“问题驱动式”教学法在“数值分析”课程教学中的应用与研究——以插值法为例

采用"问题驱动式"教学法,对《数值分析》中插值法的教学内容进行新的设计与构建;创设背景问题,知识点在被不断"驱动"中得以展现;该教学的过程、方法和思路对学生的思维能力、动手能力和创新能力的培养可发挥重要作用。

以问题为导向的案例教学法在“数值分析”课程中的应用

文章探讨在"数值分析"课程教学中引入以问题为导向的案例教学法,结果表明以数值分析问题为导向的案例教学法是提高教学效果的有效途径。

地方高校面向数学师范专业认证的“数值分析”课程教学探讨

专业认证是提高专业办学质量的措施之一,通过师范专业认证,可以规范教师教育人才的培养,提高高校教育专业人才培养质量。文章从课程目标、课堂教学、课程考核三个方面探讨“数值分析”课程的教学,以提高学生的学科核心素养,促进该课程达到数学教育专业国家认证标准并实现数学师范专业人才培养目标。

Numerical Analysis of Steady Smoldering of Biomass Rods

Understanding the steady mechanism of biomass smoldering plays a great role in the utilization of smoldering technology.In this study numerical analysis of steady smoldering of biomass rods was performed.A two-dimensional(2D)steady model taking into account both char oxidation and pyrolysis was developed on the basis of a calculated propagation velocity according to empirical correlation.The model was validated against the smoldering experiment of biomass rods under natural conditions,and the maximum error was smaller than 31%.Parameter sensitivity analysis found that propagation velocity decreases significantly while oxidation area and pyrolysis zone increase significantly with the increasing diameter of rod fuel.

Cross-section distortion and springback characteristics of double-cavity aluminum profile in force controlled stretch-bending

3D elastic-plastic FE model for simulating the force controlled stretch-bending process of double-cavity aluminum profile was established using hybrid explicit−implicit solvent method.Considering the computational accuracy and efficiency,the optimal choices of numerical parameters and algorithms in FE modelling were determined.The formation mechanisms of cross-section distortion and springback were revealed.The effects of pre-stretching,post-stretching,friction,and the addition of internal fillers on forming quality were investigated.The results show that the stress state of profile in stretch-bending is uniaxial with only a circumferential stress.The stress distribution along the length direction of profile is non-uniform and the maximum tensile stress is located at a certain distance away from the center of profile.As aluminum profile is gradually attached to bending die,the distribution characteristic of cross-section distortion along the length direction of profile changes from V-shape to W-shape.After unloading the forming tools,cross-section distortion decreases obviously due to the stress relaxation,with a maximum distortion difference of 13%before and after unloading.As pre-stretching and post-stretching forces increase,cross-section distortion increases gradually,while springback first decreases and then remains unchanged.With increasing friction between bending die and profile,cross-section distortion slightly decreases,while springback increases.Cross-section distortion decreases by 83%with adding PVC fillers into the cavities of profile,while springback increases by 192.2%.

Operation optimization of prefabricated light modular radiant heating system:Thermal resistance analysis and numerical study

The utilization of prefabricated light modular radiant heating system has demonstrated significant increases in heat transfer efficiency and energy conservation capabilities.Within prefabricated building construction,this new heating method presents an opportunity for the development of comprehensive facilities.The parameters for evaluating the effectiveness of such a system are the upper surface layer’s heat flux and temperature.In this paper,thermal resistance analysis calculation based on a simplified model for this unique radiant heating system analysis is presented with the heat transfer mechanism’s evaluation.The results obtained from thermal resistance analysis calculation and numerical simulation indicate that the thermal resistance analysis method is highly accurate with temperature discrepancies ranging from 0.44℃ to−0.44℃ and a heat flux discrepancy of less than 7.54%,which can meet the requirements of practical engineering applications,suggesting a foundation for the prefabricated radiant heating system.

VIBRATION NUMERICAL ANALYSIS OF COUNTER-ROTATING TURBINE WITH WAKE-FLOW USING FLUID-STRUCTURE INTERACTION METHOD

The design of counter-rotating turbine is one of new techniques to improve the thrust-weight ratio of jet propulsion engines.Numerical analysis of a low pressure（LP）counter-rotating turbine rotor blade is presented by using ANSYS/CFX software.Interaction of aerodynamics and solid mechanics coupling in the computation is applied.In some rating of turbine,stress distribution and vibration characteristics of low pressure turbine（LPT）blade are computed.The wake aerodynamic forces and LPT blade vibration are transformed in frequency domain using fast Fourier transform（FFT）method.The results show that under wake aerodynamic force excitation,the first order modal vibration is more easily aroused and the higher order response cannot be ignored.Moreover,with different temperature fields,the vibration responses of blade are also different.

