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.

Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.

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.

三步接骨法治疗Sanders Ⅱ型跟骨骨折的有限元研究

目的量化评估三步接骨法治疗Sanders Ⅱ型跟骨骨折效能指标,阐明其科学机制。方法利用健康成年男性踝关节CT数据,构建正常足踝模型与Sanders Ⅱ型跟骨骨折模型,在骨折模型上进行三步接骨法的力学加载,模拟拔伸牵引、提按顶复、端挤捏骨等手法,评估跟骨复位情况并求解不同手法作用下力学的变化。结果建立正常足部模型与Sanders Ⅱ A/B/C型跟骨骨折模型;三步接骨法加载复位后跟骨长、高、宽、Gissane’s角及Bohler’s角得到明显纠正;求解不同手法的力学趋势,发现拔伸牵引法能有效纠正重叠位移,提按顶复法侧重纠正前后侧移位,端挤捏骨法致力纠正内外侧移位。结论三步接骨法通过依次纠正骨折位移,能恢复跟骨解剖结构,有效治疗跟骨SandersⅡ型损伤,具有有效性及科学性。

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.

Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres

In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

Synthesis of Codon-optimized Human Interleukin-18 Gene by Combination of Chemical and Enzymatic Method

According to the amino acid sequence and codon preference of E. coli, the human interleukin-18（IL-18） gene was optimized to avoid the rare codons. The total length of the synthesized gene is 571 bp; 18 oligonucleotides, DNA fragments were designed and synthesized by the phosphoramidite four-step chemical method. The whole DNA sequence was synthesized by a one-step total gene synthesis method, and then inserted in pUC18 vector. Five positive clones identified by blue-white colony screening were sent to Shanghai Sangon Biological Engineering Technology and Service Co., Ltd. for sequencing. The sequencing result shows that one clone contained the complete correct gene in all the five positive clones.

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.

NUMERICAL METHOD FOR THREE-DIMENSIONAL NONLINEAR CONVECTION-DOMINATED PROBLEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.

INTERACTION OF A SOLITARY WAVE AND A FRONT STEP SIMULATED BY LEVEL SET METHOD

As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.

A LOW-PRESSURE AND ONE-STEP METHOD FOR THE SYNTHESIS OF ALKYLIDYNETRICOBALT NONACARBONYL CLUSTERS:RCCo_8(CO)_9

Metal clusters RCCo_3(CO)_9(R-H,C1,Br,CH_3,Ph) were prepared in 18.8-57.3% yields from the reaction of cobalt(Ⅱ)salt and RCX_a under mild PTC conditions(latm CO,25℃).The cobalt salt was reduced to Co(CO)_4 in the presence of Na_3S_2O_4.

Constraint Stabilization and One-Step Correction Method for Dynamical Systems

A computational method of constraint stabilization and correction is introduced. The method is based on the Baumgart＇s one-step method. Constraint conditions are addressed to stabilize and correct the solution. Two examples are given to illustrate the results of the method.

ZnO micro-nano composite hydrophobic film prepared by the three-step method

The hydrophobicity of the lotus leaf is mainly due to its surface micro-nano composite structure. In order to mimic the lotus structure, ZnO micro-nano composite hydrophobic films were prepared via the three-step method. On thin buffer films of SiO2, which were first fabricated on glass substrates by the so,gel dip-coating method, a ZnO seed layer was deposited via RF magnetron sputtering. Then two different ZnO films, micro-nano and micro-only flowerlike structures, were grown by the hydrothermal method. The prepared films have different hydrophobic properties after surface modification. The structures of the obtained ZnO films were characterized using x-ray diffraction and field-emission scanning electron microscopy. A conclusion that a micro-nano composite structure is more beneficial to hydrophobicity than a micro-only structure was obtained through research into the effect of structure on hydrophobic properties.

