The Clinical Observation of 80 Patients with Diseases of Lumbar Vertebrae Treated by Reinforcing and Reducing Methods of Mani

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LOCKING PROBLEM AND VARIABLE REDUCING PROCEDURE IN TREFFTZ METHOD

The Trefftz-type boundary solution methods([1]) are applied in analysing moderately thick plate bending problems. A new type of locking problem caused by the overflow of Trefftz functions has been found and a so-called variable-reducing procedure for eliminating such a phenomenon is also proposed.

Reduced-basis Method在特征值问题中的应用

在特征值问题中引入了一种快速计算方法——缩减基法(Reduced-basis Method,RBM),介绍了RBM的计算原理和计算过程,给出了RBM误差估计的方法。以一塔式起重机塔身结构自由振动分析为例,修正设计参数时,由RBM得到结构的固有频率和振型及该计算结果的误差限。与有限元结果相比较,RBM不仅计算速度快,计算精度也很高,还可对结果进行误差估计。

Evaluation of Uncertainty in Determination of Reducing Sugar Content in Sugarcane

[ Objective] This study aimed to establish an effective method for evaluating uncertainty in determination of reducing sugar content in sugarcane with Lane-Ernon method. [ Method] Based on analysis of the main sources of uncertainty in determination of reducing sugar content in sugarcane and mathematical model construction, combined uncertainty and expanded uncertainty were determined to establish the method for evaluation of uncertainty in determination. [ Result] Among uncertainties in determination of reducing sugar content in sugarcane with Lane-Ernon method, the greatest uncertainty was introduced by duplicate determination. According to results of statistical analysis, the expanded uncertainty in determination of reducing sugar content was 0.012%. [ Conclusion] This study provided theo- retical reference for evaluation of uncertainty in determination of reducing sugar content in sugarcane.

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.

Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem

In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.

Adaptive Reduced Basis Methods Applied to Structural Dynamic Analysis

The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.

The Reduced Space Method for Calculating the Periodic Solution of Nonlinear Systems

A hybrid method combined the reduced Sequential Quadratic Programming(SQP)method with the harmonic balance method has been developed to analyze the characteristics of mode localization and internal resonance of nonlinear bladed disks.With the aid of harmonic balance method,the nonlinear equality constraints for the constrained optimization problem are constructed.The reduced SQP method is then utilized to deal with the original constrained optimization problem.Applying the null space decomposition technique to the harmonic balance algebraic equations results in the vanishing of the nonlinear equality constraints and a simple optimization problem involving only upper and lower bound constraints on the optimization variables is formed and solved.Finally,numerical results are given for several test examples to validity the proposed method.The efficiency of the solution method to trace the family of energy dependent nonlinear modes is illustrated.The localization nonlinear normal modes of bladed disks related to various types of internal resonances are explored.

Studies on Reduced Extent Method for Inhibited Thermokinetics Of Enzyme－Catalyzed Reaction──Inhibition of the laccase－catalyzed oxidation of o－dihydroxybenzene by m－dihydroxybenzene

The thermokinetic reduced extent equations of reversible inhibitions for Michaiels-Menten enzymatic reaction were deduced, and then the criteria for distingushing inhibition type was given and the methods for calculating kinetic parameters, KM,Ki and Urn were suggested. This theory was applied to inverstigate the inhibited thermokinetics of laccase-catalyzed oxidation of o-dihydroxybenzene by m-dihydroxybenzene. The experimental results show the inhibition belongs to reversible competitive type, KM=6.224×10-3 mol L-1, Ki=2. 363 × 10-2 mol. L-1.

Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems

Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.

Reduced Expanding Load Method for Simulation-Based Structural System Reliability Analysis

The current situation and difficulties of the structural system reliability analysis are mentioned. Then on the basis of Monte Carlo method and computer simulation, a new analysis method reduced expanding load method (RELM) is presented, which can be used to solve structural reliability problems effectively and conveniently. In this method, the uncertainties of loads, structural material properties and dimensions can be fully considered. If the statistic parameters of stochastic variables are known, by using this method, the probability of failure can be estimated rather accurately. In contrast with traditional approaches,RELM method gives a much better understanding of structural failure frequency and its reliability index β is more meaningful.To illustrate this new idea, a specific example is given.

Reduced-order finite element method based on POD for fractional Tricomi-type equation

The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.

Application of the Generalized Reduced Gradient Method in Mechanical Optimization Design

This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.

