Analytical Calculation Method Research Articles

Technical note: A fast and accurate analytical dose calculation algorithm for 125 I seed-loaded stent applications.

The safety and clinical efficacy of 125 I seed-loaded stent for the treatment of portal vein tumor thrombosis (PVTT) have been shown. Accurate and fast dose calculation of the 125 I seeds with the presence of the stent is necessary for the plan optimization and evaluation. However, the dosimetric characteristics of the seed-loaded stents remain unclear and there is no fast dose calculation technique available. This paper aims to explore a fast and accurate analytical dose calculation method based on Monte Carlo (MC) dose calculation, which takes into account the effect of stent and tissue inhomogeneity. A detailed model of the seed-loaded stent was developed using 3D modeling software and subsequently used in MC simulations to calculate the dose distribution around the stent. The dose perturbation caused by the presence of the stent was analyzed, and dose perturbation kernels (DPKs) were derived and stored for future use. Then, the dose calculation method from AAPM TG-43 was adapted by integrating the DPK and appropriate inhomogeneity correction factors (ICF) to calculate dose distributions analytically. To validate the proposed method, several comparisons were performed with other methods in water phantom and voxelized CT phantoms for three patients. The stent has a considerable dosimetric effect reducing the dose up to 47.2% for single-seed stent and 11.9%-16.1% for 16-seed stent. In a water phantom, dose distributions from MC simulations and TG-43-DP-ICF showed a good agreement with the relative error less than 3.3%. In voxelized CT phantoms, taking MC results as the reference, the relative errors of TG-43 method can be up to 33%, while those of TG-43-DP-ICF method were less than 5%. For a dose matrix with 256 × 256 × 46 grid (corresponding to a phantom of 17.2 × 17.2 × 11.5cm3 ) for 16-seed-loaded stent, it only takes 17s for TG-43-DP-ICF to compute, compared to 25h for the full MC calculation. The combination of DPK and inhomogeneity corrections is an effective approach to handle both the presence of stent and tissue heterogeneity. Exhibiting good agreement with MC calculation and computational efficiency, the proposed TG-43-DP-ICF method is adequate for dose evaluation and optimization in seed-loaded stent implantation treatment planning.

Optimization and improvement of ac resistance calculation method for multi-phase parallel-wiring cables

Parallel-wiring cables are often used in multi-phase AC aircraft Electrical Power Systems (EPSs). However, it complicates the ac resistance estimation. To solve this issue, an analytical resistance calculation method for parallel-wiring cables in multi-phase EPS was proposed. Firstly, the existing calculation formula of proximity factor was optimized, and the calculation error was reduced from 16% to 2% when two conductors are close to each other. Afterwards, the superposition effect on current density distribution between multi-conductors was considered based on orthogonal decomposition method, and the position of the equivalent charged points were easily determined. Finally, the ac resistance calculation formula was derived according to characteristics of parallel-wiring strategy, and the general ac resistance calculation methods of multi-phase parallel-wiring cables were presented. The proposed approach considerably enhances the applicability of ac resistance analytical calculation method for multi-conductor cables. Thanks to the accuracy of the proposed method, it can be used in many cases to avoid case-by-case simulation work and facilitate efficient system design and analysis.

Damage assessment of prefabricated prestressed channel slab under plane charge blast

The study of the mechanical properties of prestressed concrete channel slabs under different plane charge air blasts for applications in civil defense engineering is significant. For this reason, similar simulation tests were conducted on the anti-explosive performance of three 1:3 scale prestressed concrete channel slabs under 9 times plane charge air blast. The positive duration was more than 260 ms to simulate the uniform distribution load of a strong blast air shock wave on the prestressed concrete channel slab. The results showed that the designed prestressed concrete channel slab had good displacement ductility without brittle destruction, which significantly reduced the damage of the blasting impact on the structure. The channel slab could resist an air shock load of 0.467 MPa without damage. On the other hand, the positive duration was not only related to the quality of the overlying soil but also related to the air shock wave overpressure design value. The channel plate is regarded as a rigid-plastic component to calculate its plastic dynamic response under explosive load. In addition, the reliability of the theoretical calculation results and ABAQUS software simulation were verified by experimental data, which provided a feasible analytical method for calculation and simulation research in civil air defense engineering.

