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This paper presents the possibilities of determining the range of stresses preceding the critical destruction process in cement composites with the use of micro-events identified by means of a sound spectrum. The presented test results refer to the earlier papers in which micro-events (destruction processes) were identified but without determining the stress level of their occurrence. This paper indicates a correlation of 2/3 of the stress level corresponding to the elastic range with the occurrence of micro-events in traditional and quasi-brittle composites. Tests were carried out on beams (with and without reinforcement) subjected to four-point bending. In summary, it is suggested that the conclusions can be extended to other test cases (e.g., compression strength), which should be confirmed by the appropriate tests. The paper also indicates a need for further research to identify micro-events. The correct recognition of micro-events is important for the safety and durability of traditional and quasi-brittle cement composites.

The detailed analytical and experimental investigation of the fracture behaviour of quasi-brittle materials is an endeavour which has been ongoing worldwide for many years. Such materials are usually characterized in terms of their mechanical fracture parameters, which are determined based on the evaluation of quasi-static fracture experiments. One of the most commonly used building materials with a quasi-brittle response is concrete, which is most often based on a cement matrix. It is sometimes also necessary to characterize concrete included in existing structures. In this case, test specimens are obtained by core drilling, and the investigation is conducted with the requirement to maximize the number of parameters obtained while minimizing the number of test specimens drilled from the structure. This paper focuses on the mechanical fracture parameters of core-drilled specimens taken from a selected concrete structure. Tests were performed on cylindrical specimens with a chevron-notched stress concentrator in the three-point bending configuration in order to determine modulus of elasticity, fracture toughness and fracture energy. Subsequently, theoretical compressive strength was estimated and tests for the determination of compressive strength values were performed focusing on dependence on the slenderness ratio, i.e. the relationship between the compressive strength and the length to diameter ratio of the cylindrical specimens. In relation to the obtained mechanical fracture parameters, selected specimens were analysed and three-dimensionally characterized via high-resolution X-ray computed tomography.

This paper presents the possibilities of determining the range of stresses preceding the critical destruction process in cement composites with the use of micro-events identified by means of a sound spectrum. The presented test results refer to the earlier papers in which micro-events (destruction processes) were identified but without determining the stress level of their occurrence. This paper indicates a correlation of 2/3 of the stress level corresponding to the elastic range with the occurrence of micro-events in traditional and quasi-brittle composites. Tests were carried out on beams (with and without reinforcement) subjected to four-point bending. In summary, it is suggested that the conclusions can be extended to other test cases (e.g., compression strength), which should be confirmed by the appropriate tests. The paper also indicates a need for further research to identify micro-events. The correct recognition of micro-events is important for the safety and durability of traditional and quasi-brittle cement composites.

The detailed analytical and experimental investigation of the fracture behaviour of quasi-brittle materials is an endeavour which has been ongoing worldwide for many years. Such materials are usually characterized in terms of their mechanical fracture parameters, which are determined based on the evaluation of quasi-static fracture experiments. One of the most commonly used building materials with a quasi-brittle response is concrete, which is most often based on a cement matrix. It is sometimes also necessary to characterize concrete included in existing structures. In this case, test specimens are obtained by core drilling, and the investigation is conducted with the requirement to maximize the number of parameters obtained while minimizing the number of test specimens drilled from the structure. This paper focuses on the mechanical fracture parameters of core-drilled specimens taken from a selected concrete structure. Tests were performed on cylindrical specimens with a chevron-notched stress concentrator in the three-point bending configuration in order to determine modulus of elasticity, fracture toughness and fracture energy. Subsequently, theoretical compressive strength was estimated and tests for the determination of compressive strength values were performed focusing on dependence on the slenderness ratio, i.e. the relationship between the compressive strength and the length to diameter ratio of the cylindrical specimens. In relation to the obtained mechanical fracture parameters, selected specimens were analysed and three-dimensionally characterized via high-resolution X-ray computed tomography.

The paper deals with the analysis of the fractal dimension of fracture surfaces of concrete specimens tested in a three-point bending configuration. Fifteen representative specimens were chosen out of a bigger set for the fractal dimension analysis. Their fracture surfaces were scanned by 2D optical profilometry and analysed by the FracDiM software created in the Java programming language. The resulting values of fractal dimensions for specimens of three different sizes are presented.

The paper deals with the analysis of the fractal dimension of fracture surfaces of concrete specimens tested in a three-point bending configuration. Fifteen representative specimens were chosen out of a bigger set for the fractal dimension analysis. Their fracture surfaces were scanned by 2D optical profilometry and analysed by the FracDiM software created in the Java programming language. The resulting values of fractal dimensions for specimens of three different sizes are presented.

