Application of the finite analytic numerical method to a flowdependent variational data assimilation

An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.

THE ANALYTICAL SOLUTIONS BASED ON THE CONCEPT OF FINITE ELEMENT METHODS

On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugguested for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.

SEMI-ANALYTICAL FINITE ELEMENT METHOD FOR FICTITIOUS CRACK MODEL IN FRACTURE MECHANICS OF CONCRETE

Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.

Similarity solutions of vertical plane wall plume based on finite analytic method

The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.

Measuring the Qatar-Kazeron Fault Dip Using Random Finite Fault Simulation of September 27, 2010 Kazeron Earthquake and Analytical Signal Map of Satellite Magnetic Data

In this research the fault parameters causing the September 27, 2010 Kazeron Earthquake with a magnitude of MW = 5.8 (BHRC) were determined using the random finite fault method. The parameters were recorded by 27 accelerometer stations. Simulation of strong ground motion is very useful for areas about which little information and data are available. Considering the distribution of earthquake records and the existing relationships, for the fault plane causing the September 27, 2010 Kazeron Earthquake the length of the fault along the strike direction and the width of the fault along the dip direction were determined to be 10 km and 7 km, respectively. Moreover, 10 elements were assumed along the length and 7 were assumed along the width of the plane. Research results indicated that the epicenter of the earthquake had a geographic coordination of 29.88N - 51.77E, which complied with the results reported by the Institute of Geophysics Tehran University (IGTU). In addition, the strike and dip measured for the fault causing the Kazeron Earthquake were 27 and 50 degrees, respectively. Therefore, the causing fault was almost parallel to and coincident with the fault. There are magnetic discontinuities on the analytical signal map with a north-south strike followed by a northwest-southeast strike. The discontinuities are consistent with the trend of Kazeron fault but are several kilometers away from it. Therefore, they show the fault depth at a distance of 12 km from the fault surface.

Elastic-plastic analytical solution for centric crack loaded by two pairs of point shear forces in finite plate

The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.

THE STABILITY AND CONVERGENCE OF THE FINITE ANALYTIC METHOD FOR THE NUMERICAL SOLUTION OF CONVECTIVE DIFFUSION EQUATION

In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.

Five-point Element Scheme of Finite Analytic Method for Unsteady Groundwater Flow

In order to improve the finite analytic method’s adaptability for irregular unit, by using coordinates rotation technique this paper establishes a five-point element scheme of finite analytic method. It not only solves unsteady groundwater flow equation but also gives the boundary condition. This method can be used to calculate the three typical questions of groundwater. By compared with predecessor’s computed result, the result of this method is more satisfactory.

HYBRID FINITE ANALYTIC SOLUTIONS OF SHALLOW WATER CIRCULATION

The hybrid finite analytic(HFA) method is a kind of numerical scheme in rectangular element. In order to simulate the shallow circulation in irregular bathymetry by HFA scheme, the model in sigma coordinate system was obtained. The model has been tested against three cases: 1) Wind induced circulation; 2) Density driven circulation and 3) Seiche oscillation. The results obtained in the present study compare well with those obtained from the corresponding analytical solutions under idealized for the above three cases. The hybrid finite analytic method and the circulation model in sigma coordinate system can be used calculate the flow and water quality in estuaries and coastal waters.

Revisiting the analytical solutions for ultimate bearing capacity of pile embedded in rocks

This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although this criterion is considered a reference value for empirical and numerical calculations,some limitations of its basic simplifications have not been clarified yet.This research compares the analytical results obtained from the novel discontinuity layout optimization(DLO)method and the numerical solutions from the finite difference method(FDM).The limitations of the analytical solution are considered by comparing different DLO failure modes,thus allowing for the first time a critical evaluation of its scope and conditioning for implementation.Errors of up to 40%in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution.The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size.The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity,presenting considerable advantages over other methods.

Axial Compression Behavior and Analytical Method of L-Shaped Column Composed of Concrete-Filled Square Steel Tubes

Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical property of the L-shaped column. The load-displacement curve for the L-shaped column, the deflection and load-strain curves for the mono columns were obtained by the axial compression experiment. The results show that the L-shaped column exhibits a flexural-torsional buckling failure mode. The numerical simulation by the finite element analysis shows that the bearing capacity and failure mode are in accordance with those of the axial compression experiment and the feasi- bility of the finite element analysis is proved. For the calculation of the bearing capacity of the L-shaped column com- posed of concrete-filled square steel tubes, an analytical method is proposed based on the theory of the elastic stability and spatial truss model. The results of the analytical method are in good agreement with those of the axial compression experiment and the finite element analysis.