Exploration of laser-induced isotope separation of BCl3

The analytical equations and theoretical calculation methods (proposed by Eerkens in 2005) are used to study the transport mechanics of the excited BCl3 molecules, including the molecular dynamic processes such as the slowing-down of epithermal molecules, the laser-excited molecules and population of epithermals, the pressure of gas source, the minimum temperature of the jet, and the nozzle throat radius. The enrichment factor β and product cuts Θo of the system are also demonstrated. When the temperature is higher, the product cuts is larger. The larger the pressure, the smaller the product cuts, and the enrichment factor is greater. Therefore, the appropriate temperature and pressure must be selected to optimize the isotope separation.

Design and Experimental Verification of Three‐Phase Medium‐Frequency Transformers for High‐Power DC‐DC Applications

The magnetically coupled three‐phase dual‐active‐bridge (DAB3) DC‐DC converter is highly suitable for high‐power applications. Although the converter has many advantages, the structure, working mode and electromagnetic effect of its key magnetic component—high‐power medium‐frequency three‐phase transformer (MFT3) is more complex, and the capacity, frequency, loss, temperature rise and leakage inductance restrict each other, forming a complex and systematic design problem. This paper focuses on the overall design method and performance of high‐power MFT3. Based on the analysis of steady‐state voltage and current waveforms of DAB3 converter, the expression of harmonic current is derived by using fundamental wave analysis, and the analytical calculation method of copper loss is proposed. According to the piecewise linear flux density waveform excited by six‐step voltage wave, the modified IGSE method is proposed to calculate the core loss. For MFT3 with three‐phase five column core topology, a lumped parameter thermal network model with 14 temperature nodes is established to obtain the temperature rise. The influence of winding arrangement on leakage inductance is analyzed, and the analytical expression of leakage inductance is presented. On this basis, the design method of high‐power MFT3 is proposed based on the free parameter scanning method. A 5 kHz, 15 kW MFT3 model with the nanocrystalline core material is made, and the leakage inductance, core loss, copper loss and temperature rise are extracted by finite element method (FEM) and experiment. The effectiveness of the proposed method is verified by comparing the design results with the FEM simulation and experimental results. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Variant selection of primary–secondary extension twin pairs in magnesium: An analytical calculation study

Twining is an important deformation mode in magnesium. In a deformed magnesium sample, an extension twin crystal, i.e., {101¯2} twin, can form inside a {101¯2} primary twin, which is named {101¯2}–{101¯2} secondary twin. These secondary twins often appear at the intersection of two primary twins, and form primary–secondary twin pairs. Experimental observations show that the most frequently observed primary–secondary twin pairs have a unique misorientation, i.e., twin variant selection exists. Such variant selection of the primary–secondary twin pairs is studied in this work. The crystallographic analysis reveals that the twin planes of the primary and secondary twins that form a twin pair have coincident intersection lines with the boundary where the twin pair adjoins. An analytical calculation method based on Eshelby's inclusion theory is developed, and the calculation results show that only for this unique misorientation, the stress fields concentrated at the rims of the primary and the secondary twins are mutually favoured. The analysis is further extended to the incoming–outgoing twin pairs across ordinary grain boundaries, and compared with the commonly used geometrical compatibility factor m′. It is found that m′ only gives good prediction for twin transmission when the shear stress component on the twin plane along the twin shear direction of the incoming twin is the major contributor to the resolved shear stress of the outgoing twin. When other stress components play a dominant role, m′ becomes ineffective in prediction, which is the case for the primary–secondary twin pairs.