The paper deals with the analysis of the fractal dimension of fracture surfaces of concrete specimens tested in a three-point bending configuration. Fifteen representative specimens were chosen out of a bigger set for the fractal dimension analysis. Their fracture surfaces were scanned by 2D optical profilometry and analysed by the FracDiM software created in the Java programming language. The resulting values of fractal dimensions for specimens of three different sizes are presented.

The paper deals with the analysis of the fractal dimension of fracture surfaces of concrete specimens tested in a three-point bending configuration. Fifteen representative specimens were chosen out of a bigger set for the fractal dimension analysis. Their fracture surfaces were scanned by 2D optical profilometry and analysed by the FracDiM software created in the Java programming language. The resulting values of fractal dimensions for specimens of three different sizes are presented.

Knowledge of the mechanical and primarily fracture parameters of composites with a brittle matrix is essential for the quantification of their resistance to crack initiation and growth, and also for the specification of material model parameters employed for the simulation of the quasi-brittle behavior of structures made from this type of composite. Therefore, the main target of this paper is to quantify the mechanical fracture parameters of alkali-activated slag composites with steel microfibers and the contribution of the matrix to their fracture response. The first alkali-activated slag composite was a reference version without fibers; the others incorporated steel microfibers amounting to 5, 10, 15 and 20% by weight of the slag. Prism specimens with an initial central edge notch were used to perform the three-point bending fracture tests. Load vs. displacement (deflection at midspan) and load vs. crack mouth opening displacement diagrams were recorded during the fracture tests. The obtained diagrams were employed as inputs for parameter identification, the aim of which was to transfer the fracture test response data to the desired material parameters. Values were also determined for fracture parameters using the effective crack model, work-of-fracture method and double-K fracture model. All investigated mechanical fracture parameters were improved by the addition of steel microfibers to the alkali-activated matrix. Based on the obtained results, the addition of 10 to 15% of microfibers by weight is optimal from the point of view of the enhancement of the fracture parameters of alkali-activated slag composite

Fine-grained cement-based composites used in civil engineering and construction industry are usually made of cement-based matrix and natural aggregate (such as sand, gravel, crushed stone, etc.). Red ceramic waste agggregate is considered as a perspective replacement of a part of natural aggregate in modern environmentally oriented building materials. Fine-grained cement compositewith natural aggregate partially replaced by ceramic waste aggregate usually show different mechanical fracture characteristics from ordinary fine-grained concrete. The specimens were tested at six different ages. This was the reason for conducting the research programme. Altogether, 6 fine-grained cement mixtures with various proportions of natural and red ceramic waste aggregate were prepared. The aim of this paper is to present and compare mechanical fracture properties obtained from static and fatigue tests. Bulk density, flexural and compressive cube strength, fracture toughness and fatigue properties (SN Wöhler curve) were of special interest. All of these tests are important for a practical application of concrete with ceramic aggregate for structures. All the results were statistically analysed and they showed that the fatigue and mechanical fracture properties were improved or at least kept up with the increasing levels of red ceramic waste aggregate. Environmental impact of application in construction industry of compositesin question is discussed.

Knowledge of the mechanical and primarily fracture parameters of composites with a brittle matrix is essential for the quantification of their resistance to crack initiation and growth, and also for the specification of material model parameters employed for the simulation of the quasi-brittle behavior of structures made from this type of composite. Therefore, the main target of this paper is to quantify the mechanical fracture parameters of alkali-activated slag composites with steel microfibers and the contribution of the matrix to their fracture response. The first alkali-activated slag composite was a reference version without fibers; the others incorporated steel microfibers amounting to 5, 10, 15 and 20% by weight of the slag. Prism specimens with an initial central edge notch were used to perform the three-point bending fracture tests. Load vs. displacement (deflection at midspan) and load vs. crack mouth opening displacement diagrams were recorded during the fracture tests. The obtained diagrams were employed as inputs for parameter identification, the aim of which was to transfer the fracture test response data to the desired material parameters. Values were also determined for fracture parameters using the effective crack model, work-of-fracture method and double-K fracture model. All investigated mechanical fracture parameters were improved by the addition of steel microfibers to the alkali-activated matrix. Based on the obtained results, the addition of 10 to 15% of microfibers by weight is optimal from the point of view of the enhancement of the fracture parameters of alkali-activated slag composite

