Analytical Calculation Method Research Articles

Analytical solution of surrounding rock stress and plastic zone of rectangular roadway under non-uniform stress field

The shape and extent of the plastic zone can effectively reflect the degree of deformation and failure of the surrounding rock. By applying complex variable functions and the theory of elasticity, a mechanical model for the surrounding rock of a rectangular roadway is established. The analytical solution for the stress in the surrounding rock of a rectangular roadway under a non-uniform stress field is derived, and the spatial stress distribution pattern in the surrounding rock of the rectangular roadway is obtained. Furthermore, using the Mohr-Coulomb criterion, the boundary equation of the plastic zone in the surrounding rock of a rectangular roadway is derived, and the morphological characteristics of the plastic zone are obtained. The results indicate that the plastic zones on both sides of the rectangular roadway are arc-shaped. The asymmetry of the stress environment has a significant impact on the plastic zones in the roof and floor of the rectangular roadway, causing the shape of the plastic zones to resemble a “petal” pattern. The lateral pressure coefficient and the height-to-width ratio have a significant impact on the stress distribution and the morphological characteristics of the plastic zone in the surrounding rock of the rectangular roadway. By validating the computational accuracy of the analytical solution through numerical simulations and conducting an engineering applicability analysis based on a coal mine roadway, it has been demonstrated that the analytical calculation method is both rational and possesses good engineering applicability. This provides reliable theoretical guidance for the design calculations and construction planning of similar roadway projects.

Analytical calculation approach for rocket nose cone structure with orthotropic material

The Authors of this research developed an analytical calculation method to estimate the strength of nose cone structures made of orthotropic materials, which were crucial components in aircraft and spacecraft. Strength analysis of nose cones had been comprehensively addressed for isotropic materials; however, the lack of efficient approaches for orthotropic materials presented a challenge. In this research, a new analytical method was proposed, combining membrane stress theory for isotropic materials with classical laminate theory for orthotropic materials. This approach enabled the determination of stresses on the nose cone shell structure in both meridional and circumferential directions in an efficient and straightforward manner. The analysis results indicated that the developed analytical method exhibited stress distribution trends similar to those obtained using the Finite Element Method. Stresses in the +45° and –45° direction, as well as in-plane shear stress and Tsai-Wu failure indices, showed trend similarity between the two methods. Despite specific numerical differences in the calculation results, these consistent trends suggested that the analytical method could serve as a tool for the preliminary design of a nose cone structure with a similar configuration analyzed in this study.

An analytical calculation method of instantaneous uncut chip thickness for cutting force prediction in five-axis flank milling

An analytical calculation method of instantaneous uncut chip thickness for cutting force prediction in five-axis flank milling

Feasibility of the analytical dose calculation method for Au-198 brachytherapy

PurposeA dose calculation algorithm Computed Tomography (CT)-based analytical dose calculation method (CTanly), which can correct for subject inhomogeneity and size-dependent scatter doses, was applied to the 198Au seed. In this study, we evaluated the effectiveness of the CTanly method by comparing the gold standard Monte Carlo (MC) method and the conventional TG43 method on two virtual phantoms and patient CT images simulating oral cancer. MethodsAs virtual phantoms, a water phantom and a heterogeneous phantom with soft tissue inserted cubic fat, lung, and bone were used. A 2-mm-thick lead plate was also inserted into the heterogeneous phantom as a dose attenuator. Virtual 198Au seeds and a 2-mm-thick lead plate were placed on the patient CT images. Dose distributions obtained via the TG43 and CTanly methods were compared with those of the MC by gamma analysis with 2%/2-mm thresholds. The computation durations were also compared. ResultsIn the water phantom, dose distributions comparable to those obtained via the MC method were obtained regardless of the algorithm. For the inhomogeneity phantom and patient case, the CTanly method showed an improvement in the gamma passing rate and dose distributions similar to those of the MC method were obtained. The computation time, which was days with the MC method, was reduced to minutes with the CTanly method. ConclusionsThe CTanly method is effective for 198Au seed dose calculations and takes a shorter time to obtain the dose distributions than the MC method.