Polarization-Insensitive Silica on Silicon Arrayed Waveguide Grating Design

A new technology for fabrication of silica on silicon arrayed waveguide grating (AWG) based on deep etching and thermal oxidation is presented.Using this method,a silicon layer is remained at the side of waveguide.The stress distribution and effective refractive index of waveguide fabricated by this approach are calculated using finite element and finite difference beam propagation method,respectively.The results of these studies indicate that the stress of silica on silicon optical waveguide can be matched in parallel and vertical direction and AWG polarization dependent wavelength (PDλ) can be reduced effectively due to side-silicon layer.

Numerical modeling of the 2D time-domain transient electromagnetic secondary field of the line source of the current excitation

To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of the line source based on the DuFort- Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force （Emf）, and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the fiat layered model with high precision--the maximum relative error is less than 0.01% between our method and the analytical method--and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.

Flexural behaviors of FRP strengthened corroded RC beams

The flexural behavior of eight FRP （ fiber reinforced polymer） strengthened RC （reinforced concrete） beams with different steel corrosion rates are numerically studied by Ansys finite element software. The influences of the corrosion rate on crack pattern, failure mechanism, ultimate strength, ductility and deformation capacity are also analyzed. Modeling results show that the beams with low corrosion rates fail by the crushing of the concrete in the compression zone. For the beams with medium corrosion rates, the bond slip between the concrete and the longitudinal reinforcement occurs after steel yielding, and the beams finally fail by the debonding of the FRP plates. For the beams with high corrosion rates, the bond slip occurs before steel yielding, and the beams finally fail by the crushing of the concrete in the compression zone. The higher the corrosion rates of the longitudinal reinforcement, the more the carrying capacity of FRP strengthened RC beams reduces. The carrying capacity of RCB-1 （the corrosion rate is 0） is 115 kN, and the carrying capacity of RCB-7 （the corrosion rate is 20% ） is 42 kN. The deformation capacity of FRP strengthened corroded RC beams is higher than that of FRP strengthened uucorroded RC beams. The ultimate deflection of RCB-1 and RCB-7 are 20 mm and 35 nun, respectively, and the ultimate deflection of RCB-5 （the corrosion rate is 10% ） reaches 60 ilUn.

Simulation Study of the Workspace of the Parallel Machine Tool

A new three dimensional simulation method is introduced to study the workspace of a 6 PSS (P denotes a prismatic kinematic pair, S denotes a spherical kinematic pair) parallel machine tool. This algorithm adopts the method of numerical analysis to investigate the boundary points in a series of sections which form the surface of the workspace. That is, to study such points that have the largest polar radius on a certain section in a system of polar coordinates according to conditions of constraint. The constraint conditions considered in the article include the maximum and minimum displacements of each dieblock, the maximum and minimum angles of oscillation in each hinge. By converting the constraint inequalities into constraint equations, the largest polar radius corresponding to every constraint condition can be evaluated and the minimum one is used to decide the boundary point. This algorithm greatly simplifies the computational process and can be used to analyze any section of the workspace. It provides a theoretical basis for the structural design of such a machine tool.

Furnace structure analysis for copper flash continuous smelting based on numerical simulation

According to the innate characteristic of four types of furnace, the copper flash continuous smelting （CFCS） furnace can be considered a synthetic reactor of two relatively independent processes： flash matte smelting process （FMSP） and copper continuous converting process （CCCP）. Then, the CFCS thermodynamic model was proposed by establishing the multi-phase equilibrium model of FMSP and the local-equilibrium model of CCCP, respectively, and by combining them through the smelting intermediates. Subsequently, the influences of the furnace structures were investigated using the model on the formation of blister copper, the Fe3O4 behavior, the copper loss in slag and the copper recovery rate. The results show that the type D furnace, with double flues and a slag partition wall, is an ideal CFCS reactor compared with the other three types furnaces. For CFCS, it is effective to design a partition wall in the furnace to make FMSP and CCCP perform in two relatively independent zones, respectively, and to make smelting gas and converting gas discharge from respective flues.

Temperature Characteristics of Bilayer Thin-Film Devices Under Organic Interface Limited Current Conduction

Temperature characteristics are important for the performance of organic thin film devices. On the basis of the hopping theory of Miller-Abrahams,an analytical model of charge transport for bilayer organic devices under the organicorganic interface limited current conduction is developed. The dependence of current, field,and carrier distribution in bilayer organic devices with the structure of ＂injection electrode/Layer Ⅰ/Layer Ⅱ/collection electrode＂ on temperature are numerically analyzed. We conclude that, for a given applied voltage, when temperature is raised, the voltage of LayerⅠ will increase,and the field will be higher. Meanwhile, the voltage of Layer Ⅲ will decrease, the field will become weaker accordingly,and the current of the device will increase.

