Practical Formula Research Articles

An efficient relaxed shift-splitting preconditioner for a class of complex symmetric indefinite linear systems

<abstract><p>In this work, by introducing a scalar matrix $ \alpha I $, we transform the complex symmetric indefinite linear systems $ (W+i T)x = b $ into a block two-by-two complex equations equivalently, and propose an efficient relaxed shift-splitting (ERSS) preconditioner. By adopting the relaxation technique, the ERSS preconditioner is not only a computational advantage but also closer to the original two-by-two of complex coefficient matrix. The eigenvalue distributions of the preconditioned matrix are analysed. An efficient and practical formula for computing the parameter value $ \alpha $ is also derived by computing the Frobenius norm of symmetric indefinite matrix $ T $. Numerical examples on a few model problems are illustrated to verify the performances of the ERSS preconditioner.</p></abstract>

Extensions of a classical mechanics “piston-model” for understanding the impact of asymmetry on ICF implosions: The cases of mode 2, mode 2/1 coupling, time-dependent asymmetry, and the relationship to coast-time

As long suspected, low mode asymmetry in inertially confined fusion (ICF) implosions has been implicated as a performance limiting factor [Casey et al., “Evidence of three-dimensional asymmetries seeded by high-density carbon-ablator nonuniformity in experiments at the national ignition facility,” Phys. Rev. Lett. 126, 025002 (2021)]. Recently a non-linear, but solvable, theory [Hurricane et al., “An analytic asymmetric-piston model for the impact of mode-1 shell asymmetry on ICF implosions,” Phys. Plasmas 27, 062704 (2020)] based upon the simple picture of a pair of asymmetric pistons has generated new insights and provided some practical formulas for estimating the degradation of an implosion due to mode-1 asymmetry and demonstrated a previously unrecognized connection between measured hot-spot drift velocity, nuclear down-scatter ratio asymmetry, and the concept of residual kinetic energy (RKE). Asymmetry of the implosion “shell,” as opposed to asymmetry of the hot-spot, was key to the classical mechanics model because the majority of the kinetic energy in an implosion is carried by the shell. Herein, the two-piston model is extended to a six-piston model in order to capture mode-2 asymmetry and coupling between mode-1 and mode-2. A key result of this new six-piston model is that the weighted harmonic mean of shell areal density is the fundamental quantity that determines the RKE and performance degradations for a three-dimensional implosion. Agreement is found between the scalings coming from the theory and ICF implosion data from the National Ignition Facility and to large ensembles of detailed simulations. The connection between the piston model's dependence upon the radius of peak velocity and coast-time is also highlighted in this paper. Finally, by extending the two-piston model to include time-dependent “swing,” it is shown in the Appendix that the shell asymmetry at the time of stagnation dominates the solution for RKE.

Confinement Effect and Efficiency of Concentrically Loaded RACFCST Stub Columns.

Recycled aggregate concrete-filled steel tubular (RACFST) columns are widely recognized as efficient structural members that can reduce the environmental impact of the building industry and improve the mechanical behavior of recycled aggregate concrete (RAC). The objective of this study is to investigate the behavior of recycled aggregate concrete-filled circular steel tubular (RACFCST) stub columns subjected to the axial loading. Three-dimensional finite element (FE) models were established using a triaxial plastic-damage constitutive model of RAC considering the replacement ratio of recycled aggregates. The FE analytical results revealed that the decreased ultimate bearing capacity of RACFCST stub columns compared with conventional concrete infilled steel tubular (CFST) columns was mainly due to the weakened confinement effect and efficiency. This trend will become more apparent with the larger replacement ratio of recycled aggregates. A practical design formula of the ultimate bearing capacity of RACFCST stub columns subjected to axial load was proposed on the basis of the reasonably simplified cross-sectional stress nephogram at the ultimate state. The derivation process incorporated the equilibrium condition and the superposition theory. The proposed equation was evaluated by comparing its accuracy and accessibility to some well-known design formulae proposed by other researchers and some widely used design codes.

