BOUNDARY ELEMENT METHODS FOR PLATES ON TwO-PARAMETER ELASTIC FOUNDATION

In this paper,the boundary element methods are applied to analyse the plates ontwo-parameter elastic foundation according to two boundary integral equations.The bending mo-ment,torsion and shear force at any point of plates are discussed by means of the theory of elasticitymechanics.An example and a plate in practital engineering are analysed.The resulta show that thereare high efficiency,good accuracy and little storage with this method.     

The Element-free Method for Elastic Foundation Plates(EFM)

The application of the element-free method in the bending problems of plates has not been found since it was proposed.In this paper,the element-free method is applied to compute the deflection and the moment of the elastic foundation plate with free boundary,and the corresponding formulas as well as the computer program are developed.Numerical examples show that the accuracy of the method used in the foundation plate problem is satisfactory.Therefore,it is reasonable and feasible for using the element-free method in the plate bending problems.     

Research on Shoelast CAD/CAM Technology

Some new developments of boundary contour method have been presented in this paper. The developments include the boundary contour method based on equivalent boundary integral equations, the traction boundary contour method as well as the application of the boundary contour method to crack problems and elastic thin plate bending problems.     

An Analysis of Thick Plates underIn-plane and Transversal Loadings by the BEM

In accordance with the behaviours of thick plates under the in-plane and transversal loadings,and introducing the concept of equivalent load, the coupled equations for the problem have been deduced with the theory of BEM in this paper.Thus a new method is presented for solving the problems of interaction of superstructure and foundation and subsoil,as well as for the problems of the thick plates under the complicated loadings.     

CYLINDRICAL BENDING PROBLEM OF RECTANGULAR PLATES STIFFENED ON ONE SIDE ALONG ONE DIRECTION WITH ELASTIC SUPPORTS AND TENSILE FORCES

On the basis of the calculated results of accurate analytic solution of stiffened rectangular plates,the general equations of cylindrical bending of the plates with tensile forces are established for engineering practice.Its solution combining with engineering problem is given for the special defor-mation conditions of elastic supports.In the paper,the numerical example is given and compared with references,it shows that the results are available.     

Remarks for Various Boundary IntegralEquations Reduced from the ExteriorNeumann Problem of Helmholtz Equation

This paper presents a discussion on various boundary integral equations reduced from the exterior Neumann problem of Helmholtz equation.The author analyses how the famous difficulty that some equations have no unique solution when the wave number k is an eigenvalue of an interior problem is arised in the course of reducing these equations from Helmholtz representations,and proposes a method of overcoming the difficulty,that is,introducing a direct boundary integral equation which has unique solution for all wave numbers k and is equivalent to the original boundary value problem.Besides,advantages and shortcomings for these integral equations are estimated respectively.     

Analyzing the StiffnesS of Foundation Plate By BEM

This.paper derives the basic solution of elastic half-space foundation plate byHankel transform,Then its boundary integral equation of distortion is estabished,The paper discuss-es bou ndary integral equation on plate of fixxing and/or simple support boundary.Then a systemof algebraic equations for the boundary values are established.A numerical example is given , its re-sult shows that this Method is correct.     

CALCULATION OF CYLINDRICAL BENDING PROBLEM FOR RECTANGULAR PLATES BY ELASTIC AND TENSILE SUPPORTS

In this paper, the solution of cylindrical bending problem for rectangular plates supported by elastic and tensile supports on particular deformation condition are derived from practical engineering problem. By examples, some considerable matters of analysing prismatic structures are suggested. The solutions are also studied when the tensions are to be determined. the results are simple and easy to be used.     

Galerkin Approximate Solutions of Displacement Including the Effect of Dead Loads for Two Kinds of Rectangular Plates

Based on the strain energy considering the effect of dead loads, the general form static equilibrium differential equations were formulated by means of the potential energy principle. The approximate solutions of live load or later load displacement including the effect of dead loads for the clamped rectangular plate and the simply supported rectangular plate were generated by the Galerkin method. These formulas are simple and clear, and their physical concepts are explicit. The correctness of these formulas was verified by the finite element method. The dead loads and other factors that influence the effect of dead loads are shown by these formulas. The effect of dead loads on the two different boundary condition rectangular plate were analyzed by these approximate solutions. The effect of dead loads improves the bending stiffness of plate and minimizes the displacement of live loads or later loads. The key physical factors governing the effects of dead loads on plates are the dead load, the ration of span to thickness and boundary condition etc. This effect of dead loads is not negligible, especial in thinner plates or plates with smaller stiffness, more attention should be paid to the effect of dead load in the calculation and analysis for plates.     

Reproducing kernel particle method for numerical analysis of Mindlin plate bending on a Winkler foundation

The reproducing kernel particle method (RKPM) is a typical meshless method based on kernel function simulation. Based on the interpolating shape function of RKPM and Mindlin plate theory, the governing equations of RKPM to the deflection solution of Mindlin plate bending on a Winkler elastic soil foundation are established. Numerical results indicate that the above method and the corresponding program are effective and accurate.     