Analytical calculation method for development dynamics of water-flooding reservoir considering rock and fluid compressibility

The existing development dynamics calculation methods for water-flooding reservoir are difficult to comprehensively consider factors such as injection-production imbalance, irregular well pattern, reservoir heterogeneity and compressibility. Therefore, leveraging reservoir engineering and material balance theory, and considering the influence of reservoir compressibility on reservoir development dynamics, a set of analytical calculation method for development dynamics of water-flooding reservoir considering rock and fluid compressibility water-flooding with clear theories and high computational efficiency were derived and constructed. Based on the oil-water two-phase Darcy law, the reservoir compression coefficient is introduced, and the development dynamics calculation method of a single injection-production unit considering compressibility is derived and established by combining the material balance theory, which can quantitatively describe the relationship between the oil and water production rates per unit. On this basis, the injection-production splitting strategy is introduced, which is extended to the calculation of development dynamics for multiple well groups in the whole reservoir. In this study, seven working conditions with various injection-production ratios were designed to validate the reliability of the new method. Subsequently, the method was applied to actual block for further verification, and the prediction accuracies of oil and water production rates were improved by 67.48% and 19.07%, respectively.

The Detection and Calculation of Design-Weighting on Indoor Environmental Elements—Illustrated by Real Interior Design Projects

In interior design projects, homeowners’ expectations and thoughts in mind are sometimes ambiguous and hard to pinpoint. This lack of clarity can lead to disagreements between owners and designers, making it difficult for designers to receive due remuneration. At the same time, the design project always has a restricted budget. Suppose the funds could be prioritized based on owners’ preferred weight of the indoor elements, with a larger portion of the budget allocated to the most crucial elements. In that case, it can significantly enhance the owner’s satisfaction. To address these challenges, this research introduces a novel analytical and computational approach that leverages the Positive And Negative Affects Schedule (PANAS) and Heart Rate Variability (HRV) to assess homeowners’ sentiments toward various indoor elements. This method aims to determine indoor elements’ design-weighting, design sequence, and distribution of project budgets, enabling designers to understand better and meet homeowners’ genuine needs and expectations in interior design projects. The efficacy of this approach was evaluated through the analysis of three real-life residential interior design projects. Data from the PANAS emotion scale and heart rate variability (HRV) measurements of the homeowners were collected before and after project completion. The findings revealed high satisfaction among homeowners following project execution. By adjusting indoor elements, owners’ negative emotions decreased significantly, positive emotions surged, and there was an improvement in the activity of sympathetic and parasympathetic nerves, leading to enhanced physical and mental well-being. Furthermore, in-depth interviews with homeowners corroborated the effectiveness of the analytical calculation method in identifying latent negative indoor elements of concern to homeowners, thereby validating the practical utility of this approach in real-world design scenarios.

Unsupervised deep learning method for single image super-resolution of the thick pinhole imaging system using deep image prior

Thick pinhole imaging system is widely used for diagnosing intense pulsed radiation sources. However, owing to the trade-off among spatial resolution, field of view (FOV) and signal-to-noise ratio (SNR), the imaging system normally falls short in achieving high-precision spatial diagnosis. In this paper, we propose an unsupervised deep learning method for single image super-resolution (SISR) of the thick pinhole imaging system. The point spread function (PSF) of the imaging system is obtained by analytical calculation and Monte Carlo simulation methods, and the mathematical model of the imaging system is established using a linear equation. To solve the ill-posed inverse problem, we adopt randomly initialized deep convolutional neural networks (DCNNs) as an image prior without pre-training, which is named deep image prior (DIP). The results demonstrate that, by utilizing the SISR technique to increase the number of pixels in reconstructed images, the proposed DIP algorithm can mitigate the spatial resolution degradation caused by an insufficient spatial sampling frequency of the camera. Compared with various classical algorithms, the proposed DIP algorithm exhibits superior capabilities in recovering high-frequency signals and suppressing ringing artifacts. Furthermore, the convergence and robustness of the proposed DIP algorithm under different random seeds and SNR conditions are also verified.