Calculation of the temperature fields spread at subzero temperature in a monolithic beam

Monolithic construction in winter is faced with problems of concrete strength gain at subzero ambient temperatures. In order to ensure the necessary temperature conditions for hardening and hardening of concrete, various methods of heating structures are used. The relevance of this article is due to the climatic conditions of construction in most of the Russian territory and lack of a unified calculation method. The existing calculation methods are either easy to use, but give approximate answers, or exact solutions, but cumbersome and inconvenient in daily use. This paper presents group analysis method of differential equations used to predict temperature regimes for concreted structures. Solving the nonlinear differential equation of thermal conductivity by group analysis made it possible to derive, using nonlinear submodels, simple and convenient for practical application calculation formulas for modeling the temperature fields of heated structures. Experimental verification of the two proposed solutions of the nonlinear equation was carried out on the basis of the monolithic girder model, subjected to heat treatment at different powers.

Аналитическое исследование теплообмена при нагреве или охлаждении лимитированного объема жидкости

The paper shows the results of analytical studies of heat transfer when heating or cooling a limited volume of liquid. The purpose of the research was to determine the size of the heat transfer surface, with the initial parameters of the coolants, the final temperature in the reactor and its thermal equivalent, as well as the flow rate of the second coolant through the heat exchanger corresponding to the water equivalent at a given cooling time τo. Moreover, if intensive mixing is carried out in the vessel, i.e., if the temperature of the second heat carrier practically does not change along the length of the heat transfer surface, then W2 → ∞. The solution was based on the Laplace --- Carson integral transform. The exact solution was converted for special cases of heat transfer. In particular, it should be noted that in many practical cases formulas give a fairly good approximation to the exact solution. Only at low values of the heat transfer coefficient, as well as when the volume occupied by the coolant inside the heat exchanger is commensurate with the volume of the liquid contained in the vessel, it is necessary to apply the given exact solution

Seismic design method and plastic hinge of square steel tube confined reinforced concrete (STRC) columns

Steel tube confined reinforced concrete columns have the advantages of high bearing capacity, good ductility and convenient construction, which meet the requirements of "building industrialization", so they are widely used in high-rise buildings. Based on the plastic-damage constitutive model of concrete and elastic-plastic mixed strengthen constitutive model of steel, finite element software ABAQUS was used to build an elaborate 3D finite element solid model and perform pseudo-static analysis of square steel tube confined RC(STRC) columns. The model considered the confinement effect of the steel tube exerting on the core concrete, as well as reasonable boundary conditions and loading modes. Good agreement was achieved between the finite element analysis results and the existing quasi static experimental results regarding to the failure modes, load-displacement hysteretic curves and load-displacement skeleton curves. Based on the validated model, 136 full scale model examples were established and extensive parametric analysis was conducted. The results show that the confinement of external steel tube can reduce the peak compressive strain and increase the peak compressive stress of concrete, thus delaying the failure of RC column and improving its bearing capacity and ductility effectively. Besides, the failure displacement angle and ultimate bearing capacity increase when the thickness of steel tube increases. Finally, the seismic design method including reasonable thickness and hoop index of the steel tube were proposed for 5 material strength matching and different axial compression ratios. A method to judge the plastic hinge based on concrete strain and steel tube strain was proposed, as well as a practical calculation formula of plastic hinge length. This study can provide basis and support for the seismic design of frame columns.