Investigation of sag behaviour for aluminium conductor steel reinforced considering tensile stress distribution.

Sag calculation plays an important role in overhead line design. Since the tensile stress of aluminium conductor steel reinforced (ACSR) is required for the sag calculation, an analysis on sag behaviour when considering the tensile stress distribution can be very useful to improve the accuracy of sag results. First, this paper analyses the ACSR tensile stress distribution arising from the temperature maldistribution through proposing a new calculation formula. A finite-element analysis (FEA) model of ACSR is conducted for the solution of the new formula. By using the results, the error and limitations of the existing sag calculation methods for ACSR are discussed. As the critical point of sag calculation, knee-point temperature is solved iteratively involving the tensile stress maldistribution phenomenon in aluminium wires. Based on this iterative solution, an improved analytical method for the ACSR sag calculation considering the creep effect is presented and also compared with the hybrid sag method. The results show that these two methods are basically coincident without the consideration of creep effect, while there are non-negligible differences between them as the creep strain is involved. Compared with the existing analytical methods, the improved sag calculation method proposed in this paper can be applied in more extensive situations.

Experimental and mathematical methods for calculation of residual stresses in production of welded pipes

The results of physical and mathematical modeling of the stress-strain state of metal and residual stresses during plastic deformation of a sheet blank and welding of large-diameter pipes are generalized. One of the analytical methods for calculation of residual stresses during elastoplastic deformation of a rectangular bar and a wide strip is described. From the standpoint of continuum mechanics, it is shown that under the action of a bending moment, tensile stresses appear in the outer layers, and compressive stresses appear in the inner layers, which change sign during unloading and residual stresses remain in the metal, compressive stresses in the outer layers, and tensile stresses on the inner surface. As a result of the studies carried out, the authors for the first time obtained a picture of residual stresses distribution and found that at each technological operation of the formed pipe billet after its completion, tangential and axial residual tensile stresses σостmax/σв ≤ 0,31, act along the entire outer perimeter and length, which after expansion-calibration of pipes decrease to the magnitude σт σост/= 0,23σв and σост∞/= 0,18σв. Ii was established that the value and distribution of residual stresses are significantly influenced by the blank shape, the order of welds imposition, welding modes and mechanical properties of the metal. This conclusion was also confirmed by experimental studies of residual stresses, which were obtained by X-ray diffractometry and sequential etching of surface layers using the MerCulon «Tensor-3» system. The results of experimental studies have shown that during plastic deformation of the sheet blank and after welding, residual tensile stresses are observed on the outer surface in the pipe metal and in the weld, which can cause pipeline failure. The paper describes the results of numerical modeling of non-uniformity of the stress-strain state and residual stresses in the metal of pipe processing at all stages of production according to the JCO scheme: bending of the sheet edges → forming on a step-forming press → re-forming of the «spline pipe» - a pipe profile with divorced edges → calibration - pipe expansion. Based on the results of modeling by the finite element method, it is shown that the required geometric shape of the pipe and the dimensional accuracy of the LDP diameter are achieved when expanding the workpiece with an ovality of no more than 5 mm, while ensuring high-quality assembly and welding of edges of pipes to be joined in the line of the pipeline system.

Modeling and analytical calculation of road damage coefficient considering tire pressure and damping of vehicles

