Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations: A Review

Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.

Comparison study on calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949

In order to study the calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949, tests on the mechanical performance of 66 rebars from different modem Chinese concrete buildings, the concrete compressive strength of 12 modem Chinese concrete buildings, and the concrete cover thickness of 9 modem Chinese concrete buildings are carried out; and the actual material properties and structural conformations of modem Chinese concrete buildings are obtained. Then, the comparison on calculation methods of bending behavior including the original Chinese calculation method, the present Chinese calculation method, the present American calculation method and the present European calculation method is studied. The results show that the original Chinese calculation method of bending behavior is based on the allowable stress calculation method, and the design safety factors are 3.55 to 4. 0. In term of the calculation area of longitudinal rebars of reinforced concrete beams, without considering earthquake action, the original Chinese structural calculation method is safer than the present Chinese structural calculation method, the present European structural calculation method, and the present American structural calculation method. The results can provide support for the structural safety assessments of modem Chinese reinforced concrete buildings.

Calculation of effective temperature for pavement rutting using numerical simulation methods

In order to predict the long-term rutting of asphalt pavement, the effective temperature for pavement rutting is calculated using the numerical simulation method. The transient temperature field of asphalt pavement was simulated based on actual meteorological data of Nanjing. 24-hour rutting development under a transient temperature field was calculated in each month. The rutting depth accumulated under the static temperature field was also estimated and the relationship between constant temperature parameters was analyzed. Then the effective temperature for pavement rutting was determined based on the rutting equivalence principle. The results show that the monthly effective temperature is above 40 t in July and August, while in June and September it ranges from 30 to 40 Rutting development can be ignored when the monthly effective temperature is less than 30 t. The yearly effective temperature for rutting in Nanjing is around 38. 5 t. The long-term rutting prediction model based on the effective temperature can reflect the influences of meteorological factors and traffic time distribution.

Simplified Calculation Methods for All-Vertical-Piled Wharf in Offshore Deep Water

All-vertical-piled wharf is a kind of high-piled wharf, but it is extremely different from the traditional ones in some aspects, such as the structural property, bearing characteristics, failure mechanism, and static or dynamic calculation methods. In this paper, the finite element method （FEM） and theoretical analysis method are combined to analyze the structural property, bearing behavior and failure mode of the all-vertical-piled wharf in offshore deep water, and to establish simplified calculation methods determining the horizontal static ultimate bearing capacity and the dynamic response for the all-vertical-piled wharf. Firstly, the bearing capability and failure mechanism for all-vertical-piled wharf are studied by use of FEM, and the failure criterion is put forward for all-vertical-piled wharf based on the ＇plastic hinge＇. According to the failure criterion and P-Y curve method, the simplified calculation method of the horizontal static ultimate bearing capacity for all-vertical-piled wharf is proposed, and it is verified that the simplified method is reasonable by comparison with the FEM. Secondly, the displacement dynamic magnification factor for the all-vertical-piled wharf under wave cyclic loads and ship impact loads is calculated by the FEM and the theory formula based on the single degree of freedom （SDOF） system. The results obtained by the two methods are in good agreement with each other, and the simplified calculation method of the displacement dynamic magnification factor for all-vertical-piled wharf under dynamic loads is proposed. Then the simplified calculation method determining the dynamic response for the all-vertical-piled wharf is proposed in combination with P-Y curve method. That is, the dynamic response of the structure can be obtained through the static calculation results of P-Y curve method multiplied by the displacement dynamic magnification factor. The feasibility of the simplified dynamic response method is verified by comparison with the FEM under different conditions.

Forward Calculation of 2-D and 3-D Structures with a Cover by the Boundary Element Method while Using Electrical Methods

This paper develops the boundary element method, the authors employ two-layered earth Green 's functions as the weighting functions of residual and derive boundary integral equations. The forward problems of point sources on 2 - D and 3-D structures with an influencing cover are solved by this method. The results show that this method markedly improves the original boundary element method. The features of the improved method are greater numerical accuracy and much smaller systems of equations and thus considerable savings for the storage capacity of computers, allowing us to solve the above problems with only ordinary microcomputers. The results in this paper extend the scope of applying the boundary element method while using electrical methods for geophysical prospecting.