Composite walls Composed of profiled steel skin and foam rubberized concrete subjected to eccentric compressions

This paper addresses the structural behaviour of profiled steel composite walls (PSCWs) infilled with foam rubberized concrete (FRC) under concentric, eccentric and flexural loads. FRC mechanical properties such as compressive strength, flexural strength, and splitting tensile strength are presented for different rubber contents; 0%, 50%, and 100% as sand replacement by volume. FRC with unit weight of 1000 kg/m3 and 50% rubber content was selected as the filler material. Three PSCWs were tested under concentric, eccentric compressive loads, and four-point bending loads. Finite element modelling (FEM) using ABAQUS software has been carried out to simulate the experimental behaviour of the PSCWs. Parametric study was carried out to investigate the effect of different concrete and steel strengths and steel sheet thicknesses. FEM results showed a good agreement with the experimental results. Practical formulas in terms of concrete strength, steel sheet buckling stress, wall geometry, and eccentricity are presented to predict interaction diagrams for PSCW structures.

Numerical derivation and validation of the angular, hemispherical and normal emissivity and reflectivity of common window glass

The thermal radiative properties of glazing materials are fundamental inputs for evaluating the energetic performance and thermal behaviour of buildings. These properties are required for many practical applications ranging from infrared thermography to building performance simulation and thermal comfort evaluations. Soda–lime–silica glass is the most widely used glass, worldwide, for glazing and the derivation of its thermal and optical properties are the subject of this work. Based on experimentally acquired spectral reference measurement data for soda-lime glass, the complex-valued Fresnel equations are solved and Monte-Carlo integration is carried out over the black-body spectrum, as well as over the hemisphere. These calculations are performed for various radiative temperatures to establish their temperature dependencies, and additionally the temperature-dependent transmittance of soda-lime glass was analysed. By applying a non-linear optimisation algorithm, computationally efficient practical fitting formulae for the angular reflectivity, emissivity and absorptivity are derived. All equations are numerically solved with a high degree of accuracy. The determination of the hemispherical total emissivity for this type of glass confirms the current accepted value (∼0.2%) originally derived by Rubin (1985). A simple yet robust experimental design, based on thermography, is used to validate the results of the numerical reflectivity model. Additionally, we provide angular functions, fitting functions and additional constants that were hitherto unavailable. The practical benefits of the fitting formulae provided are considerable in relation to modelling the reflection of thermal radiation on glazed surfaces, and are demonstrated in two case-study applications in the appendix.

A unified framework for the study of high-order energy-preserving integrators for solving Poisson systems

As is known, a system of differential equations possessing a first integral can be written in a non-canonical Hamiltonian system that often leads to a Poisson system under moderate conditions. Therefore, energy-preserving numerical integrators for such systems have become a subject of intensive investigation. In this paper, we design and analyse two classes of energy-preserving functionally-fitted integrators of arbitrary order for Poisson systems with highly oscillatory solutions using a new framework. We also show that both the order and the stage order of the proposed integrators may be affected by the used quadrature formula in practice. Furthermore, the existence and uniqueness of energy-preserving functionally-fitted integrators, their implementation issues, and the conservation of Casimir functions are investigated in detail. Finally, numerical experiments are carried out with the fourth-order and sixth-order energy-preserving integrators proposed in this paper, including the Lotka-Volterra system and the charged-particle dynamics in a strong magnetic field, and the numerical results demonstrate the remarkable accuracy and efficiency of our high-order energy-preserving integrators compared with the other energy-preserving methods in the literature.

Improvements in Quality of Life and Thyroid Parameters in Hypothyroid Patients on Ethanol-Free Formula of Liquid Levothyroxine Therapy in Comparison to Tablet LT4 Form: An Observational Study.

