РАСЧЕТ УСИЛИЯ КОНТРОЛИРУЕМОЙ ЗАТЯЖКИ В ГРУППОВОМ БОЛТОВОМ СОЕДИНЕНИИ

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

Slope stability is a topic of great importance in civil engineering, as slope failures can cause considerable damage to infrastructure and downstream properties. In this study, we applied the Fellenius slice method, using both the analytical method, as well as the numerical method, which was performed using the SLOPE/W module of the Geostudio software. The results obtained by both methods showed that the increase in soil cohesion improves the stability of the slope. The safety coefficients obtained by the analytical method vary between 0.534 and 1.086, while those obtained by the numerical method vary between 0.539 and 1.096, for cohesion values ranging from 4 kPa to 20 kPa. The safety coefficients obtained by the analytical and numerical methods follow straight lines of equation y=0.0344x+0.4092 and y=0.0345x+0.4169, respectively. The results of the analytical method show that a safety factor of 1.5 is achieved at a value of 32 kPa for the cohesion, while the numerical method shows a safety factor of 1.5 achieved at a value of 32 kPa for the cohesion. The difference between the two cohesions is explained by the smaller number of slices used in the analytical method. Nevertheless, the equation from the analytical method can be used as a general guide to evaluate the evolution of the safety coefficient of a slope with surcharge under long-term behavior with incremental cohesion, but this does not exclude verification by dedicated software based on the finite element method.

Wear mechanism is important since it leads to revisions in Total Hip Replacement (THR) surgeries. Contact pressure plays an important role in wear mechanisms and needs to be investigated in detail to obtain more accurate wear predictions to understand the wear performance of the implant in the design stage. This study proposes a methodology for verification of contact pressure and pressure distribution via numeric and analytic methods to be used in wear calculations. Based on Hertz’s contact theory, the contact pressure and the contact area ae calculated in the analytical method. The results are compared to the numeric method’s results obtained from the finite element method. The linear and volumetric wear rates of bearing couples’ surfaces were estimated by Archard’s wear equation. The effect of design parameters on pressure such as head radius, cup thickness, material combination of bearing couples, coating film material, and film thickness are investigated in this study using the proposed methodology. The minimum error between the analytical and numerical results was 0.24% for 28 mm of head diameter, while the maximum error was 11.79 % for 48- mm of head diameter. The minimum contact pressure values were obtained from 48- mm of head radius at a half contact angle of 190 (degrees) in FEM and Hertz calculations, respectively. The maximum linear wear rate was calculated at 0.0026 mm/Mc at a 1- mm cup thickness, while minimum linear wear rate was 0.0022 mm/Mc at a 10- mm cup thickness in the numeric method. The maximum survival cycles of coating materials rate were 31847 cycles for the Stainless-steel coated cup with 500 μm of coating thickness, while the minimum cycles was 2359 cycles for the Ti64 coated cup surface with 100 μm of coating thickness. It is concluded that the most important design parameters are the cup thickness and the material combinations since they have a significant effect on the contact pressure and the contact area. This study provides a verification methodology for the parametric sensitivity analysis before experimental validations. The methodology utilized in this study could be utilized by designers while optimizing the design parameters to minimize the wear.

Calculation of radial and axial forces and leakage reactance of transformer coils is performed in many papers using different analytical and numerical methods. But most of the analytical methods are extended only for transformers with uniform equal-height windings and then are not very accurate for transformer with no uniform winding arrangement. In this paper, some simple techniques for calculating leakage reactance and forces acting on the transformer coils are presented. This study is accomplished by using 2-1) planar models utilizing the finite element and Roth methods. Just by modeling the transformer and using FEM, the magnetic vector potential is calculated over each node of model and then using several post-processing procedures, the transformer leakage reactance is calculated. Also, this reactance is obtained by analytical method (Roth method) and then results are verified by experiments. The short circuit current and hence the radial and axial forces on the transformer coils during short circuit condition are calculated. Considering some especial cases, the impact of the windings arrangement on the axial force is analyzed and net axial force acting against the yoke are calculated