STOCHASTIC BOUNDARY ELEMENT METHODS FOR 3D PROBLEMS WITH BODY FORCES AND ITS APPLICATION IN RELIABILITY OF TURBINE DISKS

The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach of partial derivation with respect to stochastic variables,considering the yield limit,rotation speeds and material density to be the fundamental stochastic variables.Through analyzing a numerical example and a turbo-disk of an aeroengine,the results show that the method developed is successful.

DETERMINATION OF MATERIAL PARAMETERS FOR COMPUTER SIMULATION OF SUPERPLASTIC FORMING PROCESSES

In order to analyze and simulate the complex super-plastic forming process by computer, a method of equal height bulging for determining material parameters m and K of the superplastic alloy is presented. The formulae related to the method are deduced in this paper. The accuracy of the method is available for evaluating the examples used in simulating the superplastic sheet-metal bulging processes.

CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

Freak wave simulation based on nonlinear model and the research on the time-frequency energy spectrum of simulation results

VOF （volume of fluid） method has been used to make the numerical simulation of freak wave come true. The comparisons between the numerical results and linear theoretical results corresponding to Eq.（5） have been carried out to show that the numerical results have a better exhibition of nonlinear characteristics. Wavelet analysis method has been adopted to investigate the time-frequency energy spectrum of simulation freak waves and the results reveal strong nonlinear interaction enables energy to be transferred to high harmonics during the progress of its formation. Varying water depth can enhance the nonlinear interaction, making much more energy be transferred to high harmonics and freak waves with higher asymmetry be generated.

NUMERICAL PREDICTION OF AIRCRAFT HYDRAULIC SYSTEM BASED ON THERMAL DYNAMIC ANALYSIS

A mathematical model of principal elements of the aircraft hydraulic system is presented based on the heat transfer theory. The dynamic heat transfer process of the hydraulic oil and the pump shells within an aircraft hydraulic system are analyzed by the difference method. A kind of means for the prediction to variational trends of the aircraft hydraulic system temperature is provided during operation. The numerical prediction and simulation under the operational conditions are presented for ground trial running and the decelerated operation in flight. Computational results show that there is a good coincidence between the experimental data and the numerical predictions.

Mechanical behaviors of steel reinforced ECC / concrete composite columns under combined vertical and horizontal loading

In order to improve the load capacity, seismic performance and performance-cost ratio of the columns, the concrete at the base of reinforced concrete （RC） columns is substituted with engineered cementitious composites （ECC） to form ECC/RC composite columns. Based on the existing material properties, the mechanical behaviors of the ECC columns, ECC/RC composite columns and RC columns were numerically studied under combined vertical and horizontal loading with the software of ATENA. Then, the failure mechanism of ECC columns and ECC/RC composite columns were comprehensively studied and compared with that of the RC columns. Then, the effects of the height of the ECC, the axial compression ratio, and the transverse reinforcement ratio on the mechanical behaviors of the composite or the ECC column are studied. The calculation results show that the ultimate load capacity, ductility and crack resistance of the ECC or ECC/RC composite columns are superior to those of the RC columns. The ECC/RC composite column with a height of the ECC layer of 1.2h （ h is the height of the cross section） can achieve similar mechanical properties of a full ECC column. With high shear strength, ECC can undertake the shear force and significantly reduce the amount of stirrups, avoiding construction issues and promoting its engineering application.

Study on dynamic response of embedded long span corrugated steel culverts using scaled model shaking table tests and numerical analyses

A series of scaled-model shaking table tests and its simulation analyses using dynamic finite element method were performed to clarify the dynamic behaviors and the seismic stability of embedded corrugated steel culverts due to strong earth-quakes like the 1995 Hyogoken-nanbu earthquake. The dynamic strains of the embedded culvert models and the seismic soil pressure acting on the models due to sinusoidal and random strong motions were investigated. This study verified that the cor-rugated culvert model was subjected to dynamic horizontal forces (lateral seismic soil pressure) from the surrounding ground, which caused the large bending strains on the structure; and that the structures do not exceed the allowable plastic deformation and do not collapse completely during strong earthquake like Hyogoken-nanbu earthquake. The results obtained are useful for design and construction of embedded long span corrugated steel culverts in seismic regions.