Numerical-Analytical Method for Magnetic Field Computation in Rotational Electric Machines

A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is computed by the proposed method. The result is compared to that obtained by finite element method so as to validate the correction of the method.

Axisymmetric Finite Element Method for Analysis of Plate on Layered Soil

To obtain the fundamental solution of soil has become the key problem for the semi-analytical and semi-numerical (SASN) method in analyzing plate on layered soil. By applying axisymmetric finite element method (FEM),an expression relating the surface settlement and the reaction of the layered soil can be obtained. Such a reaction can be treated as load acting on the applied external load. Having the plate modelled by four-node elements,the governing equation of the plate can be formed and solved. In this case, the fundamental solution can be introduced into the global soil stiffness matrix and five-node or nine-node element soil stiffness matrix.The existing commercial FEM software can be used to solve the fundamental solution of soil, which can bypass the complicated formula derivation and boasts high computational efficiency as well.

SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FOUNDATION

A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb＇s solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.

FORMULATION OF A SEMI-ANALYTICAL APPROACH BASEDON GURTIN VARIATIONAL PRINCIPLE FOR DYNAMICRESPONSE OF GENERAL THIN PLATES

4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin variational principles.The formulationof time series is also investigated so that the dynamic response of plates with arbitraryshape and boundary constraints can be achieved with adequate accuracy.

Application of semi-analytical finite element method to analyze the bearing capacity of asphalt pavements under moving loads

To facilitate long term infrastructure asset management systems, it is necessary to determine the bearing capacity of pavements. Currently it is common to conduct such measurements in a stationary manner, however the evaluation with stationary loading does not correspond to reality a tendency towards continuous and high speed measurements in recent years can be observed. The computational program SAFEM was developed with the objective of evaluating the dynamic response of asphalt under moving loads and is based on a semi-analytic element method. In this research project SAFEM is compared to commercial finite element software ABAQUS and field measurements to verify the computational accuracy. The computational accuracy of SAFEM was found to be high enough to be viable whilst boasting a computational time far shorter than ABAQUS. Thus, SAFEM appears to be a feasible approach to determine the dynamic response of pavements under dynamic loads and is a useful tool for infrastructure administrations to analyze the pavement bearing capacity.

Application of semi-analytical finite element method coupled with infinite element for analysis of asphalt pavement structural response

A specific computational program SAFEM was developed based on semi-analytical finite element （FE） method for analysis of asphalt pavement structural responses under static loads. The reliability and efficiency of this FE program was proved by comparison with the general commercial FE software ABAQUS. In order to further reduce the computational time without decrease of the accuracy, the infinite element was added to this program. The results of the finite-infinite element coupling analysis were compared with those of finite element analysis derived from the verified FE program, The study shows that finite-infinite element coupling analysis has higher reliability and efficiency.

Winkler地基上四边自由正交各向异性矩形中厚板弯曲的有限积分变换解

本文应用有限积分变换法研究Winkler地基上四边自由正交各向异性矩形中厚板的弯曲问题.具体由正交各向异性矩形中厚板弯曲的基本方程组和边界条件出发,结合有限积分变换法及其对应的逆变换法推导出正交各向异性矩形中厚板弯曲问题的解析解.该解析解统一适用于计算各向同性/正交各向异性矩形薄板、中厚板和厚板的弯曲问题,并且通过具体算例验证了所得解析解的正确性.

钢绞线导波传播特性研究

导波作为一种有效的无损检测方法,在钢绞线检测中具有广阔的应用前景。钢绞线的特殊螺旋结构,使得导波在钢绞线中的传播性质尚未完全了解。该文研究了导波在七丝钢绞线中频散性质。利用FrenetSerret方法建立了螺旋坐标系,在此基础上对传统半解析有限元方法进行了改进,得到了适用于螺旋结构的波导特征方程。计算了单根高强直钢丝的频散曲线,分析了导波的频散特性,研究了导波在七丝钢绞线中传播的频散特性,得到的频散曲线“陷频”现象中心频率与实验结果一致,并且钢绞线和直钢丝的频散曲线具有很大差异。通过钢绞线超声导波应力测试实验验证了该文所提出的螺旋半解析有限元法的正确性和有效性。结果表明,实验结果与理论群速度吻合良好,并且钢绞线的轴向应力与钢绞线中导波群速度近似线性关系。