Exact Integration of Constant Element of Elastomer in Boundary Element Method

The boundary integral in Boundary Element Method affects the precision and the speed of the method. If the boundary integral with constant element, the nonsingular integrals are popularly calculated by the Gauss numerical integral, and the singular integrals are popularly calculated by the analytical integral. This paper presents an alternative way with Gauss formula to transform the double integral in elastic problem on 3-d into the linear integrals on the boundary of each subdomains, so that all the singular integrals and nonsingular integrals are calculated by analytical method. The example indicates that this method makes the precision and the speed of BEM improve.     

Elastic Analysis of Beam-Plate Foundation with Winkler Model

The beam-plate foundation is divided into two parts.The boundary element methods areapplied to analyze the plates with Winklermodel.The finite element methods are used to evaluate thebeams The coupling equation is obtained by the coodination of both force and displacement.     

A Boundary Element Method for the Electrostatic Field with Anisotropic Media

The boundary-value problem for the electrostatic field with anisotropic media is formulated on the basis of introducing the medium property coefficient tensor. The boundary integral equations for this problem are deduced by the weighted residual method. The elementary solutions to the two-and three-dimensional anisotropic problems are derived. A two dimensional example with anisotropic media is given.     

Elastic Buckling and Critical Load of an Pre- stressing Arch

According to the field theory of additional deformation on pre - stressed configuration , in the paper , the ordinary expression of the governing equation and variational equation of elastic buckling are brought forward . Under the theory system, through lowering dimensions, the governing equation and variational equation for the critical condition solution of elastic buckling of a plane arch are deduced, and the eigenvalues problem of the linear homogeneous differential equations corresponding to the equations are concluded While Abandoning the plane assumption and considering shearing deformation, the linear finite element method arithmetic of bending bar's cross section containing six degree of freedom is given. The process of derivation and calculational results show that, under this system info, the finite element equations of bending bar deduced are accurate and easy to be used to numeric calculations, and the conclusion achieved is more practical.     

Galerkin Boundary Element Method for Laplace Equation

Galerkin method based on the variation principle is used to solve differential and integral equations. The boundary problem of Laplace equation is changed into the variational equation which is equivalent to the boundary integral equation. Using linear element, it is solved by Galerkin boundary element method. In computation of stiffness matrix, the exactly integral formula is used in the first order integral expression, The numerical integral formula is used in the second order integral expression. Thus the problem of calculation of double singular integral is carried out. The numerical experiments also prove this method is reliable. The error of Galerkin boundary element is tested with numerical experimentation.     

Soil Temperature Model for CERES and Similar Crop Models

Frequently the soil heat transfer is considered as a one-dimensional (vertical) process which may be described by the differential equation (DE) of soil heat flow. Regarding the upper boundary, equations for bare and cropped fields are developed by means of data of Kiel and Michigan. For the lower boundary a theoretical and an empirical equation are given. The soil heat conductivity was estimated by the formulas of M c I nnes (1981). Equations are proposed for estimating the clay and quartz contents which are needed in these formulas. The convective term in the differential equation (DE) may be omitted without significant loss of precision. For the SALUS model in which the two upper layers are 2 resp. 5 cm thick a simple approximative solution for these two layers is given. The temperatures of the deeper layers are calculated by the DE for which in this case only two time steps per day are necessary. This yields short computing times.     

Mix Domain Decomposition Method with Boundary Element Method For Stokes Equations and Application

As the BEM was used in the knaggy domain,its approach error was big.Domain Decomposition Method change the problem in the knaggy domain to the problem in several convex domains which do not wrap.The whole solution is gained by alternating boundary conditions between Dirichlet condition and Neumann condition on the common boundary.Domain Decomposition Method for Stokes equations in the anomalistic knaggy domain is presented,the example of Domain Decomposition Method in the flow of the lake in GuiYang City is given.     

Study on the Nonlinear Vibration System with Slow-changing Parameters

In this paper a posteriori error estimates for Galerkin approximation of general operator equations is firstly presented in the framework of Sobolev spaces. Then a practical posteriori error estimates formula for the adaptive boundary element method solving the acoustic scattering problem with a finite plane screen is obtained by triangulations. The mathematical model of this problem is the three dimensional Neumann boundary value problem of Helmholtz equation with finite plane boundary.     

A Boundary Element Separation Solution to the Elastic Contact Problems and the Optimal Penalty Factor

In this paper the boundary element separation to the elastic contact problems proposed by Kamiya is improved. It gives another optimal penalty factor to accelerate the iteratively saluting procedure, which makes a theoretical foundation for the application of computers' parallel processing method to reduce the calculation time and memory. A practical example is given to confirm the validity of the present method in comparison with Kamiya method.     

Quadrature Methods and Their Extrapolations for Solving Boundary Integral Equations of Steady Navier-Stokes Problems

This paper presents an iteration method of solving non linear boundary integral equations (BIE) of the plane Navier Stokes problem,which each step of the iteration is to solve a linear BIE of nonhomogeneous Stokes problem. Using the quadrature methods of [1],we give a new algorithm with a high order accuracy.The algorithm not only saves work,but also the accuracy can be improved by Richardson extrapolation.