Fine-grained cement-based composites used in civil engineering and construction industry are usually made of cement-based matrix and natural aggregate (such as sand, gravel, crushed stone, etc.). Red ceramic waste agggregate is considered as a perspective replacement of a part of natural aggregate in modern environmentally oriented building materials. Fine-grained cement compositewith natural aggregate partially replaced by ceramic waste aggregate usually show different mechanical fracture characteristics from ordinary fine-grained concrete. The specimens were tested at six different ages. This was the reason for conducting the research programme. Altogether, 6 fine-grained cement mixtures with various proportions of natural and red ceramic waste aggregate were prepared. The aim of this paper is to present and compare mechanical fracture properties obtained from static and fatigue tests. Bulk density, flexural and compressive cube strength, fracture toughness and fatigue properties (SN Wöhler curve) were of special interest. All of these tests are important for a practical application of concrete with ceramic aggregate for structures. All the results were statistically analysed and they showed that the fatigue and mechanical fracture properties were improved or at least kept up with the increasing levels of red ceramic waste aggregate. Environmental impact of application in construction industry of compositesin question is discussed.

A study on the accuracy of an approximation of the stress field in a cracked body is presented. Crack-tip stress tensor is expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (ODM) for which results from finite element (FE) method computation are usually taken as inputs. Main attention is paid to a detailed analysis of a suitable selection of FE nodes whose results serve as the inputs to the employed method. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen body. Comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical WPS approximation of the stress field based on the FE results and the backward reconstruction of the field (again using WPS) from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study

Structural concrete of the building of Vítkovice railway station from 1970s is characterized via mechanical fracture parameters. In this paper, six core-drilled cylindrical specimens with diameter of 75 mm were provided by a Chevron type notch of depth of 12 mm. Three-point bending fracture tests were conducted on these specimens supported as beams with the span of 170 mm. Load vs. deflection and load vs. crack mouth opening displacement diagrams were recorded from which modulus of elasticity (E), fracture toughness (KIc) and fracture energy (GF) were determined using linear elastic fracture mechanics approach and work-offracture method. Mean values of these parameters (with their coefficient of variability) were obtained as follows: E = 39.4 GPa (29.1 %), KIc = 0.90 MPa·m1/2 (18.5 %), GF = 174.0 J/m2 (26.0 %). These parameters can serve as first guess or indicative values for structural assessment and life-time predictions.

A study on the approximation of the stress field in the vicinity of crack tip in a compact tension specimen made from Al 2024-T351 is presented. Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over deterministic method (ODM) for which displacements data obtained experimentally via optical measurements are taken as inputs. The stress fields reconstructed based on the displacement data obtained experimentally by means of optical measurements are verified by means of the stress field approximations derived for the normalized CT specimen via hybrid elements

A study on the approximation of the stress field in the vicinity of crack tip in a compact tension specimen made from Al 2024-T351 is presented. Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over deterministic method (ODM) for which displacements data obtained experimentally via optical measurements are taken as inputs. The stress fields reconstructed based on the displacement data obtained experimentally by means of optical measurements are verified by means of the stress field approximations derived for the normalized CT specimen via hybrid elements

A study on the accuracy of an approximation of the stress field in a cracked body is presented. Crack-tip stress tensor is expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (ODM) for which results from finite element (FE) method computation are usually taken as inputs. Main attention is paid to a detailed analysis of a suitable selection of FE nodes whose results serve as the inputs to the employed method. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen body. Comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical WPS approximation of the stress field based on the FE results and the backward reconstruction of the field (again using WPS) from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study

Structural concrete of the building of Vítkovice railway station from 1970s is characterized via mechanical fracture parameters. In this paper, six core-drilled cylindrical specimens with diameter of 75 mm were provided by a Chevron type notch of depth of 12 mm. Three-point bending fracture tests were conducted on these specimens supported as beams with the span of 170 mm. Load vs. deflection and load vs. crack mouth opening displacement diagrams were recorded from which modulus of elasticity (E), fracture toughness (KIc) and fracture energy (GF) were determined using linear elastic fracture mechanics approach and work-offracture method. Mean values of these parameters (with their coefficient of variability) were obtained as follows: E = 39.4 GPa (29.1 %), KIc = 0.90 MPa·m1/2 (18.5 %), GF = 174.0 J/m2 (26.0 %). These parameters can serve as first guess or indicative values for structural assessment and life-time predictions.

The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city., The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city.

The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city., The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city.

The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city., The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city.