Method for fabricating a mesh ripple filter for charged-particle therapy

Objective. A simple, low-cost ripple filter consisting of multiple mesh sheets (mRiFi) was previously developed to reproducibly widen the Bragg peak of heavy-ion beams. To fabricate the mRiFi, the mRiFi parameters such as the wire material, wire diameter, wire spacing, and number of mesh sheets had to be determined. However, it was unclear how these parameters contribute to shifting and widening of the Bragg peak as well as to lateral spreading of the beam passing through the mRiFi. The purposes of this study were to clarify the contributions and to propose a recipe for fabricating a mRiFi with the desired performance values. Approach. We established an analytical calculation method to estimate shifting and widening of the Bragg peak and lateral spreading of heavy-ion beams passing through the mRiFi for given mRiFi parameter values. We also performed Monte Carlo simulations to validate the analytical calculation method. The recipe for fabricating the mRiFi with desired performances was established based on the analytical calculation method. Using the recipe, we fabricated the mRiFi for multi-ion therapy and evaluated its performance through demonstration experiments with helium-, carbon-, oxygen-, and neon-ion beams. Main results. The difference between the results of the Monte Carlo simulation and the analytical calculation was less than 0.4 mm for the peak shift, 0.15 mm for the peak width, and less than 0.11 mm for the lateral beam size which validated the analytical calculation method. The experimentally observed shift and width of the Bragg peak were consistent with the analytical calculations. Significance. We proposed a method to determine mRiFi parameters for fabricating a mRiFi with a desired performance, i.e. adequate widening of the Bragg peak with an acceptable peak shift and lateral beam spread. The proposed method allows anyone to fabricate a simple and low-cost mRiFi satisfying desired specifications.

Strain concentration factor of heterogeneous materials and analytical influence functions based on Eshelby tensor

In this manuscript, Eshelby tensor is employed to assess the strain concentration that arises in the matrix phase at the interface, offering precise values and locations of maximum strain under specific loading conditions for both spherical and cylindrical inclusions. When compared to numerical simulation results, the analytical predictions grounded in the Eshelby tensor exhibit satisfactory accuracy. Then an analytical calculation method based on Eshelby tensor for the elastic strain influence functions of reduced-order homogenization (ROH) method is developed and adopted on particle-reinforced and fibrous composites, presenting its feasibility and advantage on off-line stage calculation of ROH method. The error analyses between analytical and numerical results are conducted. The numerical results also exhibit the necessity of finer interface partitioning to obtain the response on micro-scale with higher resolution.

Simplified Calculation of the Inertia Moment of the Cross Section of the Console under Loading

Introduction. Published studies on the rigidity of consoles under load focus on the issues of their deformation and destruction. Calculations of the inertia moment, fundamentally important characteristic of the strength of the rod, are described. However, the problem of significant time consumption for such calculations has not been solved. The presented study meets the lack. The objective of the work is to describe a new rapid method for analytical calculation of the shear stress distribution in the section of the console corresponding to the action of an external applied force. For the first time, tangential stresses are considered, and examples of calculating the inertia moment for two non-standard sections of the console are given in this context.Materials and Methods. To develop a new method, the console was presented as a pack of plates oriented parallel to the vector of external force. The source calculations were based on the scheme of a console beam with a dedicated plate. The deformation of the rod elements was modeled taking into account the effect of a uniform shear stress field in the plate section. To validate the simplified calculation of the inertia moment of the sections, schemes of a square, ellipse, triangle, hexagon, six-pointed star, and a figured cross were used. Analytical and mathematical research methods were applied, specifically, the Huygens–Steiner theorem.Results. A rapid valid method for calculating the inertia moment of the cross section of the console under loading has been developed. Its difference is the rejection of calculations for each section, taking into account the shape and other features. For any shape of the section, the beam is represented as a bundle of infinitely thin plates, their inertia moments are integrated, and a well-known solution for deflection of a thin plate is used. The method allows us to unambiguously show the distribution of tangential stresses at the end of the console, providing a given deflection, and tangential stresses are used for such solutions for the first time. Their profiles are obtained depending on the direction of the external applied force. Formulas for the inertia moments of complex sections — a six-pointed star and a figured cross — are derived for the first time. Each section is correlated with the stress distribution curve and its maximum value. This data is visualized in the form of diagrams. It is found that the inertia moment and the rigidity of the console do not change when the external applied force is rotated by 30° for a star-shaped section and by 45° for a square and a figured cross. In general, the tangent field depends on the geometry and on the orientation of the section relative to the external applied force.Discussion and Conclusion. The proposed simplified approach to calculating the inertia moment of the cross sections of the consoles makes it possible to uniquely determine the field of tangential stresses at the end, which provides the appropriate value of the external applied force for the given deflection. Engineers and mechanics can use the results of the presented work in the calculations and modeling of deformation of rod structural elements.

