spans and smaller depths of reinforced and prestressed concrete structures. Consequently, the condition of the limiting deflection rather than the strength requirement often is the governing design criterion. Long-term deflections might be up to 3 to 4 times larger than the short-term deflections. Such increments are caused by complex physical effects such as concrete creep, shrinkage and cracking, bond defects, etc. Long-term concrete creep and shrinkage deformations govern prestress losses. Structural analysis can be carried out either by traditional design code methods or numerical techniques. Although design code methods ensure safe design, they have significant limitations. Different techniques are used for strength, deflection, crack width and prestress loss analyses. Besides, most of the simplified approaches do not assess such factors as concrete shrinkage, cracking or tension stiffening. Based on a large number of empirical expressions and factors, they lack physical interpretation and do not reveal the actual stress-strain state of cracked structures. On the other hand, numerical techniques are universal and can take into account each physical effect. However, inadequacies made in the prediction of each effect might lead to significant inaccuracies when integral magnitudes such as deflection are to be assessed. Consequently, the predictions by the numerical... [to full text]

Modelling behaviour of cracked tensile concrete is a complicated issue. Due to bond with reinforcement, the cracked concrete between cracks carries a certain amount of tensile force normal to the cracked plane. Concrete adheres to rein-forcement bars and contributes to overall stiffness of the structure. The phe-nomenon, called tension-stiffening, has significant influence on the results of short-term deformational analysis. Assumption of a tension-stiffening law has great influence on numerical results of load – deflection behaviour of reinforced concrete members subjected to short – term loading. Under wrong assumption of this law, errors in calculated deflections, particularly for lightly members, may exceed 100 %. Most known tension-stiffening relationships relate average stresses to average strains. However, some experimental and theoretical investi-gations have shown that tension-stiffening may be affected by other parameters. The scientific supervisor of the thesis has proposed a tension-stiffening model depending on reinforcement ratio. This model has been developed using experi-mental data reported in the literature. Besides, concrete shrinkage effect was not taken into account. The main objective of this PhD dissertation is to propose a tension-stiffening law for bending RC members subjected to short-term loading with eliminated concrete shrinkage effect. / Gelžbetonis yra kompozitinė medžiaga, kurios komponentai yra betonas ir plieninė armatūra. Kaip žinoma, betono stipris tempiant yra 10-20 kartų mažesnis nei stipris gniuždant. Atrodytų, kad tempiamojo betono įtaka, atlaikant įrąžas skerspjūvyje, yra nereikšminga. Iš tiesų, nustatant lenkiamųjų elementų stiprumą normaliniame pjūvyje, tempiamo betono įtempių galima nevertinti. Kita vertus, skaičiuojant įlinkius, neįvertinus tempiamojo betono įtakos, gali būti daroma didesnė nei 100 % paklaida. Adekvatus supleišėjusio tempiamojo betono įtakos įvertinimas, nustatant trumpalaike apkrova veikiamų gelžbetoninių elementų deformacijas, yra bene svarbiausia ir sudėtingiausia problema. Plyšio vietoje betonas negali atlaikyti tempimo įtempių, todėl visą įrąžą atlaiko armatūra. Kadangi plyšyje ir gretimuose pjūviuose armatūra praslysta betono atžvilgiu, kontakto zonoje atsiranda tangentiniai įtempiai. Šie įtempiai perduodami betonui, todėl jis atlaiko tempimo įtempius. Armatūros ir betono sąveika ruožuose tarp plyšių standina gelžbetoninį elementą. Supleišėjusio betono gebėjimas atlaikyti tempimo įtempius vadinama tempimo sustandėjimu (angl. tension stiffening). Šis efektas dažniausiai modeliuojamas supleišėjusio betono įtempių ir deformacijų diagrama, taikant vidutinių plyšių koncepciją. Tuomet neatsižvelgiama į diskrečius plyšius, o supleišėjęs betonas traktuojamas kaip ortotropinė medžiaga su pakitusiomis savybėmis. Dauguma tempimo sustandėjimo modelių įvertina betono įtempių... [toliau žr. visą tekstą]

