分析应用题的思考方法(4)——设值法

有些应用题直接解答比较困难、比较抽象,但是根据题意假设一个适当的数据作为已知条件,便能使解题途径变得十分顺畅。这种思考问题的方法就是设值法。

设值法巧解竞赛题

设值法巧解竞赛题□清水县永清镇西关小学乔和平所谓设值法，就是根据题意假设与题目有某种关系的一个或几个具体的数值，再和题中已知条件一起进行推理、列式和计算，使问题得以解决的一种思维方法。在解题中，若能合理、灵活地运用“设值法”，可起到化繁为简、化难为易...

用“设值法”解题

用“设值法”解决问题，是根据题中的数量关系，给予某些特殊的数值，使问题由抽象变得直观。这是一种重要的解决问题的方法，能使看似困难的问题变得简单。

小学数学奥林匹克试题解题思路种种

五、用"设值法"解题有些题目中的未知量较多,一时无法解答,我们可根据题意假设一个或几个适当的数作为已知条件,这样可使题目变得简单易解。

A new numerical method for determining collapse load-carrying capacity of structure made of elasto-plastic material

Determination of collapse load-carrying capacity of elasto-plastic material is very important in designing structure. The problem is commonly solved by elasto-plastic finite element method （FEM）. In order to deal with material nonlinear problem involving strain softening problem effectively, a new numerical method-damped Newton method was proposed. The iterative schemes are discussed in detail for pure equilibrium models. In the equilibrium model, the plasticity criterion and the compatibility of the strains are verified, and the strain increment and plastic factor are treated as independent unknowns. To avoid the stiffness matrix being singularity or condition of matrix being ill, a damping factor a was introduced to adjust the value of plastic consistent parameter automatically during the iterations. According to the algorithm, the nonlinear finite element program was complied and its numerical example was calculated. The numerical results indicate that this method converges very fast for both small load steps and large load steps. Compared with those results obtained by analysis and experiment, the predicted ultimate bearing capacity from the proposed method is identical.

Single-jet Spray Mixing with a Confined Crossflow

In order to achieve uniform mixing between spray droplets and crossflow, cold-model experiment of a hollow-cone water spray in an air crossflow is investigated via a numerical simulation. The simulation cases are designed by using the orthogonal design method. The Eulerian-Lagrangian formulation is employed for modeling the droplets-crossflow two-phase flow while the realizable k-ε turbulence model is used to describe the turbulence. A new index, mixedness quality, is proposed to assess the overall mixing of the droplets in the crossflow. The simulation results demonstrate that the counter-rotating vortex pair (CVP) imposes a more significant impact on the spatial distribution than on the size distribution of the droplets. Pairs of CVP with smaller scales are preferable for achieving a better mixing. The influencing factors are listed in the following order in terms of the degree of their impact from the greatest to the least: the Sauter diameter of the initial droplets, the mixing tube diameter, the spray angle, the velocity of the inlet crossflow, and the vertical velocity of the initial droplets. A moderate droplet diameter, a smaller tube diameter, a moderate spray angle, a greater crossflow velocity and a moderate vertical velocity of the droplet are favorable for achieving a higher mixedness quality of the jet spray in a confined crossflow.

Protective Design of a Warship Broadside Liquid Cabin

Based on the traditional Smoothed Particle Hydrodynamics (SPH) algorithm, the linked-list search algorithm combined with the variable smoothing length and square support domain was put forward to improve the calculation efficiency and guarantee the calculation accuracy. The physical process of high velocity fragment impact on a broadside liquid cabin was programmed for simulation. The numerical results agreed well with those of the general software ANSYS AUTODYN, which verifies the effectiveness and feasibility of the numerical method. From the perspective of the outer plate thickness of the liquid cabin, the width of the liquid cabin, and incident angle of the fragment, the influence of these parameters on protective mechanisms was analyzed to provide a basis for protective design of a broadside liquid cabin. Results show that the influence of outer plate thickness is not obvious; therefore, the conventional design can be adopted in the design of the outer plate. The width of the liquid cabin has a great influence on the residual velocity of the fragment and the width of the liquid cabin should be designed to be as wide as possible under the premise of meeting other requirements. There is a certain incident angle in which the velocity attenuation of the fragment is most obvious, and the high-pressure zone near the inner plate is asymmetric. The inner plate of liquid cabin should be strengthened according to the hull form, principal dimensions, and vulnerable points.

Time Collocation Method for Structural Dynamic Problems

In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.