Construction of a measurement system and analytical solution for docking pose of large aircraft components based on draw-wire displacement sensors

Abstract Relative pose detection is a key technology in large component automatic docking systems. In this paper, a measurement system has been developed to detect the relative pose of large aircraft components with draw-wire displacement sensors, while an analytical calculation method has been proposed to determine the docking pose of large aircraft components. This method establishes a measurement model for the docking pose of large components and separates the position and orientation solutions based on the distances between seven sets of measurement points measured by the draw-wire displacement sensors. First, the principle of three-dimensional rendezvous positioning is refined to ascertain the relative position of the components. Then, by analyzing the properties of the rotation matrix and the coupling relationship between the position and orientation variables of the movable component, 15 compatible equations containing only two variables with a maximum degree of four are obtained. Based on this set of equations, a unique solution for the rotation matrix was obtained through the variable substitution method, gradually eliminating higher-order terms. Finally, the correctness of the method is verified through numerical examples. Unlike typical parallel mechanism models, this model can directly obtain 15 compatible equations without the need for methods such as Gröbner bases. Moreover, compared to the measurement method using six draw-wire displacement sensors, a unique solution can be directly determined, solving the problem of multiple solution selection. This measurement method only requires measuring the distance between measurement points to solve the relative pose, with low equipment costs and less susceptibility to external environmental factors.

Analytical calculation method of circular-section rocking steel piers under horizontal cyclic load

The research object of this paper is to investigate the mechanical behavior and develop an analytical model of the prestressed circular-section rocking steel piers with external energy-dissipating devices under the horizontal cyclic load. Based on the method of monolithic beam analogy under monotonic loading, the concept of generalized rotation angle and intercept strain in the pre-decompression state was introduced. The geometrical equations for the pre- and post-decompression stages are deduced. The calculation formulas for internal forces of each component and the analytical calculation method for the entire process of the rocking steel pier under horizontal cyclic loading are established in detail. To reproduce the hysteresis curve of the test, some special test conditions, such as the retraction effect of prestressed tendons and increase of the compressed area due to the vertical plates, were considered in the analytical model. The results show that the analytical method based on generalized rotation angle and intercept strain can ensure an ideal transition of the hysteresis curve of the pier in pre- and post-decompression stages. Except for the pier with particularly severe local buckling and ovalization deformation, the calculated results obtained from the proposed analytical model agrees well with the test results for the rocking steel bridge piers. The effect of prestressed tendons and the P–Δ effect on the lateral load–displacement curve of rocking steel bridge biers was further analyzed through parametric study using the proposed model. The analytical calculation method presented in this paper provides a theoretical tool for seismic design of the rocking steel pier in engineering practice. This paper provides important guidance for the establishment of seismic design method of rocking steel piers.

Comparing Numerical and Analytical Methods for Heat Loss Determination of District Heating Systems

Energy efficiency assessment considers the heat losses in district heating systems. For instance, life cycle assessments of such engineering structures require knowledge of the heat losses during their use phase. Therefore, it is essential to have the most accurate knowledge of the heat losses of a district heating system. In this study, three different methods for the determination of specific heat losses for buried preinsulated steel pipes are compared. The first method involves an analytical calculation in accordance with EN 13941, while the second utilizes an equivalent circuit approach. The third method employs finite element analysis. The objective was to evaluate the accuracy of the methods, the achievable range of results, and the effort required to solve the respective calculation algorithms. Therefore, typical 2-dimensional cross sections including different pipe diameters were selected. In situ measurements were not part of this study. Consequently, the analysis centres on the deviation between the methods. All three methods determine the heat loss in both the supply and return pipes. While the analytical calculation method cannot determine temperatures in the soil, the equivalent circuit method can handle more complex tasks and gives detailed results at predefined points in the model. With the finite element method, a high degree of detail can be achieved, but the requirements for solving the algorithms increase. An emerging trend in district heating involves reducing operational temperatures in both new and existing networks. This will change the relation between heat losses and heat delivered to the customers. Subsequently, an increasing interest in the actual heat losses and the precision of calculation is expected within this development. Therefore, it remains essential to evaluate the performance of different models