Accuracy of corneal astigmatism correction with two Barrett Toric calculation methods

AIM: To compare the prediction error between Barrett Toric calculator and the new online AcrySof Toric calculator which incorporated Barrett astigmatism algorithm in Chinese cataract eyes with normal axial length and anterior chamber depth(ACD). METHODS: Prospective case-control study. All the cases had axial length(21-26 mm) with ACD no less than 2.4 mm.Keratometric values were measured by LenSTAR 900. The Barrett Toric calculator was used in group 1. In group 2, SRK-T formula was used to determine the spherical power of the Toric lens, and subsequent calculation of the cylinder type was performed using the new online Alcon Toric calculator. At 1 and 3 mo after surgery, a comprehensive subjective optometry was performed. The predicted residual astigmatism calculated by the two calculators was compared with that obtained by postoperative refraction,and the difference was defined as the astigmatism correction error [error of refractive astigmatism(ERA)].The error magnitude(EM) refers to the algebraic deviation of ERA, and the error vector(EV) indicates the vector deviation of ERA. The influence of the two calculation methods on the correction accuracy of toric IOL was quantitatively analyzed. RESULTS: The |EM| obtained at 1 mo after surgery were0.21±0.12 D, 0.22±0.18 D in group 1 and group 2 respectively,and correspondingly turned to be 0.19±0.13 D, 0.20±0.19 D at3 mo after surgery, with no statistical difference(P=0.633,P=0.877). The vector analysis showed that |EV| values in two groups at 1 mo after surgery were 0.29±0.14@105(D@angle) and 0.35±0.20@113(D@angle), respectively,whereas |EV| values 3 mo after surgery were 0.27±0.16@86(D@angle) and 0.32±0.23@102(D@angle), respectively. The differences between the groups were not statistically significant(P=0.119, P=0.261). CONCLUSION: The clinical effect of Barrett Toric calculator has a much more accurate tendency than that of new online AcrySof Toric calculator, but is not evident in cases with normal axial length and normal anterior posterior ratio.

Comparative Studies on Calculation Methods of Shear Behavior of Reinforced Concrete Beams of Chinese Modern Reinforced Concrete Buildings

In order to study the calculation methods of shear behavior of reinforced concrete beams of Chinese modern reinforced concrete buildings,this paper carried out tests on the concrete compressive strength of 12 Chinese modern concrete buildings,the mechanical properties of 66 rebars from different Chinese modern concrete buildings,and the concrete cover thickness of 9 Chinese modern concrete buildings,and the actual material properties and structural configurations have been obtained. Then,the comparison on calculation methods include the Chinese original calculation method,the Chinese present calculation method,the American present calculation method and the European present calculation method is studied with case analysis method.The results show that the Chinese original calculation method of shear behavior of reinforced concrete beams is based on the allowable stress calculation method,and the design safety factors are 3. 55- 4. 00. The standard value of the compressive strength of concrete cubes is 8. 48 MPa,the standard value of the concrete tensile strength is 1.20 MPa,the standard value of the yield strength of rectangular rebars is 229. 56 MPa,and the standard value of the yield strength of round rebars is 276. 82 MPa. The average value of the concrete cover thickness of beams and columns is 35.96 mm. In term of calculation area of hoop rebars of reinforced concrete beams,without considering earthquake loads,the Chinese original structural calculation method is safer than the Chinese present structural calculation method,but is more unsafe than the American present structural calculation method and the European present structural calculation method. The results can provide the support for structural safety assessments and repair designs of Chinese modern reinforced concrete buildings.

Studies and Applications of Three Kinds of Calculation Methods by Describing Damage Evolving Behaviors for Elastic-Plastic Materials

By means of bidirectional combined coordinate system, three kinds of calculation methods are proposed with respect to the damage-evolvlng rate and the life of elastic-plastic material, which include the single-parameter method, the ratio-method and the multiplication-method. In this work a lot of new calculation equations are given; a new concept on the all-around material constant is provided, which has functional relations with each of the typical material parameters： the fatigue strength coefficient σ′f, the fatigue strength exponent b′t, the fatigue ductility coefficient ε′f, the fatigue ductility exponent c′1, the average stress, the average strain, critical loading time and so on. In addition, an example of a car part is given, and some comparisons of calculation results are made. The calculation methods will have practical significance in avoiding the unnecessary fatigue tests, saving time, manpower and capital, as well as providing the convenience for engineering applications in a certain degree.

Effective point kinetic parameters calculation in Tehran research reactor using deterministic and probabilistic methods

The exact calculation of point kinetic parameters is very important in nuclear reactor safety assessment, and most sophisticated safety codes such as RELAP5, PARCS,DYN3D, and PARET are using these parameters in their dynamic models. These parameters include effective delayed neutron fractions as well as mean generation time.These parameters are adjoint-weighted, and adjoint flux is employed as a weighting function in their evaluation.Adjoint flux calculation is an easy task for most of deterministic codes, but its evaluation is cumbersome for Monte Carlo codes. However, in recent years, some sophisticated techniques have been proposed for Monte Carlo-based point kinetic parameters calculation without any need of adjoint flux. The most straightforward scheme is known as the ‘‘prompt method'' and has been used widely in literature. The main objective of this article is dedicated to point kinetic parameters calculation in Tehran research reactor(TRR) using deterministic as well as probabilistic techniques. WIMS-D5B and CITATION codes have been used in deterministic calculation of forward and adjoint fluxes in the TRR core. On the other hand, the MCNP Monte Carlo code has been employed in the ‘‘prompt method''scheme for effective delayed neutron fraction evaluation.Deterministic results have been cross-checked with probabilistic ones and validated with SAR and experimental data. In comparison with experimental results, the relativedifferences of deterministic as well as probabilistic methods are 7.6 and 3.2%, respectively. These quantities are10.7 and 6.4%, respectively, in comparison with SAR report.