The road damage coefficient [Formula: see text] is a significant indicator to estimate the degree of the road damage caused by vehicles. The existing calculation method of [Formula: see text] is not convenient for the engineering application. To effectively evaluate the damage degree and facilitate the engineering application, this paper studied the simple and reliable analytical calculation method of [Formula: see text]. Firstly, a dynamic model of the vehicle–road system was created. The tire pressure and the tire damping were considered in the model. Moreover, the relationship between the tire vertical stiffness and the tire pressure is approximated as a linear function. Secondly, based on the dynamic model, according to the definition of [Formula: see text], a concise analytical formula of [Formula: see text] was derived and verified by numerical simulations. The relative errors of the analytical calculation results are all less than 0.1%. Thirdly, the influences of the tire pressure [Formula: see text], the damping ratio [Formula: see text] of the suspension system, and the damping ratio [Formula: see text] of the wheel system on [Formula: see text] were analyzed. Moreover, based on the analytical formula of [Formula: see text], a mathematical model of the optimal damping matching for the suspension system was established and a case study was also given. The research results show that the larger the tire pressure [Formula: see text], the larger the value of [Formula: see text] is. For each [Formula: see text], there is an optimal damping ratio [Formula: see text]. If the tire damping is ignored, it will lead to the design error for [Formula: see text]. Finally, some important conclusions were drawn. The analytical formula of [Formula: see text] and the conclusions can provide valuable references for the analysis of the road damage and the initial design of vehicle suspensions.

Analytical and numerical methods for calculation the deep of penetration the welding seam formed by the electron beam generated by glow discarge electron guns

The article is devoted to the problem of defining the focal diameter of electron beam, formed by the glow discharge electron guns, as well as the necessary pressure in the gun chamber for realising the welding process. Taking into account, that glow discharge electron guns are widely used in industry for welding of different metals, and that for providing the high quality of welding joints estimation of energetic parameters in beam focus is very important, proposed methods are very important for effective elaboration and designing of the novel glow discharge electron guns constructions for specific technological operations. With known focal beam deameter and thermodinamic parameters of welding details material the deep of penetration of welding seam, as well as the necessary pressure in discharge chamber have been estimatied. Two proposed methods are generally based on the analytical solving of explite equation and on numeracal solving of sophisticated non-linear equation. Obtained simulation results with and without taking into account the spsace charge of own beam electrons are also given

Theoretical analysis and finite element simulation of pipeline structure in liquefied soil

A mechanical analysis model for the floating of buried pipelines in soil liquefaction areas is established in this paper. In order to improve the inherent defects of the elastic foundation beam method based on the Winkler model and increase the calculation accuracy, the Pasternak model is introduced and the interaction between soil and spring is considered. A mechanical analysis method for buried pipelines in liquefaction zone considering axial load is proposed in present paper. According to the Pasternak model and the deflection curve differential equation, the pipe bending deformation curve equation and the deformation coordination equation are derived. The analytical calculation method of the pipe mechanical response is established. A new method of the mechanical analysis of the floating of buried pipelines in the liquefaction zone is provided. The mechanical response of the pipeline under the conditions of different pipeline parameters and liquefaction zone length is analyzed. The reliability of the analysis method in this paper is verified by the comparison of finite element method (FEM). Considering that the previous researches of scholars mainly focused on straight pipes, there are few studies on the pipe structure nodes in liquefied soil. The mechanical properties of the three-way pipe structure in the soil liquefaction zone are analyzed by the finite element method (FEM). The influence of pipe diameter, wall thickness, liquefied soil density, transition zone length, buried depth, and pipeline internal pressure on the mechanical response of the pipeline is analyzed.

Determination of Heat Transfer Coefficient from Housing Surface of a Totally Enclosed Fan-Cooled Machine during Passive Cooling

This paper presents the analytical calculation of the heat transfer coefficient of a complex housing shape of a Totally Enclosed Fan-Cooled (TEFC) industrial machine when it works below 20% of its nominal speed or close to stall. Therefore, passive cooling is dominant, and most of the heat is extracted by the combination of natural convection and radiation phenomena. Under these conditions, the area-based composite approach was used for the development of the analytical calculation method. A test rig using a TEFC Synchronous Reluctance Motor (SynRM) was constructed, and the collected experimental data was used to validate the proposed analytical method successfully.

Efficient calculations of NSS-based gaze similarity for time-dependent stimuli.

