Use Of 2D Models Research Articles

JUSTIFICATION OF THE CHOICE OF THE CALCULATION MODEL OF THE ESCALATOR TUNNEL IN FLAT AND SPATIAL SETTINGS

Purpose. To perform an analysis of analytical and numerical methods of mathematical modeling of an escalator tunnel. To identify the main characteristics and differences of methods based on flat or spatial settings. To justify the choice of the calculation model of the escalator tunnel and its setting. To justify the choice of the calculation model of the escalator tunnel and its construction. Methodology. To achieve the goal, a number of analytical methods based on a flat (2D) setting (Gap method, Volume loss control method, Convergence-confinement method) were analyzed. Approaches in numerical methods, in particular in the method of finite elements, which have successfully applied flat setting, are considered. The spatial (3D) setting in the finite element method is also analyzed. Analysis of a numerical experiment based on 3D models shows that the three-dimensional structure forces interpretation decisions that are not taken into account in the cross-section, that is, in the two-dimensional model. Findings. Finite-element models of the escalator tunnel were developed in flat and spatial settings, and the 2D model with a thickness of 1 m repeated the conditions of the 3D model in its middle part. The obtained parameters of the stress-strain state were subjected to comparative analysis. It was found that the values of the norms of horizontal and vertical stresses in the fragment of the 3D model (middle) and in the 2D model differ by 3.2 and 7.2 %, respectively. Originality. Based on the results of the justification of the choice of the calculation model of the escalator tunnel, it was proved that the use of 2D models is adequate for the system of interaction of the escalator tunnel with the surrounding massif. This statement is evidenced by the almost identical distribution of stresses and strains in finite-element models in flat and spatial settings. Practical value. In the course of research, it has been proven that the flat finite-element model of the escalator tunnel is adequate for the given task, provided that it is used in several characteristic sections of the escalator tunnel, that is, the creation of a number of models in 2D, which allows considering its position along the length of the calculated tunnel.

Study of the Elastic and Elastoplastic Properties of a Dispersed Composite Based on Computational Experiments

In the paper, the averaging method was used to determine the effective elastic moduli of dispersed B4C/2024Al composites and porous geomaterials using 2D and 3D X-ray images of their internal structure. A comparison of calculated values of Young’s modulus with experimental data showed that the use of 2D models of the real structure led to underestimated values of Young’s modulus, especially for porous materials. It was found that 3D models with model inclusions in the form of ellipsoids could be used to estimate the effective elastic moduli for composites with inclusion concentrations to 20%. Computational experiments on 3D models of the B4C/2024Al composite showed that the stress concentration in its inclusions and matrix was significantly higher when the real inclusions were considered instead of ellipsoidal ones. The dynamic behavior of the dispersed B4C/2024Al composite was studied using models with inclusions in the form of ellipsoids. Stress concentrations under dynamic loading were significantly higher than those in statics. The elastoplastic behavior of the real structure of the B4C/2024Al composite was investigated in computational experiments on uniform compression, pure shear, and a combination of pure shear and uniform compression. Calculations considering the real structure of inclusions showed that the pure shear diagram depended on the uniform compression, although such a dependence was absent for the matrix material.

Integrated Methodology for Urban Flood Risk Mapping at the Microscale in Ungauged Regions: A Case Study of Hurghada, Egypt