[pt] A utilização de barras de polímero reforçado por fibras de vidro (glass fiber reinforced polymer, GFRP, em inglês) como reforço de estruturas de concreto armado, vem ganhando popularidade principalmente devido à sua resistência à corrosão e resistência mecânica. Entretanto, seu baixo módulo de elasticidade pode acarretar em problemas na estrutura em serviço, como grandes aberturas de fissuras e deflexões quando comparado com concreto armado por barras de aço. No presente estudo, um programa experimental foi realizado com o objetivo de avaliar a influência da adição de 10 kg/m3 de fibras de polipropileno (PP) em elementos de concreto armado por barras de GFRP submetidos à tração direta e flexão. Caracterização mecânica e ensaios de arrancamento (pullout) foram realizados para avaliar as propriedades dos materiais constituintes e de sua interface, respectivamente. A formação e evolução das fissuras, bem como o efeito de enrijecimento à tração no material proposto, foram avaliados por meio de ensaios de tração direta em prismas de concreto armado. Ensaios de flexão em quatro pontos foram realizados para investigar o desenvolvimento da deflexão com o carregamento, o padrão de fissuração e o comportamento momento-curvatura dos espécimes. Correlação de imagem digital (digital image correlation, DIC, em inglês) foi utilizada para monitoramento de deformações, distâncias e aberturas de fissuras relevantes para a análise. Por fim, os resultados dos ensaios de flexão foram comparados com um modelo analítico. Uma redução considerável da abertura de fissuras e um melhor comportamento de múltipla fissuração foi observado para os espécimes com adição de fibras, além de um pequeno acréscimo de rigidez à flexão. / [en] Glass-fiber reinforced polymer (GFRP) bars have been more often used in reinforced concrete (RC) structures mainly due to superior corrosion resistance and mechanical strength. However, the low modulus of elasticity leads to serviceability issues such as wider crack openings and larger deflections when compared to conventional RC. To improve the performance and allow for a more effective use of GFRP reinforcement, the addition of randomly disperse short polypropylene fibers (PP) to the concrete matrix is proposed. In the present study, an experimental program intending to investigate the flexural and tensile behavior of concrete members reinforced with GFRP bars and 10 kg/m3 of PP is carried out. Mechanical characterization and pull-out tests were carried out respectively to characterize the materials and interface between GFRP bar and concrete. Crack formation and growth, and tension stiffening effect in the proposed construction material were investigated by tension tests in reinforced concrete prisms. Four points bending tests were performed to evaluate the mid-span deflection, crack opening and moment-curvature relationship of the specimen. Digital image correlation was used to gather information about relevant data. It was proposed an analytical model to compare the results obtained in bending tests. A considerable reduction in crack openings, a better multiple cracks behavior and a slightly stiffer behavior was obtained due to fiber addition.

