Aerodynamic design method of cascade profiles based on load and blade thickness distribution

A cascade profile design method was proposed using the aerodynamic load and blade thickness distribution as the design constraints, which were correspondent to the demands from the aerodynamic characteristics and the blade strength. These constraints,together with all the other boundary conditions , were involved in the stationary conditions ofa variational principle , in which the angle-function was employed as the unknown function.The angle-function ( i. e. , the circumferential angular coordinate) was defined in the image plane composed of the stream function coordinate ( circumferential direction ) and streamline coordinate. The solution domain, i.e., the blade-to-blade passage, was transformed into a square in the image plane, while the blade contour was projected to a straight line ; thus, the difficulty of the unknown blade geometry was avoided. The finite element method was employed to establish the calculation code. Applications show that this method can satisfy the design requests on the blade     

High order multiplication perturbation method for singular perturbation problems

This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.     

Precise integration method for solving singular perturbation problems

This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.     

A coupling difference scheme for the numerical solution of a singular perturbation problem

In this paper, we consider a singularly perturbed problem without turning points. On a special diseretization mesh, a coupling difference scheme, resulting from central difference scheme and Abrahamsson-Keller-Kreiss box scheme, is proposed and the second order convergence, uniform in the small parameter, is proved. Finally, numerical resulls are provided.     

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

ＡＵＮＩＦＯＲＭＬＹＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＦＯＲＡＳＥＭＩＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＣＯＮＤＩＴ...     

Coupling of high order multiplication perturbation method and reduction method for variable coefcient singular perturbation problems

Based on the precise integration method(PIM), a coupling technique of the high order multiplication perturbation method(HOMPM) and the reduction method is proposed to solve variable coefcient singularly perturbed two-point boundary value problems(TPBVPs) with one boundary layer. First, the inhomogeneous ordinary diferential equations(ODEs) are transformed into the homogeneous ODEs by variable coefcient dimensional expansion. Then, the whole interval is divided evenly, and the transfer matrix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efcient.     

Coupling of high order multiplication perturbation method and reduction method for variable coefficient singular perturbation problems

Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.     

Asymptotic solution for singular perturbation problems of difference equation

In this paper, we constructed a new asymptotic method for singular perturbation problems of difference equation with a small parameter.Project Supported by the Science Fund of the Chinese Academy of Sciences.     

An exponentially fitted difference scheme for the hyperbolic-hyperbolic singularly perturbed initial-boundary value problem

In this paper we discuss,an initial-boundary value problem of hyperbolic type with firstderivative with respect to x.The asymptotic solution is constructed and its uniform validityis proved under weader compatibility conditions.Then we develop an exponentially fitteddifference scheme and establish discrete energy inequality.Finally,we prove that thesolution of difference problem uniformly converges to the solution of the original problem.     

部分应力杂交动力分析模型的混合变分原理

本文通过对具有单重卷积积分的二类变量的Ｇｕｒｔｉｎ型混合变分原理进行修正，采用“部分应力杂交”的概念，建立了线弹性动力分析 部分应力杂交变分格式，并在此基础上构造出时间有限元模型，这种模型对于分层复合板的动力分析尤其适用。     

A NEW VARIATIONAL INEQUALITY FORMULATION FOR SEEPAGE PROBLEMS WITH FREE SURFACES

IntroductionTherearetwoclassesofsolutionsforseepageproblemswithfreesurfaces ,i.e .,theadaptivemeshmethodsandthefixedmeshmethods.Theadaptivemeshmethodsinvolvetoolargeamountofcomputationforinhomogeneoussoilsandoftenleadtodivergentcalculations,andhence,arenowbeingsupercededbythefixedmeshmethods.Thefixedmeshmethodsfallintotwocategories,theintuitivemethodsandthevariationalinequalitymethods.Theintuitivemethods[1- 3]establishusuallytheiterativeproceduresbaseduponthefactthatthereisnodischargebetweenth…     

非线性Reissner板杂交元及边界元解

首先改进文[1]的互补变分原理。再建议一种较为普遍性的方法,导出精确的边界积分方程。最后给出变分有限元及边界元解,算例证实有限元格式及迭代方式有效。     

Generalized sub-region mixed and hybrid variational principlesin nonlinear elastodynamics

In this paper, the Hu-Washizu generalized variational principle isextended to nonlinear elastodynamics with five independent fields. The twokinds of framework of functional, the potential energy and complementaryenergy expressions containing the subsidiary conditions with Lagrangemultipliers are suggested. According to the principle of stationaryfunctional, we have the governing equations and Lagrange multipliersdetermened by the results of variation. The generalized sub-region mixed andhybrid variational principle in nonlinear elastodynamics is presented.Supported by National Natural ScienceFoundation of China.     

P-version hybrid analytical finite element method for plate bending problems

Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China.     

Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems

An adaptive mixed least squares Galerkin/Petrov finite element method (FEM) is developed for stationary conduction convection problems. The mixed least squares Galerkin/Petrov FEM is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. Using the general theory of Verfürth, the posteriori error estimates of the residual type are derived. Finally, numerical tests are presented to illustrate the effectiveness of the method.     

Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems

An adaptive mixed least squares Galerkin/Petrov finite element method (FEM) is developed for stationary conduction convection problems. The mixed least squares Galerkin/Petrov FEM is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. Using the general theory of Verfürth, the posteriori error estimates of the residual type are derived. Finally, numerical tests are presented to illustrate the effectiveness of the method.     

Effective numerical methods for elasto-plastic contact problems with friction

Several effective numerical methods for solving the elasto-plastic contact problems with friction are presented. First, a direct substitution method is employed to impose the contact constraint conditions on condensed finite element equations, thus resulting in a reduction by half in the dimension of final governing equations. Second, an algorithm composed of contact condition probes and elasto-plastic iterations is utilized to solve the governing equation, which distinguishes two kinds of nonlinearities, and makes the solution unique. In addition, Positive-Negative Sequence Modification Method is used to condense the finite element equations of each substructure and an analytical integration is introduced to determine the elasto-plastic status after each time step or each iteration, hence the computational efficiency is enhanced to a great extent. Finally, several test and practical examples are presented showing the validity and versatility of these methods and algorithms. The Project Supported by National Natural Science Foundation of China.     

MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD

The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.     

非饱和多孔介质有限元分析的基本控制方程与变分原理

本文在对问题研究现状进行阐述的基础上较系统地给出了骨架可变形非饱和多孔介质的全耦合分析模型，模型中考虑了孔隙气体，水（油）流动对介质力学性能的影响，多孔介质的饱和度，渗透系数与毛吸压力的关系，由实验给出，所导出的控制方程以固体骨架的位移与孔隙流体压力为基本未知量，由于问题的非自共轭特征，文中构造了非饱和介质动力问题的参数变分形式，并在此基础上给出有限元离散方程。     

Variational principles for hydrodynamic impact problems

We first establish the rigorous field equations of the two continuous stages before and after entering water. Then correspondently, we obtain the specific variational principles, bounded theorems, and boundary integral equations of the second stage problems. The existence of solutions are proved and the scheme of solving the solutions are provided. Finally, as a numerical example, the ship's wave resistence problem is used to demonstrate the specific application of the second stage problems and its accuracy. Then we provide a rigorous and sound theoretical basis of variational finite element method and boundary element method for calculating the accurately fundamental equations.