The risk of sand production must be evaluated from very early stages of field development planning to select the optimum well completion, and if required, identify the appropriate sand control options. However, during the appraisal or early development stages, sand production predictions often cannot be verified against field data because the lack of sanding observations. The analysis of predicting the onset and severity of sand production generally consists of using analytical or numerical rock mechanical models and ideally calibration with field sand production data. In this paper we show how in the absence of field sanding data, reliable sanding predictions can still be achieved by combining commonly used analytical and numerical prediction methods. This approach has been validated using a brown field dataset from South East Asia with several sand producing wells and multiple pressure depleted reservoirs. The analytical method uses a poro-elastic model and core-calibrated log-derived rock strength profiles with an empirical effective rock strength factor (ESF). The ESF should be calibrated against documented field sanding observations from wells with credible formation and drawdown pressures. The numerical method uses a poro-elasto-plastic model defined from triaxial core tests. The rock failure criterion in the numerical method is based on a critical strain limit (CSL) corresponding to the failure of the inner wall of thick-walled cylinder core tests or if existing field sanding data. In the brown oil field example, both analytical and numerical methods accurately predict the onset of sanding in the sand-prone wells. The core-based CSL defined by the numerical method match very well with the field sanding data with a very small margin of error. In contrast, the default and non-calibrated ESF values commonly used in the analytical method required considerable tuning to match with the field sanding data. This suggests that the core-based CSL can be used with a reasonable confidence for sand production prediction purposes in the field and the prediction can be as reliable as field-calibrated models. After the field validation, the predictions for planned infill wells by both analytical and numerical methods were consistent and similar. The paper will show how this approach is used in two other fields from the Asia Pacific region both at appraisal stages and with no field sanding data. Both cases show that different ESF values are required to match with the numerical simulations. In the absence of field sanding observation, particularly in the early stages of field development, the use of non-calibrated default ESF values in the analytical method could lead to erroneous sanding assessment and poor sand management decisions. Application of a combined analytical and numerical sanding evaluation enhances the reliability of sand production predictions. After a calibration is obtained, either with field sanding data or calibration against numerical simulation and core-based CSL criteria, the analytical method can be used with confidence and has the added benefits of simplicity and quick realizations of various scenarios and output plotting capabilities and inputs for sand control and well completion decisions.

Computational costs limit large scale reservoir simulations to coarse grid systems. Determination of an effective permeability for a simulation grid block requires a proper scale-up of small scale permeability heterogeneities within that grid block. Conventional scale-up techniques are limited to a diagonal tensor representation of effective permeability. Therefore, such techniques cannot handle general permeability anisotropy (full tensor) exemplified by cross-bedded permeability structures that may be present on a smaller scale. An analytical method is developed to calculate an effective permeability tensor for a grid block by accounting for small scale heterogeneities within the grid block. The method honors both the location and the orientation of the small scale heterogeneities. Effective permeability tensors calculated using the analytical method and a numerical method show excellent agreement. Miscible displacement simulations show that the effective permeability tensor method outperforms conventional scale-up techniques in predicting flood front locations in cases of general permeability anisotropy.

Spatial Vibration and Its Numerical Analytical Method of Four-high Rolling Mills

Two-layer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. In this paper, the formability of two-layer sheet is investigated through analytical, experimental and numerical approaches. An analytical model is developed based on Marciniak-Kuczynski method associated Hill’s non-quadratic yield criterion. Forming limit diagrams are also obtained numerically based on finite element method using Bifurcation theory and ductile fracture criteria. Furthermore, experiments are carried out on Al3105-St14 two-layer sheet. Theoretical results from various methods are compared with results obtained from experiments to evaluate the competency of discussed analytical and numerical methods to predict the formability of two-layer sheets. The results show that analytical and numerical approaches discussed in this paper have good capabilities to predict the formability of two-layer sheets. However, the analytical method based on M-K model and numerical approach based on bifurcation theory are more suitable to determine the forming limit diagram of Al3105-St14 two-layer sheets.