The degree of spatial similarity between the gaze of participants viewing dynamic stimuli such as videos has been previously measured using metrics which are based on the NSS (Normalized Scanpath Saliency). Methods currently used to calculate this metric rely upon a numerical grid, which can be computationally prohibitive for a variety of otherwise useful applications such as Monte Carlo analyses. In the present work we derive a new analytical calculation method for the same metric that yields equal or more accurate results, but with speeds than can be orders of magnitude faster (depending on parameters). Our analytical method scales well with dimensionality, and could also be of use for other applications. The drawback is that it can become very slow if the number of participants in the study is very large or if the gaze sampling rate is high. We provide performance benchmarks for a Fortran implementation of our method, and make available the source code developed.

Determining the Layout Parameters of the Gas Drainage Roadway: A Study for Sima Coalmine China

To determine the layout parameters of the gas drainage roadway (GDR) serving for the working face, an analytical calculation method of fracture zone and the modelling experiment were adopted, and the overburden fissure induced by mining and the height of fracture zone were analyzed. For the research on the distribution of fracture zone by analytical calculation method, the multiple factors influencing the failure mode of strata and the height of fracture zone were considered. The #1207 working face in Sima mine was taken as an engineering background, and the layout parameters of GDR were given by analyzing the height of fracture zone. Combining the results obtained by analytical calculation and scale modelling experiment, the suggested height of GDR was 10.7–32.8 m away from the coal seam roof, and the projection distance of GDR in the horizontal was within the range of 0–35 m from the airway. By monitoring the gas drainage effects in different heights away from coal seam roof in #1207 working face and in different horizontal distances away from the ventilation roadway in the #1211 working face, the results showed that the optimal height was 17.5–22 m away from coal roof, and the optimal horizontal distance was 17–21 m away from airway for GDR. The gas drainage effect of GDR indicated that the proposed parameters are scientific and reasonable.

Development of analytical calculation method for axisymmetric oscillations of circular and annular plates on variable Winkler elastic foundation

An analytical method for calculating axisymmetric vibrations of circular and annular plates on a variable elastic Winkler base is presented. The proposed calculation method is based on the exact solution of the oscillation equation with the subsequent development of a method for its numerical implementation. To construct an exact solution, the direct integration method is used, which was previously developed by one of the authors for differential equations with continuous variable coefficients. The proposed method does not require the discretization of the considered structure and it is a real alternative to the application of approximate methods during solving this types of problems. Based on the exact solution of the differential equation, this method will allow to obtain better picture of oscillations in comparison with approximate methods. In fact, the exact solution has qualitative information and forms the most complete picture of the physical phenomenon that is researched.

Design and testing of polar-orthotropic multi-layered composites under rotational load

The growing requirements for efficient and reliable high-performance rotors have led to an increased application of advanced fiber-reinforced composites. For an efficient feasibility analysis, analytical calculation methods for composite structures can provide a first design draft of typical composite components without cumbersome finite element models to engineers having low experience with anisotropic materials. In these investigations, an analytical solution for polar-orthotropic multi-layered composite rotors under rotational load is presented by transferring the well-known formulation of the classical laminate theory given in Cartesian coordinates into a formulation given in a polar coordinate system taking into consideration of centrifugal loads. The analytical results are verified under different rotational speeds with standard finite element solutions and also with experimental results at selected positions from strain gauges and diffraction grating strain sensors. The results show the usefulness of analytical solutions for the design engineer and can be further expanded to take into consideration temperature and shrinkage effects.

A High-Precision Analytical Method for Vibration Calculation of Slotted Motor Based on Tooth Modeling

The analytical methods are widely used to predict the vibration and noise of the permanent magnet motors in industry applications. In the traditional analytical method, the influence of the teeth is ignored and a large error of vibration calculation will occur in the slotted motor. In this article, a high-precision analytical method is proposed for vibration calculation of motors based on tooth modeling. First, the electromagnetic forces on each tooth of stator of the motor under no load and load are calculated. Then, the transfer function from the force acting on the teeth to the vibration on the surface of the shell is derived and verified by finite-element method (FEM). Next, the superposition method is introduced and used to superimpose the vibration excited by the force of all teeth to calculate the total vibration acceleration of the motor surface. Finally, the FEM and experiments are conducted to verify the effectiveness of the proposed method.