2D Model of Guide Vane for Low Head Hydraulic Turbine： Analytical and Numerical Solution of Inverse Problem

Low-head hydraulic turbines are the subjects to individual approach of design. This comes from the fact that hydrological conditions are not of a standard character. Therefore, the design method of the hydraulic turbine stage has a great importance for those who may be interested in such an investment. As a first task in a design procedure the guide vane is considered. The proposed method is based on the solution of the inverse problem within the flame of 2D model. By the inverse problem authors mean a design of the blade shapes for given flow conditions. In the paper analytical solution for the simple cylindrical shape of a guide vane is presented. For the more realistic cases numerical solutions according to the axis-symmetrical model of the flow are also presented. The influence of such parameters as the inclination of trailing edge, the blockage factor due to blade thickness, the influence of loss due to dissipation are shown for the chosen simple geometrical example.

A product module mining method for PLM database

Modular technology can effectively support the rapid design of products, and it is one of the key technologies to realize mass customization design. With the application of product lifecycle management(PLM) system in enterprises, the product lifecycle data have been effectively managed. However, these data have not been fully utilized in module division, especially for complex machinery products. To solve this problem, a product module mining method for the PLM database is proposed to improve the effect of module division. Firstly, product data are extracted from the PLM database by data extraction algorithm. Then, data normalization and structure logical inspection are used to preprocess the extracted defective data. The preprocessed product data are analyzed and expressed in a matrix for module mining. Finally, the fuzzy c-means clustering(FCM) algorithm is used to generate product modules, which are stored in product module library after module marking and post-processing. The feasibility and effectiveness of the proposed method are verified by a case study of high pressure valve.

Deformation tests and failure process analysis of an anchorage structure

In order to study the failure process of an anchorage structure and the evolution law of the body＇s defor- mation field, anchor push-out tests were carried out based on digital speckle correlation methods （DSCM）. The stress distribution of the anchorage interface was investigated using the particle flow numerical simulation method. The results indicate that there are three stages in the deformation and fail- ure process of an anchorage structure： elastic bonding stage, a de-bonding stage and a failure stage. The stress distribution in the interface controls the stability of the structure. In the elastic bonding stage, the shear stress peak point of the interface is close to the loading end, and the displacement field gradually develops into a ＂V＂ shape, in the de-bonding stage, there is a shear stress plateau in the center of the anchorage section, and shear strain localization begins to form in the deformation field. In the failure stage, the bonding of the interface fails rapidly and the shear stress peak point moves to the anchorage free end. The anchorage structure moves integrally along the macro-cracl~ The de-bonding stage is a research focus in the deformation and failure process of an anchorage structure, and plays an important guiding role in roadway support design and prediction of the stability of the surrounding rock.

Optimal Order-of-Addition Experiments under a Prior Constraint

The order-of-addition experiments are widely used in many fields,including food and industrial production,but the relative research under prior constraints is limited.The purpose of this paper is to select an optimal sequence under the restriction that component i is added before component j,while it is unachievable to compare all sequences when the number of components m is large.To achieve this,a constrained PWO model is first provided,and then the D-optimal designs for order-of addition experiments with minimal-points via the modified threshold accepting algorithm is established.The effectiveness of the proposed method is demonstrated through a job scheduling problem with a prior constraint for teaching cases.

Free return orbit design and characteristics analysis for manned lunar mission

A circumlunar free return orbit design model that satisfies manned lunar mission constraints is established. By combining analytical method with numerical method,a serial orbit design strategy from initial value design to precision solution is proposed. A simulation example is given,and the conclusion indicates that the method has excellent convergence performance and precision. According to a great deal of simulation results solved by the method,the free return orbit characters such as accessible moon orbit parameters,return orbit parameters,transfer delta velocity,etc. are analyzed,which can supply references to constitute manned lunar mission orbit scheme.

The Effect of Blade Outlet Angle on Performance and Internal Flow Condition of Mini Turbo-Pump

Mini turbo-pumps having a diameter smaller than 100mm are employed in many fields;automobile radiator pump,ventricular assist pump,cooling pump for electric devices,washing machine pump and so on.Further,the needs for mini turbo-pumps would become larger with the increase of the application of it for electrical machines.It is desirable that the mini turbo-pump design is as simple as possible due to restriction to make precise manufactures.But the design method for the mini turbo-pump is not established because the internal flow condition for these small-sized fluid machineries is not clarified and conventional theory is not conductive for small-sized pumps.Three types of rotors with different outlet angles are prepared for an experiment and a numerical analysis.The performance tests are conducted with these rotors in order to investigate the effect of the blade outlet angle on performance and internal flow condition of mini turbo-pumps.It is clarified from the experimental results that head of the mini turbo-pump increases and maximum efficiency flow rate shifts to larger flow rate according to the increase of the blade outlet angle,however the maximum efficiency decreases with the increase of it.In the present paper,the performance of the mini turbo-pump is shown and the internal flow conditions are clarified with the results of the experiment and the numerical flow analysis.Furthermore,the effects of the blade outlet angle on the performance are investigated and high performance design with simple structure for the mini turbo-pump would be considered.