A study of laboratory testing and calculation methods for coal sorption isotherms

Measurement of the volume of gas adsorbed per unit mass of coal with increasing pressure at a constant temperature produces an isotherm that describes the gas storage capacity of this type of coal. The accurate testing and interpretation of coal sorption isotherm plays an important role in the areas of coal mine methane drainage, coalbed methane （CBM） reservoir resource assessment, enhanced coalbed methane （ECBM） recovery, as well as the carbon dioxide （CO2） sequestration in deep coal seams or similar geological formations. Different coal sorption isotherm testing apparatus and associated calculation methods are critically reviewed and presented in this paper. These include both volumetric and gravimetric based methods, as well as experimental sorption tests with confining stress and direction sorption methods. The volumetric techniques utilise experimental apparatus with sample cell and injection pump and that with both sample cell and reference cell. Whilst the gravimetric approachesinclude methods with sample cell and suspension magnetic balance and that with both sample cell and reference cell. Different testing methods are compared and discussed in this study. A unique in-house-built coal sorption isotherm testing apparatus at the University of Wollongong was presented together with the calculation method, procedures and experimental results. The isotherm results can be calculated by both Soave-Redlich-Kwong （SRK） equation and calibration cure methods which can be used directly to convert the volume of adsorbed gas in different test conditions to standard condition （NTP）.

Comparison of Calculation Methods for Potential Reference Crop Evapotranspiration ET_0 in North Xinjiang

Reference crop evapotranspiration (ET_0) is a critical part in water cycle and water balance of ecosystem, which is greatly important to effective utilization of agricultural water resources and for making reasonable irrigation system. In order to propose a suitable method for computing ET_0 in North Xinjiang, based on daily meteorological data from May 1 to September30, 2010 provided by Weather Station of Fuhai County, we used FAO56 Penman-Monteith as the standard formula to compute ET_0, compared the differences and relations between such the method and other 4 calculation formulas, and analyzed the cause of the deviation, finally evaluated the applicability of computational method in North Xinjiang. The results showed that the calculation results by FA056 PM Method was approximate to that by FAO Penman method and IA method, of which the relative error was 9.26% and 13.51% respectively, the ET_0 results calculated by PT method and HS method were generally greater than the results by FAO56 PM, and their deviation was very obvious.

A Review of the Calculation Methods of Lifting Capacity in Wind Loads on Ocean Platforms

Wind load is a control load that affects the safety of structures in the design of ocean platforms. It has not only direct and powerful effects that may cause structure resonance but also has indirect effects causing waves or currents in the ocean. By analyzing the domestic and international norms, this study presents a review of calculation methods of wind load on ocean platforms, which belongs to large-scale non-entity structure used in the open sea while surrounding wind has no fixed direction. Current computations according to the norms are not accurate, which even not takes the force of the wind against the surface perpendicular to the structure into consideration. Additionally, this study also introduces and compares the lift model of platforms based on different theories, such as vortex-excitation and vibration, engineering structure dynamics, gas flow pressure theory, analyzing their applicability, advantages, and disadvantages. This paper analyzes the limitations and applicable conditions of the existing calculation method itself, such as the lift model is suitable for the existence of stable vortex wake;the calculation method of the structural dynamics of marine engineering must be combined with the wind tunnel test and consider the mistakes caused by the position relationship;the numerical simulation method is accurate but tedious. This study provides an insight into the calculation methods of lift in designing ocean platforms, including the finite element method for simulating fluid force and updating formulas in Chinese norms.