The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city., The unprecedented growth of today’s cities together with increased population mobility are fueling the avalanche in the numbers of vehicles on the roads. This development led to the new challenges for the traffic management, including the mitigation of road congestion, accidents, and air pollution. Over the last decade, researchers have been focusing their efforts on leveraging the recent advances in sensing, communications, and dynamic adaptive technologies to prepare the deployed road traffic management systems (TMS) for resolving these important challenges in future smart cities. However, the existing solutions may still be insufficient to construct a reliable and secure TMS that is capable of handling the anticipated influx of the population and vehicles in urban areas. Along these lines, this work systematically outlines a perspective on a novel modular environment for traffic modeling, which allows to recreate the examined road networks in their full resemblance. Our developed solution is targeted to incorporate the progress in the Internet of Things (IoT) technologies, where low-power, embedded devices integrate as part of a next-generation TMS. To mimic the real traffic conditions, we recreated and evaluated a practical traffic scenario built after a complex road intersection within a large European city.

A quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. The stress field approximation using Williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. An automatic utility created to determine the values of coefficients of the higher order terms of Williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode I test geometry is one of the tested procedures. The second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated Williams expansion. The developed procedures are based on the support of Java programming language and considerably simplify analyses of the mechanical fields’ description in a farther distance from the crack-tip. The presented research is focused on optimization of selection of FE nodal results for improvement of accuracy of the approximation.

A quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. The stress field approximation using Williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. An automatic utility created to determine the values of coefficients of the higher order terms of Williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode I test geometry is one of the tested procedures. The second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated Williams expansion. The developed procedures are based on the support of Java programming language and considerably simplify analyses of the mechanical fields’ description in a farther distance from the crack-tip. The presented research is focused on optimization of selection of FE nodal results for improvement of accuracy of the approximation.

For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in large distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. The stress intensity factor K, T-stress and even higher-order terms of William series were determined and subsequently utilized for analytical approximation of the stress field., For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in large distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. The stress intensity factor K, T-stress and even higher-order terms of William series were determined and subsequently utilized for analytical approximation of the stress field.

For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in large distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. The stress intensity factor K, T-stress and even higher-order terms of William series were determined and subsequently utilized for analytical approximation of the stress field., For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in large distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. The stress intensity factor K, T-stress and even higher-order terms of William series were determined and subsequently utilized for analytical approximation of the stress field.

This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains., This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains.

This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains., This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains.

This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains., This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains.

This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains., This paper is a contribution to the discussion about the fall of the New York World Trade Center (WTC) towers in 2001. The differential equation of the collapse of a high building is derived by taking into account many infuences. A computer simulation of the collapse the WTC building is presented using two independent programs with parameter variations. The results of both, differential equation and computer simulation, are compared resulting correspondences. The authors consider certain probable parameters with would have lessened both the observable speed of the collapse and its extent, however uncertainty regarding the magnitudes of the parameters remains.

Práce se zabývá fyzikálním a numerickým modelováním zmenšeniny konstrukce komínu a jeho následné demolice. Vlastnosti zmenšeného fyzikálního modelu, tvořeného dřevěnými kostkami, jsou zkoumány a ověřeny pomocí experimentů. Dále jsou tyto experimenty simulovány numericky v programu FyDiK. Numerický model je zjednodušen na 2D problém, přičemž jsou do výpočtu zahrnuty dynamické jevy. Dále je testována shoda výpočtového modelu s reálným experimentem. Cílem práce je dosažení co největší možné shody fyzikálních a numerických modelů., The thesis deals with physical and numerical modelling of downsized model of chimney and its demolition. The properties of downsized physical model, which is made of wooden cubes, are being researched and experimentally tested. The physical experiments are then designed using software FyDiK. Numerical Model is simplified to 2D problem, whereas the problem includes dynamic effects. Conformity of designed software model and physical experiment is tested. The aim of this thesis is to achive the best possible conformity of physical and numerical models.

Diplomová práce se zabývá numerickým modelováním lanového skluzu a jeho experimentálním ověřením v malém měřítku. Je provedena identifikace vlastností experimentálního lanového skluzu a následně porovnány výsledky s výstupy numerického modelu. Cílem je dosáhnout zhodnocení schopnosti numerického modelu simulovat lanový skluz., The diploma thesis deals with the numerical modeling of the zip-line and its experimental verification on a small scale. An experimental zip-line is identified and then the results are compared with the numerical model outputs. The goal is to validate abilities of the numerical model in the case of simulation of a zip-line.

