Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Thermodynamic analysis of combined reforming process using Gibbs energy minimization method: In view of solid carbon formation

Thermodynamic analysis was applied to study combined partial oxidation and carbon dioxide reforming of methane in view of carbon formation. The equilibrium calculations employing the Gibbs energy minimization were performed upon wide ranges of pressure （1-25 atm）, temperature （600-1300 K）, carbon dioxide to methane ratio （0-2） and oxygen to methane ratio （0-1）. The thermodynamic results were compared with the results obtained over a Ru supported catalyst. The results revealed that by increasing the reaction pressure methane conversion decreased. Also it was found that the atmospheric pressure is the preferable pressure for both dry reforming and partial oxidation of methane and increasing the temperature caused increases in both activity of carbon and conversion of methane. The results clearly showed that the addition of O2 to the feed mixture could lead to a reduction of carbon deposition.

3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization

Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches.

Numerical Methods for a Class of Quadratic Matrix Equations

Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.

NONDESCENT SUBGRADIENT METHOD FOR NONSMOOTH CONSTRAINED MINIMIZATION

A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.

Numerical Solution of the Rotating Shallow Water Flows with Topography Using the Fractional Steps Method

The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting the multi-dimensional matrix inversion problem into an equivalent one dimensional problem which is successively integrated in every direction along the characteristics using the Riemann invariant associated with the cubic spline interpolation. The height and the velocity field of the shallow water equations over irregular bottom are discretized on a fixed Eulerian grid and time-stepped using the fractional steps method. Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and the free surface elevation have been studied and the results are plotted.

Continuous-time System Identification with Nuclear Norm Minimization and GPMF-based Subspace Method

To improve the accuracy and effectiveness of continuous-time (CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization (NNM) with the generalized Poisson moment functional (GPMF) based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method (SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers (ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods. © 2014 Chinese Association of Automation.

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.

Application of the “Six-Step Teaching Method” in the Nursing Teaching of Obstetric Interns

Objective: The “six-step teaching method” is a teaching method, which is summarized based on practical experience. This study aimed to explore the effect of “six-step teaching method” in clinical teaching of obstetrics. Methods: A quasi-experimental study design was used, 30 nursing students who entered obstetrics practice from March 2022 to July 2022 were selected as the control group according to the order of time, and traditional teaching methods were adopted. From August to December 2022, 30 interns were selected as the experimental group, and the “six-step teaching method” was adopted. After 8 weeks of clinical practice, the assessment results and teaching effect satisfaction of the two groups were compared. Results: The scores of obstetrical specialty in the experimental group were higher than those in the control group, and the difference was statistically significant (P < 0.05);The evaluation of teaching methods, teaching quality, classroom atmosphere and individual observation ability, clinical thinking ability and nurse-patient communication ability of the experimental group were higher than those of the control group, and the differences were statistically significant (P Conclusion: “six-step teaching method” can effectively master the professional knowledge of obstetrics, stimulate the clinical thinking ability of interns, and improve the teaching effect and satisfaction. .

Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early

This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (Vmax), maximum tardy job, denoted by (Tmax), and maximum earliness (Emax). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (Vmax, Tmax, Emax) and 1//(Vmax + Tmax + Emax). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time.

Synthesis of Vanadium Nitride by a One Step Method

Vanadium nitrides were prepared via one step method of carbothermal reduction and nitridation of vanadium trioxide. Thermalgravimetric analysis （TGA） and X-ray diffraction were used to determine the reaction paths of vanadium carbide, namely the following sequential reaction： V2O3→V8C7 in higher temperature stage, the rule of vanadium nitride synthesized was established, and defined conditions of temperature for the production of the carbides and nitrides were determined. Vanadium oxycarbide may consist in the front process of carbothermal reduction of vanadium trioxide. In one step method for vanadium nitride by carbothermal reduction and nitridation of vanadium trioxide, the nitridation process is simultaneous with the carbothermal reduction. A one-step mechanism of the carbothermal reduction with simultaneous nitridation leaded to a lower terminal temperature in nitridation process for vanadium nitride produced, compared with that of carbothermal reduction process without nitridation. The grain size and shape of vanadium nitride were uniform, and had the shape of a cube. The one step method combined vacuum carborization and nitridation （namely two step method） into one process. It simplified the technological process and decreased the costs.

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.

Nonmonotone Adaptive Trust Region Algorithms with Indefinite Dogleg Path for Unconstrained Minimization

In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.

A New Infeasible Interior-point Method for Linear Complementarity Problem Based on Full Newton Step

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present.

A multiplicative Gauss-Newton minimization algorithm:Theory and application to exponential functions

Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.

Improvement of the minimal residual method for solving nonsymmetric linear systems

In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.

Gradient Step Method to Predict the Ozone Solubility in Water

In this work it presents a strategy to obtain the ozone solubility in water by gradient step method. In this methodology, the ozone in mixture with oxygen is bubbling in a reactor with distilled water at 21℃ and pH 7. The ozone concentration on gas phase is continually increased after the saturation is reached. The method proposed is faster than conventional method （isocratic method）. The solubility from the gradient method is compared with that values obtained from correlations founded in the literature.

Noether＇s theorem and one-step corrections method for holonomic system

In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.

On“The Five-Step Method”in Teaching Junior English for China

Junior English for China’ is based on the ’Five-Step’ teachingmethod: Revision, Presentation, Drilling, Practice, Consolidation. Each step has itsown particular methodology and requires the teacher to adopt a certain role. Thispaper is a discussion of the "Five-Step Method".

Temperature-dependent photoluminescence on organic inorganic metal halide perovskite CH_3NH_3Pb I_(3-)Cl_ prepared on ZnO/FTO substrates using a two-step method

Temperature-dependent photoluminescence characteristics of organic-inorganic halide perovskite CH3NH3Pb I3-xClx films prepared using a two-step method on ZnO/FTO substrates were investigated. Surface morphology and absorption characteristics of the films were also studied. Scanning electron microscopy revealed large crystals and substrate coverage. The orthorhombic-to-tetragonal phase transition temperature was-140 K. The films＇ exciton binding energy was 77.6 ± 10.9 meV and the energy of optical phonons was 38.8 ± 2.5 meV. These results suggest that perovskite CH3NH3Pb I（3-x）Clx films have excellent optoelectronic characteristics which further suggests their potential usage in perovskitebased optoelectronic devices.