Software for designing structural frameworks in civil engineering is getting more and more complex. By offering reliable and efficient calculation methods, economic goals can be reached as well as the civil engineer's demands. Furthermore, opportunities for special developments are created and acceptance of new building systems is increased. The work presented here introduces a method for the physically nonlinear analysis of different composite beam designs for building and bridge structures which are subjected mainly to bending stresses under quasi-static, long-term loading. In addition, the utilization of these methods, including materials and modelling concepts, are shown in a newly developed software package. Present developments for composite construction and civil engineering requirements are the basis for the materials and modelling possibilities discussed. Particular attention is given to a realistic description of time and load dependent variables characterizing the state of the composite structures and their interactions. The selection of material models is based on experimental results. The main points of interest are concrete properties like creep, shrinkage, effluent hydration heat, cracking and boundary behaviour between different materials. Material behaviour under load and reload conditions was taken into account as well. The static solution is based on the incremental iterative application of the deformation method. Each iteration starts with the numerical integration of the beam system of differential equations. Based on the effects at the beam boundaries, the consideration of load and system modifications, as well as time dependent and independent constraint processes, is shown. An essential extension of the composite beam structure model is obtained using the system of differential equations for the flexible bond. Several detailed models are linked to a time dependent simulation for the entire system, which has been incorporated into a software package visualizing the time dependent variables. Finally, some practical application examples are presented. The validation of the implemented approach is demonstrated by correlating the calculated results with real life measurements. / Softwareentwicklungen für die Tragwerksplanung im Bauwesen werden zunehmend komplexer. Mit der Bereitstellung zuverlässiger und effizienter Berechnungsmethoden, welche sowohl ingenieurgemäße Ansprüche als auch wirtschaftliche Zielsetzungen erfüllen, werden neue Möglichkeiten für eine zielgerichtete Entwicklung oder verstärkte Etablierung von neueren Bauweisen geschaffen. Die vorliegende Arbeit beschreibt ein Verfahren zur physikalisch nichtlinearen Analyse vorwiegend biegebeanspruchter Verbund-Stabtragwerke des Hoch- und Brückenbaues unter quasi-statischer Langzeitbeanspruchung. Die zugehörige programmtechnische Umsetzung wird veranschaulicht. Die Modellierungsmöglichkeiten bezüglich der Werkstoffe orientieren sich an baupraktisch relevanten Erfordernissen sowie an den Besonderheiten und aktuellen Entwicklungen der Verbundbauweise. Besonderes Augenmerk wird zunächst auf eine realitätsnahe Darstellung der den Gebrauchs¬zustand von Verbundtragwerken charakterisierenden zeit- und lastabhängigen Einflussgrößen sowie ihrer Wechselwirkungen gelegt. Zur objektiven Beurteilung möglicher Materialmodelle wird zuerst auf das prinzipielle Verhalten im Experiment eingegangen, danach erfolgt eine Auswahl geeigneter Modelle. Schwerpunkte stellen dabei insbesondere die Betoneigenschaften Kriechen, Schwinden, abfließende Hydratationswärme und die Rissbildung sowie das Verbundverhalten zwischen den Werkstoffen dar. Diese Betrachtungen schließen das Werk¬stoffverhalten unter Be- und Entlastung ein. Die statische Lösung basiert auf einer inkrementell-iterativen Anwendung der Deformations¬methode. Ausgangspunkt der Berechnungen in einem Iterationsschritt ist die numerische Integration des Stab-Differentialgleichungssystems. Ausgehend von der Formulierung der Wirkungsgrößen an einem Stabrändern wird die Berücksichtigung von Belastungs- und Systemmodifikationen sowie zeitabhängigen und -unabhängigen Zwangsprozessen aufgezeigt. Eine wesentliche Erweiterung der Anwendungen im Stahl-Beton-Verbundbau stellt die Herleitung des Stab-Differentialgleichungssystems für den nachgiebigen Verbund dar. Mit der Verknüpfung einzelner Detailmodelle zu einem zeitabhängigen Lösungsverfahren und deren Integration in einen entsprechenden Softwareentwurf wird die programmtechnische Basis für eine modellhafte, zeitvariante Erfassung der beschreibenden Kenngrößen bereitgestellt. Ausgewählte praktische Beispiele demonstrieren abschließend die Anwendungsmöglichkeiten des Verfahrens und stellen die Verifikation der Simulationsergebnisse anhand von Messungen dar.