Hlavním tématem práce je nalezení optimálních průřezů pro danou rámovou konstrukci a nabídnout investorovi nejlepší řešení pro realizaci. Cílem je obecně dostat do podvědomí statické chování této konstrukce, zaznamenat průběhy vnitřních sil při měnících se parametrech (zatížení, profil…) a ve výsledku navrhnout ideální řešení pro daný případ. Práce kombinuje statiku s navrhováním ocelových konstrukcí v praxi a mohla by posloužit jako informační zdroj pro praktické navrhování rámových konstrukcí s možností rozšiřování o další vstupní parametry a okrajové podmínky., The main subject of this work is to find ideal solution of the steel frame structure and offer the best solution to investors. The aim is to get know how steel structures works, write down internal forces when parametres are changing. Parameters can be profiles, loads or many others. The output should be perfectly optimized construction. The content combines theory of structural mechanics and designing steel structures. This project could be very useful in practice designing of steel frame structures with the possibility of expansion by other parameters.

Táto práca sa snaží popísať vplyv voľby základnej sústavy na riešenie staticky neurčitých konštrukcií pomocou silovej metódy. Posúdenie základných sústav je založené na podmienenosti matice pretvárnych súčiniteľov popísanej troma číslami podmienenosti. Každá zo štyroch vybraných staticky neurčitých konštrukcií je skúmaná mierne odlišne, na základe jej špecifických charakteristík. Výsledkom práce je niekoľko poznatkov o závislosti podmienenosti sústavy od niektorých parametrov konštrukcie a jej vplyve na výsledky výpočtu silovou metódou., This bachelor thesis deals with effect of chosen basic determinate structure on solution of statically indeterminate structures obtained by using force method. Evaluation of basic determinate structure is based on conditioning of flexibility matrix, defined by three different condition numbers. Each of the four analyzed structures is examined in different way, due to their individual characteristics. As a result, few findings about dependence of conditioning of used basic structure on structures parameters and its effect on solution by force method were obtained.

Tato práce se zabývá zkoumáním tvaru skutečné klenby a jejím modelováním. Modelování vychází z výpočtu tlakové čáry pomocí řetízkového modelu. Je zde zkoumáno, zdali stavitelé mohli v minulosti odvozovat tvar klenby pomocí řetězu, na který zavěšovali závaží. Pro srovnání skutečné klenby s modelem byla vybrána vchodová klenba kostela svatého Jakuba v Brně., Thesis deals with the study of the shape of the actual vault and its modeling. Modeling is based on the computation of the pressure line using a chain model. It is investigated whether the builders could in the past derive the shape of the vault by means of a chain on which they suspended the weights. To compare the actual arch with the model, the entrance vault of St. Jacob's Church in Brno was selected.

Práce se zabývá fyzikálním a numerickým modelováním zmenšeniny konstrukce komínu a jeho následné demolice. Vlastnosti zmenšeného fyzikálního modelu, tvořeného dřevěnými kostkami, jsou zkoumány a ověřeny pomocí experimentů. Dále jsou tyto experimenty simulovány numericky v programu FyDiK. Numerický model je zjednodušen na 2D problém, přičemž jsou do výpočtu zahrnuty dynamické jevy. Dále je testována shoda výpočtového modelu s reálným experimentem. Cílem práce je dosažení co největší možné shody fyzikálních a numerických modelů., The thesis deals with physical and numerical modelling of downsized model of chimney and its demolition. The properties of downsized physical model, which is made of wooden cubes, are being researched and experimentally tested. The physical experiments are then designed using software FyDiK. Numerical Model is simplified to 2D problem, whereas the problem includes dynamic effects. Conformity of designed software model and physical experiment is tested. The aim of this thesis is to achive the best possible conformity of physical and numerical models.