Levothyroxine (LT4) is a standard therapy in hypothyroidism; however, its bioavailability and therapeutic effects might be affected by many factors. Data shows that therapy with liquid LT4 characterized by quicker pharmacokinetics provides better thyroid hormones control than tablet LT4. We addressed the quality of life (QoL) and efficacy of the new ethanol-free formula of liquid LT4 (Tirosint®SOL) treatment in 76 euthyroid patients with primary (PH, n = 46) and central hypothyroidism (CH, n = 30), and compared the results to retrospective data on equivalent doses of tablet L-T4 therapy. After 8 weeks of liquid LT4 therapy, we found a significant improvement in QoL in both PH and CH patients. TSH levels were unaltered in PH patients. Free hormone levels (fT4 and fT3) increased in all the patients, with the exception of fT3 in the CH group. SHBG and low-density lipoprotein (LDL) also improved. Liquid LT4 therapy provided a better thyroid hormone profile and improvement in patients’ QoL than the tablet form, which was possibly due to the more favorable pharmacokinetics profile resulting in better absorption, as suggested by the increased free thyroid hormone levels. In summary, this is the first study addressing the QoL in hypothyroid patients, including primary and central hypothyroidism, treated with liquid LT4 formula in everyday practice.

Experimental and numerical study on compressive behavior of welded hollow spherical joints with external stiffeners

Welded hollow spherical joints are one of the most popular joints used in reticulated shell structures. Welded hollow spherical joints in service may need to be strengthened due to age-related damage or unexpected overloading. Adding external stiffeners to the welded hollow spherical joint is an effective way to strengthen it. In this paper, experimental and numerical studies are performed to investigate the enhanced behavior of welded hollow spherical joint with external stiffeners. Axial compression tests of five specimens are performed with a particular focus on the effects of the number, height, and thickness of the external stiffeners on the load-bearing capacity of the joint. A 3D finite element model is developed and calibrated against the experimental results. Parametric studies on a number of design variables are conducted using the calibrated finite element model. The results show that the external stiffeners significantly enhanced the compressive capacity of the joint, and the compressive capacity of the joint is increasing with the number, height, and thickness of the external stiffeners increasing. It is also found that the diameter of the hollow sphere has little impact on the enhanced behavior of the welded hollow spherical joint with external stiffeners. Practical formulas for axial load-bearing capacity and initial axial stiffness of the welded hollow sphere joint with external stiffeners are developed, based on the results of parametric studies.

On the Number of Conjugate Classes of Derangements

The number of conjugate classes of derangements of order n is the same as the number h n of the restricted partitions with every portion greater than 1. It is also equal to the number of isotopy classes of 2 × n Latin rectangles. Sometimes the exact value is necessary, while sometimes we need the approximation value. In this paper, a recursion formula of h n will be obtained and also will some elementary approximation formulae with high accuracy for h n be presented. Although we may obtain the value of h n in some computer algebra system, it is still meaningful to find an efficient way to calculate the approximate value, especially in engineering, since most people are familiar with neither programming nor CAS software. This paper is mainly for the readers who need a simple and practical formula to obtain the approximate value (without writing a program) with more accuracy, such as to compute the value in a pocket science calculator without programming function. Some methods used here can also be applied to find the fitting functions for some types of data obtained in experiments.

Seismic performance of a new S-shaped mild steel damper with varied yielding cross-sections

In this paper, a novel replaceable metallic energy dissipation device named S-shaped mild steel damper with varied yielding cross-sections (VYSSD) is proposed. The VYSSD mainly consists of consumption plate, outer limit plates and fixed bottom plate, in which the consumption plate is the energy dissipation element and can be easily replaced after earthquakes. Under action of external loads, section curvature of each segment of the consumption plate changes and the sections gradually enter yielding state to dissipate energy through flexural plasticity. A total of 18 VYSSD specimens were cyclically tested under quasi-static and fatigue loads to investigate the hysteretic behavior and seismic performance. The results show that the VYSSD has pump hysteretic loops, good low cycle fatigue performance and desirable displacement capacity. It is capable of avoiding plastic deformation concentration of traditional metallic dampers, and the failure mode is dominated by fatigue crack propagation. Moreover, a solid finite element model which can effectively simulate the hysteretic behavior and plasticity development of VYSSD was built, and the practical design formulas were suggested through parametric studies considering different geometric dimensions. Finally, a representative 20-story benchmark model was employed for seismic resilient application of the VYSSD. The structures with and without damper retrofitting were numerically modelled for conducting nonlinear dynamic analysis and seismic fragility analysis. The analyses illustrate that the VYSSD can significantly enhance the structural seismic performance, and exceedance probabilities of damage, demolition and collapse for the damper-fused structure are much lower than that of the original structure.