Direct Calculation of the Group Velocity for Two-Dimensional Complex, Composite and Periodic Structures Using a Wave and Finite Element Scheme

Guided waves have immense potential for structural health monitoring applications in numerous industries including aerospace. It is necessary to evaluate guided wave dispersion characteristics, i.e., group velocity and phase velocity profiles, for using them effectively. For complex structures, the profiles can have highly irregular shapes. In this work, a direct method for calculating the group velocity profiles for complex, composite, and periodic structures using a wave and finite element scheme is presented. The group velocity calculation technique is easy to implement, highly computationally efficient, and works with the standard finite element formulation. The major contribution is summarised in the form of a comprehensive algorithm for calculating the group velocity profiles. The method is compared with the existing analytical and numerical methods for calculation of dispersion curves. Finally, an experimental study in a multilayered composite plate is conducted and the results are found to be in good agreement. The technique is suitable to be used in all guided wave application areas such as material characterisation, non-destructive testing, and structural health monitoring.

Geometric Analysis of Ground-Target Coverage from a Satellite by Field-Mapping Method

This paper proposes an analytical calculation method of the ground point visibility from a satellite in a circular orbit for an arbitrary sensor field considering the perturbation based on the geometric analysis of the sensor, satellite, and ground-point target. First, to describe an arbitrary field of view accurately, the concept of the field-element vector is introduced to parameterize the field discretely. Also, based on the geometric projection, the field-element equations related to the satellite orbit, field parameters, and ground point, which can be solved analytically, are derived. Furthermore, using a two-dimensional map composed of the argument of latitude and ascending node, the problem of calculating visible intervals is transformed into the intersection problem of a group of parallel lines and single or double regions generated by the field of view and the target ground point, which can be solved rapidly. The proposed method is verified by simulations considering different types of sensor fields. The simulation results show that the proposed method is rapid, efficient, intuitive, and accurate, which makes it be suitable for different types of fields and have wide application prospects.

Analytical method of calculation of thermal fields of foundry cores

The aim of the work is to create on the basis of the analysis of thermophysical parameters and regularities of mathematical methods, which allows to calculate the distribution of thermal fields in molds and rods using a system of analytical formulas. The method of calculating thermal fields in foundry molds and rods developed and presented in this publication is based on the finite difference method. Much attention is paid to the calculations of the dynamics of changes in the surface temperatures of the casting rod and its center. The article shows that the basis for the correct calculation of the thermal field of the rod is to establish the change in surface temperature in the first few seconds after the start of contact with the melt. All currently available methods do not take into account this change in temperature. A new concept is introduced - the period of thermal inertia of the rod. This is the period of time during which its surface temperature rises from the initial value (ambient temperature) to a value corresponding to the surface temperature of the casting. The period of thermal inertia depends exclusively on the thermophysical properties of the rod. To calculate the temperature change in the center of the casting rod, a modified method of S. Schwartz was used: instead of the constant contact temperature of the "casting-rod" in the formula takes into account the previously estab- ?ished dynamics of changes in this temperature. The thermal fields of cylindrical foundry rods with diameters of 50 mm and 16 mm were calculated according to the created mathematical method. A comparison of the results of calculations according to the developed method and with the use of existing software is presented. The difference in design temperatures is 100 oC and more. The difference in determining the thermal fields of a smaller diameter rod is particularly noticeable, which is due to the rapid dynamics of changes in the surface temperature of the casting, which is currently not taken into account by current methods. The developed mathematical technique can be offered as a theoretical basis for refining applied computer programs for foundry production.