Cílem předkládané práce je vytvoření nelineárního dynamického modelu volného prutu zatíženého sledující silou. Reálným předobrazem modelu je štíhlá pružná raketa zatížená tahem reaktivního motoru. Vzhledem k povaze úlohy musí model umožňovat velké deformace. Dalšími požadavky na aplikovaný model je vystižení materiálového tlumení, tlumení vlivem interakce modelu s okolním prostředím a zavedení vlivu gravitačního pole. Model bude v budoucnu použit pro studium pokritického chování uvažované konstrukce. Proto je jednou z priorit nízká časová náročnost simulace. Vlastní vytvořená formulace numerického modelu bude implementována v programovacím jazyku Java. Pro zobrazení průběhu simulace a sledování stavových proměnných bude vytvořeno odpovídající grafické prostředí. Správnost odvozeného modelu bude ověřena porovnáním vybraných hodnot s analytickým řešením., The aim of the presented thesis is to create a non-linear dynamical model of a free rod loaded by a follower force. The model is inspired by a slender flexible missile loaded by an end thrust. Because of the nature of the problem, the model has to be capable of large deflections. Another requirements on the model are to implement material the damping and the damping due to the interaction of the model with a surrounding medium and the influence of gravitational field. In the future, the model will be used for examination of the post-critical behavior of such construction. Therefore low computational demands of the simulation are required. The derived formulation of the numerical model will be implemented using the Java programming language. For observation of the simulation process and for monitoring of the state variables, an appropriate graphic interface will be created. The accuracy of the derived model will be verified by the comparison of selected values to the analytical solution.

Práce se zabývá sestavením a řešením diskrétního mechanického modelu z dynamického hlediska. Jako příklad dynamické soustavy ze skutečného světa, kterou lze takto modelovat, je zvoleno dynamické chování luku a šípu při výstřelu. Pro účely řešení zvoleného modelu je vyvinut specializovaný počítačový program, schopný tuto úlohu dynamicky simulovat. Pomocí této metody a vyvinuté aplikace byla provedena simulace výstřelu z vybraného přímého luku o konkrétních parametrech. Byly porovnány dvě varianty tvaru lučiště., The thesis deals with constructing and solving a discrete mechanical model from the point of view of dynamics. As an example of a real-world problem which can be approximated in this way, the dynamical behaviour of a bow and arrow during loose have been chosen. In order to solve this particular type of model, a specialized piece of software has been developed. This method and software have been deployed to simulate shooting a straight bow of specific parametres. Two variants for the shape of the bowstaff have been evaluated.

Úkolem této práce bylo vyhodnocení rozsáhlé série vybraných lomových zkoušek tříbodovým ohybem těles z drátkobetonu stáří 7, 28 a 126 dní. V první fázi byla naměřená data upravena programem GTDiPS. Dále proběhla aproximace předpokládaného příspěvku drátků v zatěžovacím diagramu pomocí polynomické regresní funkce. Odečtením aproximované části od celého diagramu byl získán vliv matrice. Použitím programu StiCrack byly získány hodnoty modulu pružnosti, lomové houževnatosti a lomové energie, a to z původního diagramu, i z diagramu vystihujícího chování matrice. Všechny výsledky jsou přehledně vyhodnoceny v tabulkách., The goal of this thesis was evaluation of extensive series of selected three point bending tests on fibre reinforced concrete specimens of ages 7, 28 and 126 days. First the measured data were adjusted by GTDiPS software. Than the assumed contribution of fibres in load--deflection diagram was approximated by regressive function. Contribution of matrix was calculated by deducting the approximated part from full diagram. Using StiCrack software the Young modulus, fracture toughness and fracture energy were calculated for both original and approximated diagram. All results were evaluated and tabled.

Práce se zabývá řešením diskrétního dynamického 2D modelu komína při jeho demolici. Konkrétním cílem práce je objasnění pozorovaného fenoménu zlomení komína při pádu. V rámci práce je komín navržen a řešen v programu FyDiK, který umožňuje výpočty úloh se zahrnutím dynamických jevů. Pro vzájemné ověření výsledků byly vypracovány dva modely komína., The thesis deals with solving of a discrete dynamic 2D model of a chimney during its demolition. Specific goal of the thesis is to clarify observed phenomenon that is a break of the chimney while falling. The model of the chimney is designed and solved using software FyDiK which is able to solve dynamic effects. For verification of results, two models of chimney have been designed.

Práca sa zaoberá návrhom optimalizovaných tvarov nosníkov, ich následnou výrobou pomocou technológie 3D tlače a experimentálnym overovaním ich vlastností. Sleduje sa spôsob porušenia pri dosiahnutí medznej pevnosti. Informácie získané pri experimentoch sú zrovnávané s predpokladmi z numerických metód., The thesis deals with design of beams of optimized shapes, which are than manufactured by 3D printer and their features are experimentally verified. When the limit strength of a given component is reached, ways of fracture development are observed. Information obtained from the experiments are then compared with assumptions generated by numerical methods.