Significado de los nombres de los enerpuntos y su sinfonía en la clínica

The Chinese names of enerpoints (acu-points) to Western scholars are a mystery. Given their Western nomenclature (H 5, E 36), we assume that they do not affect when selecting a point formula in clinical practice. However, there is always the doubt if the name contains something else. Most were born in a time known as the great cultural renaissance of China, between the first and fourth century, and consist of two or more characters within a certain syntax. Each of the characters that compose them can be a verb, a noun, and even an adjective. According to the interpretation, meanings emerge that are not only interesting but also particularly useful in the clinic. For example, in Zusanli (E 36) 足 zu means “foot”; 三 san “three”; 里 li “close to”, and 理 li “regulate, control” allows to interpret the point as a regulator of the three heaters, located in the foot. Given the number of points in the 14 channels, only the names of some points have been discussed to present this proposal for further search of the meaning of the points; thanks to whose knowledge it is possible to increase the clinical efficacy of acupuncture.

Numerical Simulation and Shear Capacity Study of a New Double-Steel-Plate Shear Wall

This paper presents a new type of double-steel-plate shear wall. Through the finite element software, the stress and plastic strain of steel plate and concrete in different loading stages of the wall are analyzed, the mechanical properties and failure rules of the wall are revealed, and the failure mechanism of the wall is obtained. The comparison with the test results verifies the correctness of the finite element analysis. Through nonlinear finite element parameterization analysis, the composition of shear capacity of each composite wall is obtained. Based on the superposition theory, practical calculation formula of its shear capacity is given, and through a comparative analysis with simulation test results, the goodness-of-fit is satisfying.

A Study on Steel-Concrete-Steel Wall to Resist Perforation from Rigid Projectile Impact

A calculation method of SCS wall which is used in the third generation of nuclear power plants to resist perforation from rigid projectile based on energy method is proposed in this paper. The energy is divided into four parts including the energy dissipated by front steel plate, concrete, back steel plate, and tie bars. The method accounts for the perforation of the concrete and steel plates separately and accounts for the interaction between them, and a practical antiperforation calculation formula of SCS wall with tie bars is given. The most formular results are close to the test results and the FEM results with a deviation less than 10%, which shows that the calculation formula given in this paper is reasonable and credible to effectively evaluate the perforation failure of the SCS wall and carry out a relevant design. The energy dissipated by the steel plate is much larger than that of the tie bars through a comparative analysis of dissipated energy. The effects of various factors on perforation velocity are analyzed according to finite element calculation results, which can be roughly divided into three categories: the influence of the thickness of steel plate and distance of tie bar is the largest effect, followed by that of yield strength of steel plate, yield strength of tie bar and diameter of tie bar, and that of compressive strength of concrete is the smallest effect.

EXPERIMENTAL STUDY ON THE MECHANICAL PROPERTY OF STEEL BAR-PIERCED JOINTS OF RC BEAMS AND RECTANGULAR CONCRETE-FILLED STEEL TUBULAR COLUMNS