Investigation of micro vortex generators on controlling flow separation over SCCH high-lift configuration

For the problem that the flow separation on the flap lowers the aerodynamic performance of high lift system,an investigation was carried out on using micro vortex generators(VGs) to control the separation on flap of the swept constant chord half-model(SCCH) high-lift configuration,at a small to medium angle of attack,by experimental and numerical methods.The basic flow characteristics of SCCH landing configuration were analyzed by using numerical method to provide required information for the design of micro VGs.Then,by keeping the cruise configuration intact,the preliminary design procedure and design methods of micro VGs were established.In addition,the micro VGs were designed.The effects of VG's arrangement and geometric parameters,such as the arrangement mode,chordwise position,arrangement angle,height and spanwise distance,on controlling efficiency were investigated by using numerical method.Then the parameters of preliminary VGs were adjusted as the basis configuration for wind tunnel test.The experiments were accomplished in NH-2 wind tunnel for validating the numerical method,as well as obtaining the design principles and methods of micro VGs.The parameters of VGs were also optimized based on the experiments.The experimental results showed that the numerical design method can serve as an efficient and accurate design tool.The lift and drag were increased by 10% and 14%,respectively in landing state,which satisfied the requirements for landing.Finally,it was concluded that the established design principles and methods for micro VGs in this investigation can be used in engineering application.

Adjusting principle of gas jet controlling inlet and numerical verification

To improve the inlet performance of a ramjet working under variable conditions,a design is proposed by controlling the inlet with jet controlling,which combines the method of reducing the sealing Mach number of the external waves and the technique of controlling inlet by jet controlling.Three inlets were designed to analyze the feasibility and a numerical simulation method was used to simulate the three inlet flow fields.The adjustment mechanism of the design was studied through analysis of the simulation results.The design was verified by comparing the performances of the three inlets.The study showed that the method of reducing the sealing Mach number of the external wave system can improve the flow coefficient when the inlet works at low Mach numbers.The technique of controlling inlet by jet controlling can homogenize inlet flow fields at high Mach numbers,reduce effective throat area and increase the total pressure recovery(TPR).Adjustable inlets controlled by jet controlling demonstrate good performance at certain working ranges.

Design of a novel RTD-based three-variable universal logic gate

Traditional CMOS technology faces some fundamental physical limitations. Therefore, it has become very important for the integrated circuit industry to continue to develop modem devices and new design methods. The threshold logic gate has attracted much attention because of its powerful logic function. The resonant tunneling diode （RTD） is well suited for imple- menting the threshold logic gate because of its high-speed switching capability, negative differential resistance （NDR） charac- teristic, and functional versatility. In this paper, based on the Reed-Muller （RM） algebraic system, a novel method is proposed to convert three-variable non-threshold functions to the XOR of multiple threshold functions, which is simple and has a program- mable implementation. With this approach, all three-variable non-threshold functions can be presented by the XOR of two threshold functions, except for two special functions. On this basis, a novel three-variable universal logic gate （ULG3） is proposed, composed of two RTD-based universal threshold logic gates （UTLG） and an RTD-based three-variable XOR gate （XOR3）. The ULG3 has a simple structure, and a simple method is presented to implement all three-variable functions using one ULG3. Thus, the proposed ULG3 provides a new efficient universal logic gate to implement RTD-based arbitrary n-variable functions.

A design method and numerical study for a new type parabolic trough solar collector with uniform solar flux distribution

The non-uniform concentrated solar flux distribution on the outer surface of the absorber tube can lead to large circumferential temperature difference and high local temperature of the absorber tube wall,which is one of the primary causes of parabolic trough solar receiver(PTR)failures.In this paper,a secondary reflector used as a homogenizing reflector(HR)in a conventional parabolic trough solar collector(PTSC)was recommended to homogenize the solar flux distribution and thus increase the reliability of the PTR.The design method of this new type PTSC with a HR was also proposed.Meanwhile,the concentrated solar flux distribution was calculated by adopting the Monte Carlo ray-trace(MCRT)method.Then,the coupled heat transfer process within the PTR was simulated by treating the solar flux calculated by the MCRT method as the heat flux boundary condition for the finite volume method model.The solar flux distribution on the outer surface of the absorber tube,the temperature field of the absorber tube wall,and the collector efficiency were analyzed in detail.It was revealed that the absorber tube could almost be heated uniformly in the PTSC with a HR.As a result,the circumferential temperature difference and the maximum temperature could be reduced significantly,while the efficiency tended to decrease slightly due to the inevitably increased optical loss.Under the conditions studied in this paper,although the collector efficiency decreased by about 4%,the circumferential temperature difference was reduced from about 25 to 3 K and the maximum temperature was reduced from667 to 661 K.