Vibration Diagnosis and Optimization of Industrial Robot Based on TPA and EMD Methods

This paper proposedmethod that combined transmission path analysis(TPA)and empirical mode decomposition(EMD)envelope analysis to solve the vibration problemof an industrial robot.Firstly,the deconvolution filter timedomain TPA method is proposed to trace the source along with the time variation.Secondly,the TPA method positioned themain source of robotic vibration under typically different working conditions.Thirdly,independent vibration testing of the Rotate Vector(RV)reducer is conducted under different loads and speeds,which are key components of an industrial robot.The method of EMD and Hilbert envelope was used to extract the fault feature of the RV reducer.Finally,the structural problems of the RV reducer were summarized.The vibration performance of industrial robots was improved through the RV reducer optimization.From the whole industrial robot to the local RV Reducer and then to the internal microstructure of the reducer,the source of defect information is traced accurately.Experimental results showed that the TPA and EMD hybrid methods were more accurate and efficient than traditional time-frequency analysis methods to solve industrial robot vibration problems.

A Real-Time Transient Analysis of a Functionally Graded Material Plate Using Reduced-Basis Methods

Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.

降阶单元的新进展:内置了最大模误差估计器的自适应有限元法初探

该文基于初值问题中降阶单元的成功实践,进一步对一般边值问题提出无需超收敛计算、无需结构化网格、无需结点位移修正的降阶单元;进而提出以降阶单元作为最终解,且内置了最大模误差估计器的自适应有限元算法。该文对这一研究进展做简要介绍,并给出一维和二维边值问题的初步算例,以展示本法的可行性、有效性和可靠性。

主减速器台架疲劳试验等效方法研究

为了提高主减速器台架疲劳试验的准确性和效率,提出了基于实际行驶载荷谱的台架疲劳试验等效方法。在采集用户和试验场实际行驶载荷谱基础上,基于雨流计数和精英策略非支配排序遗传算法关联用户路面,等效重构试验场道路工况和道路载荷谱。为验证等效方法的有效性,建立主减速器有限元模型并进行静强度分析,验证了网格无关性和模型有效性。结合瞬态动力学模型研究了不同转矩、转速与齿轮应力之间的关系,得到程序载荷谱幅值所对应的频次等效关系;结合转速与齿轮应力之间的关系和各转矩区间的转速概率密度分析,确定了各个等级载荷谱对应的转速,编制了旋转弯曲疲劳试验程序载荷谱;结合有限元模型,验证了编制载荷谱与原始载荷谱的等效关系。结果表明,齿轮在等效载荷谱的作用下与原始载荷谱的损伤部位一致,损伤值最大误差为0.15%,并且加速了4.7倍。

杯形谐波减速器齿廓修形方法及寿命预测分析

杯形谐波减速器柔轮与波发生器装配时产生的径向变形量理论与实际不符,柔轮与刚轮轮齿出现啮合干涉,基于柔轮装配的变形情况提出了柔轮齿廓修形方法。通过有限元法装配仿真确定了合适的修形量,修形后柔轮经过装配和运转有限元分析,最后基于Miner线性疲劳理论采用Fe-safe软件对柔轮寿命进行了预测。结果表明,修形后柔轮装配时最大应力从962.2 MPa降低至532.7 MPa,负载运转时应力为609.9 MPa,轮齿应力有较大改善且啮合干涉情况得到解决,柔轮寿命循环次数为4.28×10^(6)。

发酵玉米芯多糖、还原糖含量近红外模型的建立

本实验旨在应用近红外光谱技术(NIRS)结合化学计量学法快速预测发酵玉米芯中多糖、还原糖含量,为定量检测发酵玉米芯多糖、还原糖含量提供理论依据以及为玉米芯深加工利用提供技术支持。以105份微生物发酵的玉米芯为供试材料,采用苯酚-硫酸法和DNS法分别测定多糖和还原糖含量。利用偏最小二乘法(PLS),通过不同预处方式和不同波长建立发酵玉米芯多糖、还原糖含量的近红外分析模型。结果表明:多糖模型采用标准正态变量变换(SNV)+1阶导数的方法对全谱图进行预处理的效果较好,优化后的模型决定系数(R2)、校正均方根误差(RMSEC)、校准标准差(SEC)分别为0.82、9.28、9.34,其相对分析误差(PRD)为2.37;还原糖模型采用1阶导数+标准正态变量变换(SNV)+去趋势化(Detrend)的方法对全谱图进行预处理的效果较好,优化后的模型决定系数(R2)、校正均方根误差(RMSEC)、校准标准差(SEC)分别为0.84、4.03、4.04,其相对分析误差(PRD)为2.48;预测集决定系数分别为0.85、0.88。本研究构建的NIRS模型校正和交互验证决定系数均较大,相对分析误差均大于2,说明模型预测性能较好,建立的模型有助于发酵玉米芯多糖、还原糖含量活性成分的筛选。