A review of monitoring,calculation,and simulation methods for ground subsidence induced by coal mining

Subsidence data acquisition methods are crucial to mining subsidence research and an essential component of achieving the goal of environmentally friendly coal mining.The origin and history of the existing methods of field monitoring,calcula-tion,and simulation were introduced.It summarized and analyzed the main applications,flaws and solutions,and improve-ments of these methods.Based on this analysis,the future developing directions of subsidence data acquisition methods were prospected and suggested.The subsidence monitoring methods have evolved from conventional ground monitoring to combined methods involving ground-based,space-based,and air-based measurements.While the conventional methods are mature in technology and reliable in accuracy,emerging remote sensing technologies have obvious advantages in terms of reducing field workload and increasing data coverage.However,these remote sensing methods require further technological development to be more suitable for monitoring mining subsidence.The existing subsidence calculation methods have been applied to various geological and mining conditions,and many improvements have already been made.In the future,more attention should be paid to unifying the studies of calculation methods and mechanical principles.The simulation methods are quite dependent on the similarity of the model to the site conditions and are generally used as an auxiliary data source for subsidence studies.The cross-disciplinary studies between subsidence data acquisition methods and other technologies should be given serious consideration,as they can be expected to lead to breakthroughs in areas such as theories,devices,software,and other aspects.

Advanced characterization and calculation methods for rechargeable battery materials in multiple scales

The structure-activity relationship of functional materials is an everlasting and desirable research question for material science researchers,where characterization and calculation tools are the keys to deciphering this intricate relationship.Here,we choose rechargeable battery materials as an example and introduce the most representative advanced characterization and calculation methods in four different scales:real space,energy,momentum space,and time.Current research methods to study battery material structure,energy level transition,dispersion relations of phonons and electrons,and time-resolved evolution are reviewed.From different views,various expression forms of structure and electronic structure are presented to understand the reaction processes and electrochemical mechanisms comprehensively in battery systems.According to the summary of the present battery research,the challenges and perspectives of advanced characterization and calculation techniques for the field of rechargeable batteries are further discussed.

THE BROAD SENSE CONCEPT AND CALCULATION METHODS OF TREE CROWN OVERLAP

The broad sense overlap concept and types of tree crown overlap were defined in the paper through analping function between the factors of tree crown overlap. The formulas of overlap area and overlap rate were derived from definite integral form. At the same time, many formulas were acquired while the projective figures of tree crown were circle. Application ways of these formulae were illustrated with a concrete caculation process.

A Review on Sources,Extractions and Analysis Methods of a Sustainable Biomaterial:Tannins

Condensed and hydrolysable tannins are non-toxic natural polyphenols that are a commercial commodity industrialized for tanning hides to obtain leather and for a growing number of other industrial applications mainly to substitute petroleum-based products.They are a definite class of sustainable materials of the forestry industry.They have been in operation for hundreds of years to manufacture leather and now for a growing number of applications in a variety of other industries,such as wood adhesives,metal coating,pharmaceutical/medical applications and several others.This review presents the main sources,either already or potentially commercial of this forestry by-materials,their industrial and laboratory extraction systems,their systems of analysis with their advantages and drawbacks,be these methods so simple to even appear primitive but nonetheless of proven effectiveness,or very modern and instrumental.It constitutes a basic but essential summary of what is necessary to know of these sustainable materials.In doing so,the review highlights some of the main challenges that remain to be addressed to deliver the quality and economics of tannin supply necessary to fulfill the industrial production requirements for some materials-based uses.

Calculation methods of lubricant film pressure distribution of radial grooved thrust bearings

In order to calculate the pressure distribution of radial grooved thrust bearing, analytical and numerical methods were applied respectively. Grooved region and land region were linked by u- sing the mass conservations principle at the groove/land boundary in each method. The block-weight approach was implemented to deal with the non-coincidence of mesh and radial groove pattern in nu- merical method. It was observed that the numerical solutions had higher precision as mesh number exceed 70 x 70, and the relaxation iteration of differential scheme presented the fastest convergence speed when relaxation factor was close to 1.94.

Numerical Calculation Methods for Wavemaking Response Induced by Explosion in Harbour

Using the axial symmetry results of marker and cell (MAC) method as initial value in this paper, two numerical calculating methods are presented for the late wavemaking response induced by explosion in harbour. One of the methods is the superposition method of the vibration mode based on fluid slosh in container. Another one is the joining method of the MAC results with the shallow wave theory calculation in time domain. As a practical example, it is conducted to the numerical calculation about 1000 ton TNT equivalent explosion within touch of water surface. The results show that it can be rationally described with the methods to the wavemaking progress and character. The numerical results are identical with the observed scene on the spot experiment. The methods are simple and applicable in the engineering design.

Simulation on Calculation Accuracy of Three Methods for Live Line Measuring the Parameters of Transmission Lines with Mutual Inductance

Live line measurement methods can reduce the loss of power outages and eliminate interference. There are three live line measurement methods including integral method, differential method and algebraic method. A simulation model of?two coupled parallel transmission lines spanning on the same towers is built in PSCAD and the calculation errors of these three methods are compared with different sampling frequencies by using of Matlab. The effect of harmonic on calculation is also involved. The simulation results indicate that harmonic has the least effect on the algebraic method which provides stable result and small error.