An analytical calculation method of SiC MOSFET junction temperature based on thermal network theory and Laplace transform

AbstractIn order for full utilization of the switching devices and safe continued operation of the power converter at the same time, the junction temperature of the switching devices needs to be accurately monitored without shutting down the motor drive. This paper derives an analytical junction temperature calculation method by using Laplace transformation and thermal network theory. Based on an actual motor drive, a simulation model is established using platform for power electronic systems (PLECS). Through comparison, the derived method is proven to be able to calculate junction temperature accurately.

Evaluation of Kenten Main Substation Grounding System Based on IEEE 80-2013

Grounding system in a Substation has an important role in human and equipment safety therefore the grounding system condition should always be under observation. Maintenance and evaluation regularly should be carried out in line with the possibility of fault current increasing that embark in the system and disturbances from lightning strokes. In this study, the grounding system at the Kenten substation was analysed by using an analytic calculation method and a numerical method software. The calculation was based on IEEE Std. 80-2013 (IEEE Guide for Safety in AC Substations Grounding). From the study, it was obtained that the grounding system of Kenten substation just fulfils the safety standard regulation.

A methodology for the selection of low friction/anti-seize coating in applying bolted joints of ITER blanket modules

The application of bolted joints with the Spiralock®/Selflock® technology for remote handling system in fusion machines leads to develop a methodology for selection a low friction/anti-seize coating in applying sliding surfaces of high-loaded threaded fasteners. This study discusses the analytical engineering method for calculation the maximum/minimum allowable friction coefficients in the thread and on the bearing surface during the tightening/untightening procedure. Calculations were made to determine the maximum/minimum allowable coefficient of friction in threaded pairs used for the ITER Blanket Module Connections and enhanced flux First Wall Panel fasteners (bolts with a regular metric thread/nuts with a self-locking thread, Spiralock®/Selflock® technology) of the ITER fusion experimental reactor under maximum torque conditions of the robot manipulator (remote handling system) and tensile load (preload) generated in the bolt during the tightening/untightening procedure. Design features of the Spiralock® technology were derived for calculation the working ranges of thread friction coefficient in the threaded pairs of the Blanket Module Connection and enhanced Heat Flux First Wall Panels fasteners at different coefficient of thread proportionality values (ζ=0.45–1.00). The lowest thread friction coefficients were obtained by the coefficient of thread proportionality ζ=1.00: 0.022≤μth≤0.171 for the M24 × 3 SB Electrical strap central bolts, 0.013≤μth≤0.047 for the М52 × 4 Outboard Flexible Cartridge central bolts, 0.010≤μth≤0.055 for the M64 × 4 Inboard Flexible Cartridge central bolts. The new method of determining the total tightening torque of the M24 × 3, M52 × 4, M64 × 4 bolted joints fastened to the Spiralock® female thread under conditions of elastoplastic, plastic deformation was applied to assess the suitability the solid lubricating coating MoS2 (VNIINP-212) under preload force Fa=10–1200 kN. The performed design verification indicated the significant differences in the calculated tightening torque obtained according to the standard and proposed method for the Spiralock® female thread by the plastic deformation of the tip of bolt thread and change of sliding friction coefficient depending on the contact pressure.