Bakalářské práce se věnuje navržením dvou různých variant konstrukce domu ve tvaru koule. Návrhy konstrukcí vznikali v zájmu investora, s kterým byli obě varianty konzultovány a mají sloužit jako ideový návrh pro budoucí projekční činnost. Varianty se liší druhem použitého materiálu a geometrií nosné konstrukce., This bachelor thesis is dedicated to designing of two different versions of the construction for a spherical house. The design was developed upon an interest of the investor, with whom were both versions also consulted and is supposed to lead to an actual project and realization. The two versions will differ in usage of building materials and the construction geometry.

Předkládaná práce poukazuje na pozoruhodný potenciál fyzikálně diskretizačního lattice modelu FyDiK pro prostorové modelování nelineárních problémů stavební mechaniky. K dosažení cílů práce byla naprogramována aplikace, implementující model FyDiK společně s 3D grafickým uživatelským prostředím zajišťující sestavení modelu pružinových sítí. Ta byla následně využita k modelování vzniku trhlin a lomu v betonových vzorcích a k modelování plastizace stojiny ocelového I profilu, přičemž výpočty byly realizovány prostřednictvím masivní paralelizace na platformě CUDA. V úvodní části jsou nejprve představeny základní principy, z nichž práce vychází. Následně jsou podrobněji rozebrány jednotlivé prvky modelu a přiblížena problematika paralelizace prostřednictvím grafických karet. Vytvoření potřebného software a ladění modelu na uvedených materiálech se věnuje další část, která je následována vyhodnocením dosažených výsledků ve srovnání s jinými programy pro modelování. Závěrem jsou shrnuty dosažené výsledky a předestřeny další možnosti vývoje představeného způsobu modelování., The presented work highlights the remarkable potential of physical discretization – lattice model FyDiK in three-dimensional modelling of non-linear problems in structural mechanics. To achieve the objectives a software application, that implements the model FyDiK along with the 3D graphical user interface has been developed and thus is able to assemble a spring network model. Such a model was used for modelling the formation of cracks and fracture in the concrete specimens and also to model a plastic behaviour of steel I-beam. The calculations were performed by a massive parallelization on CUDA platform. In the first part the basic principles on which the work is based are introduced. Subsequently, a detailed description of individual parts of the model and the issue of parallelization by graphics cards are presented. In the next part the creation of the required software and improving of the model properties of mentioned materials are described. That is followed by evaluation of the achieved results with the comparison of other modelling software. The conclusion summarizes the achievements and suggestions for the further development possibilities of the presented method of modelling.

Práce se zabývá řešením diskrétního dynamického 2D modelu komína při jeho demolici. Konkrétním cílem práce je objasnění pozorovaného fenoménu zlomení komína při pádu. V rámci práce je komín navržen a řešen v programu FyDiK, který umožňuje výpočty úloh se zahrnutím dynamických jevů. Pro vzájemné ověření výsledků byly vypracovány dva modely komína., The thesis deals with solving of a discrete dynamic 2D model of a chimney during its demolition. Specific goal of the thesis is to clarify observed phenomenon that is a break of the chimney while falling. The model of the chimney is designed and solved using software FyDiK which is able to solve dynamic effects. For verification of results, two models of chimney have been designed.

Práca sa zaoberá návrhom optimalizovaných tvarov nosníkov, ich následnou výrobou pomocou technológie 3D tlače a experimentálnym overovaním ich vlastností. Sleduje sa spôsob porušenia pri dosiahnutí medznej pevnosti. Informácie získané pri experimentoch sú zrovnávané s predpokladmi z numerických metód., The thesis deals with design of beams of optimized shapes, which are than manufactured by 3D printer and their features are experimentally verified. When the limit strength of a given component is reached, ways of fracture development are observed. Information obtained from the experiments are then compared with assumptions generated by numerical methods.

Diplomová práce se zabývá numerickým modelováním lanového skluzu a jeho experimentálním ověřením v malém měřítku. Je provedena identifikace vlastností experimentálního lanového skluzu a následně porovnány výsledky s výstupy numerického modelu. Cílem je dosáhnout zhodnocení schopnosti numerického modelu simulovat lanový skluz., The diploma thesis deals with the numerical modeling of the zip-line and its experimental verification on a small scale. An experimental zip-line is identified and then the results are compared with the numerical model outputs. The goal is to validate abilities of the numerical model in the case of simulation of a zip-line.