Study on the wind field and pollutant dispersion in street canyons using a stable numerical method

A stable finite element method for the time dependent Navier-Stokes equations was used for studying the wind flow and pollutant dispersion within street canyons. A three-step fractional method was used to solve the velocity field and the pressure field separately from the governing equations. The Streamline Upwind Petrov-Galerkin(SUPG) method was used to get stable numerical results. Numerical oscillation was minimized and satisfactory results can be obtained for flows at high Reynolds numbers. Simulating the flow over a square cylinder within a wide range of Reynolds numbers validates the wind field model. The Strouhal numbers obtained from the numerical simulation had a good agreement with those obtained from experiment. The wind field model developed in the present study is applied to simulate more complex flow phenomena in street canyons with two different building configurations. The results indicated that the flow at rooftop of buildings might not be assumed parallel to the ground as some numerical modelers did. A counter-clockwise rotating vortex may be found in street canyons with an inflow from the left to right. In addition, increasing building height can increase velocity fluctuations in the street canyon under certain circumstances, which facilitate pollutant dispersion. At high Reynolds numbers, the flow regimes in street canyons do not change with inflow velocity.

ELEMENT－BY－ELEMENT MATRIX DECOMPOSITION ANDSTEP－BY－STEP INTEGRATION METHOD FOR TRANSIENTDYNAMIC PROBLEMS

In this paper a general matrix decomposition scheme as well as an element-by-clement relaxation algorithm combined with step-by -step integration method is presented for transient dynamic problems thus the finite element method can be fromforming global stiffness matrix global mass matrix as well as solyin large scale sparse equations Theory analysis and numerical results show that the presented matrix decomposition scheme is the optimal one The presented algoithm has else physicalmeaning and can be busily applied to finite element codes

The convergence ball and error analysis of the two-step Secant method

Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order,we obtain an estimate of the radius of the convergence ball for the two-step secant method.Moreover,we also provide an error estimate that matches the convergence order of the two-step secant method.At last,we give an application of the proposed theorem.

Signal-to-noise ratio comparison of angular signal radiography and phase stepping method

Grating-based x-ray phase contrast imaging has the potential to be applied in future medical applications as it is compatible with both laboratory and synchrotron source. However, information retrieval methods are important because acquisition speed, scanning mode, image quality, and radiation dose depend on them. Phase-stepping （PS） is a widely used method to retrieve information, while angular signal radiography （ASR） is a newly established method. In this manuscript, signal-to-noise ratios （SNRs） of ASR are compared with that of PS. Numerical experiments are performed to validate theoretical results. SNRs comparison shows that for refraction and scattering images ASR has higher SNR than PS method, while for absorption image both methods have same SNR. Therefore, our conclusions would have guideline in future preclinical and clinical applications.

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid （CLEAR-VOF） method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.

基于子循环自适应串行交错时间匹配算法的油浸式变压器绕组瞬态温升计算

针对传统算法存在的步长调整及耦合点选择问题,该文提出基于子循环自适应串行交错(SCAS)的时间匹配算法。首先,在步长调整方面,通过加入自适应(ATS)-启发式(HTS)混合变步长算法,解决步长无法实时调整的问题;然后,针对耦合点选择问题,该文在传统常规串行交错(CSS)时间匹配算法及现有改进方案子循环常规串行交错(SCSS)的基础上,提出SCAS时间匹配算法,采用自适应方案确定计算时间窗及预定耦合点,并引入指数平滑法对其精度进行保证;最后,该文基于110 kV油浸式电力变压器建立二维瞬态单分区分匝绕组模型,并将所提算法与其他传统方法进行对比分析。结果表明:在精度方面,与传统CSS算法相比SCAS算法的流场及温度场最大平均相对误差均不超过0.45%,在可接受误差范围内;在效率方面,SCAS算法总体计算效率较CSS算法提高了近20倍。同时,为了说明所提算法的工程价值,该文搭建基于110 kV变压器绕组模型的温升实验平台,将SCAS时间匹配算法应用于该模型中,实验结果表明:在精度方面,SCAS算法与实验达到稳态时最大绝对误差为2.7 K;在计算效率上,本文所提算法的计算效率较传统算法提升约46倍,计算步数约为传统的1/47,减少了计算冗余。