In this paper, the steady laminar boundary layer flow of non-Newtonian second grade conducting fluid past a permeable stretching sheet, under the influence of a uniform magnetic field is studied. Three different methods are applied for solving the problem; numerical Finite Element Method (FEM), analytical Collocation Method (CM) and 4th order Runge-Kutta numerical method. The FlexPDE software package is used for modeling and solving the problem by FEM. In most new analytical methods used for solving nonlinear equations, it is impossible to solve problems with infinity boundary conditions. In this article by using a special technique, the infinity boundary condition transformed to a finite one, then the governing equation solved analytically. In the physical aspect, the effects of the non-Newtonian, magnetic and permeability parameters on the velocity distribution have been investigated. As a result, the present suggested technique can be used for the analytical solution of many such problems with infinite boundary conditions. Moreover, the comparison between the results obtained from our modified analytical method and numerical solutions shows an excellent agreement.

This study offers a comparative study of the analytical and numerical methods for investigating a contact problem. The contact problem comprises a functionally graded layer supported by a half‐plane and loaded with a distributed load from the top surface. First, the analytical and numerical solutions to the problem are acquired by utilizing a theory of elasticity and finite element method, respectively. The problem is transformed into a system of integral equations in which the contact stress is an unknown function. The solution of the integral equation was achieved with Gauss–Jacobi integration formulation. The finite element model of the problem is created using ANSYS software, and the two‐dimensional analysis of the problem is performed. Results were obtained from the samples for different material properties and loading conditions. The distributed load width and non‐homogeneity parameters significantly impact on contact mechanics. The results indicate that the contact area and the contact stress obtained from finite element method (FEM) are close to the analytical results. As a result, acceptable error rates were obtained. Finally, this study provides evidence of a good agreement between the two methods.

For the better management of available groundwater, it is essential to understand the flow behavior within the aquifer systems. The groundwater flow behavior in the complex aquifer system can be studied by solving the governing equations using either analytical or numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method (FEM) are generally used. The Meshless method is a recently developed alternative numerical approach for the solution of existing problem. A variety of Meshless methods like point interpolation method, smooth particle hydrodynamics, Galerkin methods, etc. are under the development for the solution of many solid mechanics and fluid mechanics problems. Meshless method eliminates many of the drawbacks of grid-based methods such as difficulties in meshing and re-meshing as in FDM and FEM which require huge efforts in pre-processing and with Meshless method it translates in the lesser computational time and costs. In this paper, Meshless Local Petrov-Galerkin (MLPG) method with strong form of collocation with exponential/Gaussian radial basis function is used for solving the groundwater flow problem. A computer model in MATLAB has been developed in 1D and 2D for the solution of confined aquifer problems. The developed 1D model is verified with available analytical solution for a hypothetical problem and found to be satisfactory. Further, the 2D model is applied to two case studies and results are compared with the FEM based solutions and found to be satisfactory. The present study shows that the MLPG based Meshless method is very effective in the simulation of groundwater flow problems.

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring during CCUS. We have demonstrated this method by deploying strainmeters at shallow depths (30 to 40m) and then conducting injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. We have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS. Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and our objective was to evaluate opportunities for strain monitoring during characterization and monitoring for CCUS. Our approach was to deploy strainmeters at shallow depths (30 to 40m) and then conduct injection well tests in an underlying reservoir at 530m depth. The results indicate that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. In conclusion, we have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS.

Abstract: A circular plate is one of the important structures in many industrial fields. In static analysis of a circular plate, we may obtain an exact solution by analytical method, but it is limited to a simple circular plate. Thus, many researchers and designers have used numerical methods such as the finite element method. The authors of this paper developed the finite element-transfer stiffness coefficient method (FE-TSCM) for static and dynamic analyses of various structures. FE-TSCM is the combination of the modeling technique of the finite element method (FEM) and the transfer technique of the transfer stiffness coefficient method (TSCM). FE-TSCM has the advantages of both FEM and FE-TSCM. In this paper, the authors formulate the computational algorithm for the static analysis of axisymmetric circular plates under lateral loading using FE-TSCM. The computational results for three computational models obtained by FE-TSCM are compared with those obtained by FEM in order to confirm the accuracy of FE-TSCM.