Flood risk mapping forms the basis for disaster risk management and the associated decision-making systems. The effectiveness of this process is highly dependent on the quality of the input data of both hazard and vulnerability maps and the method utilized. On the one hand, for higher-quality hazard maps, the use of 2D models is generally suggested. However, in ungauged regions, such usage becomes a difficult task, especially at the microscale. On the other hand, vulnerability mapping at the microscale suffers limitations as a result of the failure to consider vulnerability components, the low spatial resolution of the input data, and the omission of urban planning aspects that have crucial impacts on the resulting quality. This paper aims to enhance the quality of both hazard and vulnerability maps at the urban microscale in ungauged regions. The proposed methodology integrates remote sensing data and high-quality city strategic plans (CSPs) using geographic information systems (GISs), a 2D rainfall-runoff-inundation (RRI) simulation model, and multicriteria decision-making analysis (MCDA, i.e., the analytic hierarchy process (AHP)). This method was implemented in Hurghada, Egypt, which from 1996 to 2019 was prone to several urban flood events. Current and future physical, social, and economic vulnerability maps were produced based on seven indicators (land use, building height, building conditions, building materials, total population, population density, and land value). The total vulnerability maps were combined with the hazard maps based on the Kron equation for three different return periods (REPs) 50, 10, and 5 years to create the corresponding flood risk maps. In general, this integrated methodology proved to be an economical tool to overcome the scarcity of data, to fill the gap between urban planning and flood risk management (FRM), and to produce comprehensive and high-quality flood risk maps that aid decision-making systems.

On operational flood forecasting system involving 1D/2D coupled hydraulic model and data assimilation

In the context of hydrodynamic modeling, the use of 2D models is adapted in areas where the flow is not mono-dimensional (confluence zones, flood plains). Nonetheless the lack of field data and the computational cost constraints limit the extensive use of 2D models for operational flood forecasting. Multi-dimensional coupling offers a solution with 1D models where the flow is mono-dimensional and with local 2D models where needed. This solution allows for the representation of complex processes in 2D models, while the simulated hydraulic state is significantly better than that of the full 1D model. In this study, coupling is implemented between three 1D sub-models and a local 2D model for a confluence on the Adour river (France). A Schwarz algorithm is implemented to guarantee the continuity of the variables at the 1D/2D interfaces while in situ observations are assimilated in the 1D sub-models to improve results and forecasts in operational mode as carried out by the French flood forecasting services. An implementation of the coupling and data assimilation (DA) solution with domain decomposition and task/data parallelism is proposed so that it is compatible with operational constraints. The coupling with the 2D model improves the simulated hydraulic state compared to a global 1D model, and DA improves results in 1D and 2D areas.

Modeling Flood Disasters: Issues Concerning Data for 2D Numerical Models

Flood disasters are one of the worst natural disasters and they occur almost daily. Correspondingly, city managers are nowadays increasingly investing in data collection and modelling activities. Typically, flows in pipes and channels have been modelled using a one-dimensional (1D) approach. Also, if the flood flows on the ground are confined to streets and curbs, the use of 1D/1D modelling approach (a.k.a. as dual drainage concept) may be a feasible way forward. However, if the flows are two-dimensional with complex interactions taking place through surface/sub-surface links, then the required approach would be the so-called 1D/2D modelling approach. The ever-increasing power of computers is now allowing a 3D fluid dynamics analysis of overflow and manhole structures, and in time these may be coupled with 1D models that may be used in situations where flow characteristics require with higher dimensionality. With the use of 2D models, the importance of terrain data has become a growing issue. The current paper discusses some of the key modelling approaches and makes particular reference to the terrain data processing and collection which can either improve or deteriorate their predictive capability.

Von mises stress for two-dimensional elasticity problems

The internal stresses arising from the misfit between the {gamma} and {gamma}{prime} phases of singlecrystal superalloy have a great influence on the mechanical properties of such materials at high temperatures. Several authors have determined these stresses by finite element calculations. These authors used a two dimension model (2D) to describe the approximately cubic shape of the {gamma}{prime} precipitates. Two questions arise from the use of 2D models for 3D structures. The first concerns the uncertainty of such models and this has been evaluated by Muller in a recent paper. The second involves the Von Mises (VM) stress. The authors use this stress as defined for 3D to describe the state of stress that can bring about plastic 2D strain. This stress is directly related to the distortion energy and is appropriate for single crystal material undergoing plastic deformation through dislocation gliding; however careful consideration is required for 2D analyses. In this paper, a VM stress in 2D is defined having the same physical significance as for 3D. Then, the difference is evaluated between these two stresses (VM for 2D and VM for 3D) for the case of a spherical precipitate.