Práce se zabývá simulací dynamického systému s kontaktní úlohou v podobě kontaktu cyklistické duše a pláště při nafukování a zatěžování kola. Teoretická část objasňuje základní pojmy z problematiky dynamických systémů a kontaktních úloh a představuje metody použité pro simulace v praktické části. V praktické části je popsán proces převodu reálného systému ráfek-duše-plášť na výpočetní model v podobě zjištění jeho geometrie a materiálových charakteristik jako spojitého objektu a jeho následné diskretizace, představen program použítý pro simulace (FyDiK 2D) a provedeny vybrané simulace a jejich vyhodnocení., This work deals with the simulation of a dynamical system with a contact problem represented by the contact of a bicycle tube with a tire during inflation and loading of a bicycle wheel. In the first part the work defines the basics of dynamical systems a contact problems and introduces the methods used for following simulations. The practical part of the work desribes the process of converting a real system of rim-tube-tire objects to a computional model by determining its geometry and material characteristics as a continuous object and its subsequent discretization, introduces the program used for the subsequent simulations (FyDiK 2D) and shows the results of said simulations.

Předkládaná práce poukazuje na pozoruhodný potenciál fyzikálně diskretizačního lattice modelu FyDiK pro prostorové modelování nelineárních problémů stavební mechaniky. K dosažení cílů práce byla naprogramována aplikace, implementující model FyDiK společně s 3D grafickým uživatelským prostředím zajišťující sestavení modelu pružinových sítí. Ta byla následně využita k modelování vzniku trhlin a lomu v betonových vzorcích a k modelování plastizace stojiny ocelového I profilu, přičemž výpočty byly realizovány prostřednictvím masivní paralelizace na platformě CUDA. V úvodní části jsou nejprve představeny základní principy, z nichž práce vychází. Následně jsou podrobněji rozebrány jednotlivé prvky modelu a přiblížena problematika paralelizace prostřednictvím grafických karet. Vytvoření potřebného software a ladění modelu na uvedených materiálech se věnuje další část, která je následována vyhodnocením dosažených výsledků ve srovnání s jinými programy pro modelování. Závěrem jsou shrnuty dosažené výsledky a předestřeny další možnosti vývoje představeného způsobu modelování., The presented work highlights the remarkable potential of physical discretization – lattice model FyDiK in three-dimensional modelling of non-linear problems in structural mechanics. To achieve the objectives a software application, that implements the model FyDiK along with the 3D graphical user interface has been developed and thus is able to assemble a spring network model. Such a model was used for modelling the formation of cracks and fracture in the concrete specimens and also to model a plastic behaviour of steel I-beam. The calculations were performed by a massive parallelization on CUDA platform. In the first part the basic principles on which the work is based are introduced. Subsequently, a detailed description of individual parts of the model and the issue of parallelization by graphics cards are presented. In the next part the creation of the required software and improving of the model properties of mentioned materials are described. That is followed by evaluation of the achieved results with the comparison of other modelling software. The conclusion summarizes the achievements and suggestions for the further development possibilities of the presented method of modelling.

Cílem předkládané práce je vytvoření počítačové aplikace, která spočítá kritické zatížení pro ztrátu stability rovinných prutových konstrukcí pomocí metody konečných prvků. Úvod je věnován seznámení se s problematikou a odvození nezbytných vztahů. Poté jsou popsány všechny důležité kroky a numerické metody nezbytné pro správný chod aplikace. Nakonec je provedena analýza několika vybraných úloh a výsledky jsou porovnány se známými analytickými řešeními a s dalšími dostupnými aplikacemi., The aim of this theses is to create application, which is able to calculate buckling load of structure made from 1D bar elements, using finite element method. introduction is devoted to basic principles of buckling and derivation of necessary formulas. Then are described all operations and numerical methods needed for the application. At the and is in detail analyzed few structures and results are compared with known solutions or with other applications.

Cílem předkládané práce je vytvoření počítačové aplikace, která spočítá kritické zatížení pro ztrátu stability rovinných prutových konstrukcí pomocí metody konečných prvků. Úvod je věnován seznámení se s problematikou a odvození nezbytných vztahů. Poté jsou popsány všechny důležité kroky a numerické metody nezbytné pro správný chod aplikace. Nakonec je provedena analýza několika vybraných úloh a výsledky jsou porovnány se známými analytickými řešeními a s dalšími dostupnými aplikacemi., The aim of this theses is to create application, which is able to calculate buckling load of structure made from 1D bar elements, using finite element method. introduction is devoted to basic principles of buckling and derivation of necessary formulas. Then are described all operations and numerical methods needed for the application. At the and is in detail analyzed few structures and results are compared with known solutions or with other applications.