ТЕПЛОВИЙ РОЗРАХУНОК СУХИХ ТРАНСФОРМАТОРІВ З ЛИТОЮ ІЗОЛЯЦІЄЮ ТА З ФОЛЬГОВИМИ ОБМОТКАМИ

The method of analytical thermal calculation of dry transformers with cylindrical conductors with cast insulation and foil windings is presented. The surface and volume averaged temperatures of the magnetic system core and the wind-ings are determined from the one-dimensional non-linear substitute thermal circuit of the transformer. To clarify the temperature distribution across the cross-section of the anisotropic foil winding, the solution of the boundary value problem in the form of a two-dimensional Poisson equation with heat transfer coefficients calculated from the substitute scheme is used. Calculation example of a dry transformer with a capacity of 2500 kVA is given. Numerical CFD model-ing was performed to verify the calculation results. Bibl. 10, fig. 9, tab. 3.

Calculation method and analysis of residual stress in the strip bending roller straightening process

Taking thin gauge strip as an example, the deformation process of metal strip in bending roll straightening was studied. Based on the theory of discrete, curvature integral and elastic–plastic mechanics, the strip travel trajectory of the bending roll straightening process is analyzed, and the numerical analytical calculation method of the continuous straightening process of the strip bending roll is established. The results are verified by establishing MARC finite element simulation and designing straightening experiment. The effects of yield strength, plastic rate and bending amount on residual stress after straightening were studied. In the straightening process, with the increase of the amount of bending roll, the residual strain converges to the region Γ, and with the increase of the yield strength, the region Γ decreases. With the increase of the yield strength, the amount of bending roll and the plastic rate, the wave height increases. The results of the calculation of residual stress, finite element simulation and experiment are close and the trend is consistent. The results show that the logic of the calculation method is reasonable, and the prediction error is within the scope of engineering application, which is helpful to the realization of process intelligence in the process of bending roller straightening.

Analytical Solution for the Deformation of Pipe Galleries Adjacent to Deep Excavation

Deep excavations clearly impact adjacent existing properties and threaten their operational safety. Predicting the deformation of existing infrastructure induced by nearby underground construction is the main concern of urban underground development. This paper presents an analytical calculation method for predicting underground pipe gallery deformations induced by adjacent deep excavations. First, the authors assume the existing pipe gallery to be nonexistent in the soil and propose a solution to calculate the excavation-induced vertical movements of the soil at the position of the existing pipe gallery. Thereafter, the authors simplify the existing pipe gallery as an elastic beam on a Winkler foundation to calculate its deformation. Finally, the method is verified by the good agreement found between the calculated result and the field measurement of the construction of the Shanghai Hongqiao CBD project. The proposed analytical method of this work can provide accurate evaluation results for similar engineering projects.

Development of a Novel Lightweight Utility Pole Using a New Hybrid Reinforced Composite—Part 1: Fabrication and Experimental Investigation

This paper is the first part of a two-part paper that discusses the development of a novel lightweight and cost-effective hybrid 3D composite material and its and utilization for constructing utility poles. The main objective was to generate a material/pole with a comparable performance to the commercially available poles made of 2D fiber-reinforced polymer (FRP) and examine its feasibility. The novel hybrid composite was configured using a recently developed and marketed 3D E-glass fabric–epoxy composite reinforced with wood dowels, referred to as 3D dowel-reinforced FRPs (3D-drFRPs) hereafter. Firstly, the compressive and flexural properties of the 3D-drFRPs are evaluated. Then, the development of the 3D pole is discussed followed by the fabrication details of two 3D-drFRPs using the standard test method, and their responses are compared. For the second part, robust finite element (FE) models were developed in an LS-DYNA environment and calibrated based on the experimental results. A sophisticated nonlinear FE model was used to simulate the performances of ASTM standard-size compression and three-point bending specimens and tapered 2D and prismatic 3D poles. Moreover, the responses of equivalent 2D and 3D poles were simulated numerically, as the task could not be accommodated experimentally due to our laboratory’s deficiencies. The integrity of the numerical simulation results was validated against experimental results, confirming the accuracy of the developed model. As an example, the stiffness values for the 3-pt bending specimens and the 3D poles obtained through the simulations were very close to the experimentally obtained results, with small margins of errors of 3.2% and 0.89%, respectively. Finally, a simplified analytical calculation method was developed so practicing engineers can determine the stiffnesses of 3D-DrFRP poles very accurately and quickly.