Software for designing structural frameworks in civil engineering is getting more and more complex. By offering reliable and efficient calculation methods, economic goals can be reached as well as the civil engineer's demands. Furthermore, opportunities for special developments are created and acceptance of new building systems is increased. The work presented here introduces a method for the physically nonlinear analysis of different composite beam designs for building and bridge structures which are subjected mainly to bending stresses under quasi-static, long-term loading. In addition, the utilization of these methods, including materials and modelling concepts, are shown in a newly developed software package. Present developments for composite construction and civil engineering requirements are the basis for the materials and modelling possibilities discussed. Particular attention is given to a realistic description of time and load dependent variables characterizing the state of the composite structures and their interactions. The selection of material models is based on experimental results. The main points of interest are concrete properties like creep, shrinkage, effluent hydration heat, cracking and boundary behaviour between different materials. Material behaviour under load and reload conditions was taken into account as well. The static solution is based on the incremental iterative application of the deformation method. Each iteration starts with the numerical integration of the beam system of differential equations. Based on the effects at the beam boundaries, the consideration of load and system modifications, as well as time dependent and independent constraint processes, is shown. An essential extension of the composite beam structure model is obtained using the system of differential equations for the flexible bond. Several detailed models are linked to a time dependent simulation for the entire system, which has been incorporated into a software package visualizing the time dependent variables. Finally, some practical application examples are presented. The validation of the implemented approach is demonstrated by correlating the calculated results with real life measurements. / Softwareentwicklungen für die Tragwerksplanung im Bauwesen werden zunehmend komplexer. Mit der Bereitstellung zuverlässiger und effizienter Berechnungsmethoden, welche sowohl ingenieurgemäße Ansprüche als auch wirtschaftliche Zielsetzungen erfüllen, werden neue Möglichkeiten für eine zielgerichtete Entwicklung oder verstärkte Etablierung von neueren Bauweisen geschaffen. Die vorliegende Arbeit beschreibt ein Verfahren zur physikalisch nichtlinearen Analyse vorwiegend biegebeanspruchter Verbund-Stabtragwerke des Hoch- und Brückenbaues unter quasi-statischer Langzeitbeanspruchung. Die zugehörige programmtechnische Umsetzung wird veranschaulicht. Die Modellierungsmöglichkeiten bezüglich der Werkstoffe orientieren sich an baupraktisch relevanten Erfordernissen sowie an den Besonderheiten und aktuellen Entwicklungen der Verbundbauweise. Besonderes Augenmerk wird zunächst auf eine realitätsnahe Darstellung der den Gebrauchs¬zustand von Verbundtragwerken charakterisierenden zeit- und lastabhängigen Einflussgrößen sowie ihrer Wechselwirkungen gelegt. Zur objektiven Beurteilung möglicher Materialmodelle wird zuerst auf das prinzipielle Verhalten im Experiment eingegangen, danach erfolgt eine Auswahl geeigneter Modelle. Schwerpunkte stellen dabei insbesondere die Betoneigenschaften Kriechen, Schwinden, abfließende Hydratationswärme und die Rissbildung sowie das Verbundverhalten zwischen den Werkstoffen dar. Diese Betrachtungen schließen das Werk¬stoffverhalten unter Be- und Entlastung ein. Die statische Lösung basiert auf einer inkrementell-iterativen Anwendung der Deformations¬methode. Ausgangspunkt der Berechnungen in einem Iterationsschritt ist die numerische Integration des Stab-Differentialgleichungssystems. Ausgehend von der Formulierung der Wirkungsgrößen an einem Stabrändern wird die Berücksichtigung von Belastungs- und Systemmodifikationen sowie zeitabhängigen und -unabhängigen Zwangsprozessen aufgezeigt. Eine wesentliche Erweiterung der Anwendungen im Stahl-Beton-Verbundbau stellt die Herleitung des Stab-Differentialgleichungssystems für den nachgiebigen Verbund dar. Mit der Verknüpfung einzelner Detailmodelle zu einem zeitabhängigen Lösungsverfahren und deren Integration in einen entsprechenden Softwareentwurf wird die programmtechnische Basis für eine modellhafte, zeitvariante Erfassung der beschreibenden Kenngrößen bereitgestellt. Ausgewählte praktische Beispiele demonstrieren abschließend die Anwendungsmöglichkeiten des Verfahrens und stellen die Verifikation der Simulationsergebnisse anhand von Messungen dar.