The paper attempts to provide a generic proposal on the influence of various microwave load parameters based on results accumulated during an investigation using a specific microwave multimode heating cavity configuration. The results have been obtained by numerical analysis using the Finite Element Method within a 3D environment. The load parameters considered were dielectric constant, loss factor, load thickness and load position. Load material properties are typical of those used in industrial relevant applications. Of the four load parameters investigated, the configuration with a high loss factor was seen to dominate the load impact regardless of load thickness, load position or dielectric constant. With decreasing loss factor or increasing load thickness, the influence of the dielectric constant increases. Minor adjustments in the load position (10%) is generally seen to have minimal impact for all load properties considered. The paper also investigates the numerical impact of varying load properties. As the dielectric constant increases, which requires a higher number of mesh elements, so does the average iterations per numerical cycle. The number of numerical cycles and time to reach a convergence is also seen to be inversely proportional to the load loss factor.

Hydraulic fracturing has attracted a tremendous amount of attention due to its abundant applications, such as magma-driven dykes, fracturing of oil and gas reservoirs, heat pro-duction from geothermal reservoirs, ice melt, and fault reactivation in mining. Therefore, the development of fracture propagation models is of great significance to provide more effective technical tools for the dynamic simulation of fracture formation and propagation. Hydraulic fracturing involves a complex process due to the strong coupling between the fluid and solid rock. The finite element method (FEM) is a traditional method for solving the fracture propagation problem. FEM has the advantage of being robust and flexible. However, special treatment is required when dealing with complex fracture problems such as fracture intersection and branching because of discontinuities across fracture surfaces. Instead of seeking to approximate partial differential equations in a conventional framework, the peridynamic approach (PD) uses spatial integral equations that overcome the limitations of defining partial derivatives at discontinuities, which makes it quite suitable for solving complex fracture problems. Therefore, it is of great importance to combine the advantages of both FEM and PD to develop a more robust and flexible fracture propagation model. The main contribution of the thesis is to study fracture propagation problems in fully saturated porous media based on both FEM and PD. Three fracture models based on FEM, PD, hybrid FEM and PD are developed to simulate and explore more “realistic” fracture propagation processes. The main research work of the thesis contains the following four parts.First, comprehensive reviews of the fracture propagation literature, crack branching and PD theory are given. The fracture propagation review includes a review of the fracture propagation process, fracture models and various numerical methods for predicting fracture propagation. The review of crack branching provides a state-of-the-art review of crack branching, including experimental observations, physics, fracture models and associated numerical methods. The latest advances and existing issues of crack branching are discussed. The review of PD theory provides a review of theoretical aspects of PD and related applica-tions of PD in different fields, especially in the field of fracture mechanics. The challenges and new prospects for the development of PD are discussed.Then, a fully implicit, FEM-based fracture model using zero thickness cohesive interface elements is developed. The rock formation is considered as a fully saturated porous medium. The fracture surface is deemed to be permeable, the fracturing fluid is treated as an impressible Newtonian fluid, and the cohesive zone model is employed for the fracture propagation criterion. After verifying the model, the stepwise phenomenon, which has been observed in the field and experiments and reported recently in the numerical modelling literature, is investigated with the model.Then, an explicit PD approach for simulating fracture propagation in saturated porous media is developed. A staggered method is adopted to solve the coupled system. The solid deformation equation is solved for the displacement field, and the fluid flow equation is solved for the pressure field with PD. After verification via benchmark examples, including a 1D consolidation problem and a 2D fluid-filled crack propagation problem, a series of tests are conducted to study the fracture propagation phenomena in porous media, including the crack branching phenomenon and the stepwise phenomenon. Effects of pore pressure in fracture propagation branching are investigated, and the stepwise phenomenon is successfully reproduced. All the examples presented demonstrate the capability of the approach in solving fracture propagation problems in saturated porous media.Finally, a fully coupled hybrid FEM-PD approach for simulating fracture propagation in saturated porous media is presented. Considering the ability of PD in solving discontinuous problems, the area where cracks can potentially occur is discretised by PD and the crack-free area is discretised by FEM. The solid deformation and fracture propagation are captured by PD and FEM, while the fluid flow in both the reservoir and fracture is simulated with FEM. The whole process is solved in a monolithic way with an implicit scheme. The approach demonstrates the capability of modelling complex dynamic crack propagation via benchmark examples. The branching phenomenon is then investigated with the proposed approach. In conclusion, complex crack patterns are prone to form with faster loading rate, more brittle and impermeable media, and with lower energy release rate.