To overcome the problems of RC beam-and-rectangular concrete-filled steel tubular column joints in high-rise buildings such as the indirect force transmission, complex construction and unguaranteed construction quality, a steel bar-pierced joint of RC beams and rectangular concrete-filled steel tubular columns was proposed for the Z13 project of the Beijing CBD core area. Low-cycle reciprocating loading tests were performed on the steel bar-pierced joints of RC beams and rectangular concrete-filled steel tubular columns with different reinforcement ratios to study the hysteretic performance, failure mode, energy dissipation capacity and ductility, which were compared with those of the conventional welded bracket joints and the joints of sleeves and brackets for RC beams and rectangular concrete-filled steel tubular columns. Based on the experimental results, the theoretical analysis of the mechanical properties of the steel bar-pierced joints of RC beams and rectangular concrete-filled steel tubular columns was conducted. Practical design formula were derived. It was indicated that the steel bar-pierced joint of RC beams and rectangular concrete-filled steel tubular columns had higher bearing capacity than the other two types of joints, which could meet the structural design requirements of “strong joints and weak components” and vertical load transmission. They are convenient to construct and reliable in quality. On this basis, the design formula for the bending bearing capacity of the joint is proposed. The section design of the steel corbel section is recommended to bear 80% of the beam end shear force to provide technical support for the optimization of the design of the rectangular concrete-filled steel tubular column-concrete beam through-reinforced joints.

The standardizing texture of thickened barium stimuli in the videofluoroscopic swallowing study at a medical center in Taiwan

This study aimed to establish more practical standardized barium stimuli formulas for the videofluoroscopic swallowing study (VFSS) for clinical use. For clinical practice, we established the formula for preparing barium stimuli to comply with different International Dysphagia Diet Standardization Initiative (IDDSI) levels. To comply with the definition of IDDSI levels 0-4, the gum-based thickener concentration of thickened barium was 0, 0.3, 0.6, 1.0, and 2.0g/100mL, respectively. The formulas established in this study may replace traditional barium stimuli for dysphagia assessment in clinical settings.

Stress concentration factors in steel tubular KT-connections with FRP-Wrapping under bending moments

Stress concentration factors (SCF) in steel tubular joints have gained considerable attention since it is the crucial parameter for fatigue design of steel tubular structures. Meanwhile, among various strengthening methods, Fiber Reinforced Polymer (FRP) wrapping has shown to be an effective scheme for reinforcing steel structures. This study is dedicated to the numerical investigation of SCF values in FRP-strengthened tubular KT-joints under the action of In-Plane Bending (IPB) and Out-of-Plane Bending (OPB) moments on the central as well as outer braces with three various practical loading patterns per each moment. The Finite Element (FE) modeling methodology for joint geometry and FRP generation was validated against the available data in the literature and well-known codes. The effects of different geometrical parameters along with the FRP parameters on the SCF values were studied through post-analyzing a total of 2920 FE models. The numerical parametric studies indicated that FRP strengthening could lower the SCF values in KT-connections by about 30 and 55 percent under IPB and OPB moments, respectively. Using the driven data, practical fatigue design formulas were developed for predicting SCF in FRP-strengthened KT-joints under bending moments, and reliability of the proposed equations was examined using Fatigue Guidance Review Panel recommendations.

Integrated assessment of the hydraulic and structural performance of crown walls on top of smooth berms

The introduction of crown walls with parapets on top of dikes and berms represents a relatively economic and efficient solution to reduce the wave overtopping discharge and therefore the hazard exposure of the inshore areas. However, the inclusion of parapets and bullnoses leads to increased wave pressures on the crown walls that may compromise their resistance. Literature studies have so far addressed separately the effects of crown walls, parapets and bullnoses on the hydraulic efficiency and on the structural stability. The purpose of this contribution is to fill the gap between these two streams of research, proposing an integrated analysis of the wave loads and of the wave overtopping discharges at smooth berms that are supposed to be upgraded with crown walls and parapets. The study is based on the results of a recent campaign of 2D small-scale laboratory tests on wave overtopping at smooth berms with crown walls under breaking and non-breaking waves. Relevant parameters of the sensitivity analysis are the berm slope, width and relative emergence, the crown wall height, and the inclusion of a parapet. The main outcome of the investigation consists of a set of indications for the optimized reduction of the discharge with a limited increase of structural loads. A simple and practical formula linking forces and overtopping discharges at walls and highlighting the strict correlation between the two variables is also proposed.