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Global structural analyses in civil engineering are usually performed considering linear-elastic material behavior. However, for steel structures, a certain degree of plasticization depending on the member classification may be considered. Corresponding plastic analyses taking material nonlinearities into account are effectively realized using numerical methods. Frequently applied finite elements of two and three-dimensional models evaluate the plasticity at defined nodes using a yield surface, i.e. by a yield condition, hardening rule, and flow rule. Corresponding calculations are connected to a large numerical as well as time-consuming effort and they do not rely on the theoretical background of beam theory, to which the regulations of standards mainly correspond. For that reason, methods using beam elements (one-dimensional) combined with cross-sectional analyses are commonly applied for steel members in terms of plastic zones theories. In these approaches, plasticization is in general assessed by means of axial stress only. In this paper, more precise numerical representation of the combined stress states, i.e. axial and shear stresses, is presented and results of the proposed approach are validated and discussed.
Burning of clinker is the most influencing step of cement quality during the production process. Appropriate characterisation for quality control and decision-making is therefore the critical point to maintain a stable production but also for the development of alternative cements. Scanning electron microscopy (SEM) in combination with energy dispersive X-ray spectroscopy (EDX) delivers spatially resolved phase and chemical information for cement clinker. This data can be used to quantify phase fractions and chemical composition of identified phases.
The contribution aims to provide an overview of phase fraction quantification by semi-automatic phase segmentation using high-resolution backscattered electron (BSE) images and lower-resolved EDX element maps. Therefore, a tool for image analysis was developed that uses state-of-the-art algorithms for pixel-wise image segmentation and labelling in combination with a decision tree that allows searching for specific clinker phases. Results show that this tool can be applied to segment sub-micron scale clinker phases and to get a quantification of all phase fractions. In addition, statistical evaluation of the data is implemented within the tool to reveal whether the imaged area is representative for all clinker phases.
Chemical glass frosting processes are widely used to create visual attractive glass surfaces. A commonly used frosting bath mainly contains ammonium bifluoride (NH4HF2) mixed with hydrochloric acid (HCl). The frosting process consists of several baths. Firstly, the preliminary bath to clean the object. Secondly, the frosting bath which etches the rough light scattering structure into the glass surface. Finally, the washing baths to clean the frosted object. This is where the constituents of the preceding steps accumulate and have to be filtered from the sewage. In the present contribution, phosphoric acid (H3PO4) was used as a substitute for HCl to reduce the amount of ammonium (NH4+) and chloride (Cl−) dissolved in the waste water. In combination with magnesium carbonate (MgCO3), it allows the precipitation of ammonium within the sewage as ammonium magnesium phosphate (MgNH4PO4). However, a trivial replacement of HCl by H3PO4 within the frosting process causes extensive frosting errors, such as inhomogeneous size distributions of the structures or domains that are not fully covered by these structures. By modifying the preliminary bath composition, it was possible to improve the frosting result considerably. To determine the optimal composition of the preliminary bath, a semi-automatic evaluation method has been developed. This method renders the objective comparison of the resulting surface quality possible.
This study demonstrates the application and combination of multiple imaging techniques [light microscopy, micro-X-ray computer tomography (μ-CT), scanning electron microscopy (SEM) and focussed ion beam – nano-tomography (FIB-nT)] to the analysis of the microstructure of hydrated alite across multiple scales. However, by comparing findings with mercury intrusion porosimetry (MIP), it becomes obvious that the imaged 3D volumes and 2D images do not sufficiently overlap at certain scales to allow a continuous quantification of the pore size distribution (PSD). This can be overcome by improving the resolution and increasing the measured volume. Furthermore, results show that the fibrous morphology of calcium-silicate-hydrates (C-S-H) phases is preserved during FIB-nT. This is a requirement for characterisation of nano-scale porosity. Finally, it was proven that the combination of FIB-nT with energy-dispersive X-ray spectroscopy (EDX) data facilitates the phase segmentation of a 11 × 11 × 7.7 μm3 volume of hydrated alite.
According to Eurocode, the computation of bending strength for steel cantilever beams is a straightforward process. The approach is based on an Ayrton-Perry formula adaptation of buckling curves for steel members in compression, which involves the computation of an elastic critical buckling load for considering the instability. NCCI documents offer a simplified formula to determine the critical bending moment for cantilevers beams with symmetric cross-section. Besides the NCCI recommendations, other approaches, e.g. research literature or Finite-Element-Analysis, may be employed to determine critical buckling loads. However, in certain cases they render different results. Present paper summarizes and compares the abovementioned analytical and numerical approaches for determining critical loads and it exemplarily analyses corresponding cantilever beam capacities using numerical approaches based on plastic zones theory (GMNIA).
Bolted connections are commonly used in steel construction. The load-bearing behavior of bolt fittings has extensively been studied in various research activities and the bearing capacity of bolted connections can be assessed well by standard regulations for practical applications. With regard to tensile loading, the nut does not have strong influence on resistances, since the failure occurs in the bolts due to higher material strengths of the nuts. In some applications, so-called “blind holes” are used to connect plated components. In a manner of speaking, the nut is replaced by the “outer” plate with a prefabricated hole and thread, in which the bolt can be screwed and tightened. In such connections, the limit load capacity cannot solely be assessed by the bolt resistance, since the threaded hole in the base material has strong influence on the structural behavior. In this context, the available screw-in depth of the blind hole is of fundamental importance. The German National Annex of EN 1993-1-8 provides information on a necessary depth in order to transfer the full tensile capacity of the bolt. However, some connections do not allow to fabricate such depths. In these cases, the capacity of the connection is unclear and not specified. In this paper, first experiments on corresponding connections with different screw-in depths are presented and compared to limit load capacities according to the standard.
One of the most important subjects of hydraulic engineering is the reliable estimation of the transverse distribution in the rectangular channel of bed and wall shear stresses. This study makes use of the Tsallis entropy, genetic programming (GP) and adaptive neuro-fuzzy inference system (ANFIS) methods to assess the shear stress distribution (SSD) in the rectangular channel.
To evaluate the results of the Tsallis entropy, GP and ANFIS models, laboratory observations were used in which shear stress was measured using an optimized Preston tube. This is then used to measure the SSD in various aspect ratios in the rectangular channel. To investigate the shear stress percentage, 10 data series with a total of 112 different data for were used. The results of the sensitivity analysis show that the most influential parameter for the SSD in smooth rectangular channel is the dimensionless parameter B/H, Where the transverse coordinate is B, and the flow depth is H. With the parameters (b/B), (B/H) for the bed and (z/H), (B/H) for the wall as inputs, the modeling of the GP was better than the other one. Based on the analysis, it can be concluded that the use of GP and ANFIS algorithms is more effective in estimating shear stress in smooth rectangular channels than the Tsallis entropy-based equations.
This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp-estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices.
The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computationbased, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios.
In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.