Calculating Critical Loads of Thin Plates With Method of Weighted Residuals

In elastic mechanics, it is common practice to calculate critical loads in buckle of thin plates by means of double triangle series. The calculation process is more complex, this method has not facility in engineering application. In many cases critical loads of thin plates can not obtain precise analytic solutions. It is very important to solve approximate resolutions of critical loads of plates in engineering. The method of weighted residuals is an available measure to solve proximal resolutions of differential equations and has extensive application in egineering. In order to simplify calculation process and obtain profitble result, by means of method of weighted residuals and Cantorovich variational principle, taking the second Tchebychev's polynomials as trial functions, it was calculated, critical loads of rectangle thin plates in different supporting conditions. Calculation results indicate that this calculation method is simple and has some precision, it is applied conveniently in engineering.     

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.     

THE CALCULATION OF INTERNAL FORCES AND DISPLACEMENTS IN FRAME-SHEARING WALL STRUCTURE UNDER THE HORIZONTAL LOADS

In general,the calculating result of a comparatively regular frame-shearing wall system in tall buildings,a 4-order differential equations are established according to the deformation-coordination of beams,columns and four boundary conditions.Then a series of formulas concerning internal forces and displacement is obtained These formulas are hyperbolic functions.This paper presents a method,which changes 4-order differential equations into 2-order and solves them by the expressions of new homogeneous solutionThen the formulas of internal forces and displacements become exponential functions By this method,the calculation is very convenient The result of suggested method agrees well with the general by comparison This paper is also applicable to buildings with some part of different height of storey or stiffness.     

Application of sequential response surface method tothin wall beam lightweight design

It is proposed to introduce approximate model method to crashworthiness optimization design of thin wall beam,and the approximate model can be optimized by using sequential response surface method.In order to solve the parameterization design problem of finite element model,a parameterization model about material,cross section size and spotweld of thin wall beam is established by developing corresponding procedures.The results show that optimization design can not only improve the performance of absorbing energy of thin wall beam,but also reduce the weight greatly;the approximate model method can greatly improve optimization efficiency.     

Finite Element Modeling of Stainless Steel Plates in Compression and Structural Behavior

The behavior of plate in compression plays a basic role in relevant research. There are significant differences between stainless steel and carbon steel plates in structural behavior. Analysis on the behavior of stainless steel plate in compression was presented. The development of FE models for analyzing stainless steel plates in compression was described based on the results of Rasmussen's test. And the strength curve was achieved by such advanced FE models with a high degree of accuracy. The explicit strength equations and design method were proposed for determining the local buckling strength of stainless plate and cold formed rectangular hollow section in compression. It is shown that the numerical simulation results achieved by using Quach model are accurate.     

Boundaty Element Method for Analysis of Thick Plates on Two- Parameter Elastic Foundations

This paper discusses the Reissner's plates on elastic foundation.The elastic foundation is considered as two- paramerer and its effect to thick plates are taken into account by a set of govering differential equations. According to the foundamental solutions for bending problem on two- parameter foundation derived, three boundary integral equations denoted by generalized displacement functions are established. This method is suitable to solve the bending problem of thin or thick plates on two- parameter foundation with arbitary boundary condition, arbitary shape and arbitary load conditions     

STUDY OF SOLUTION METHODS FOR SEPARATOR EQUATIONS OF HIGH GRADIENT MAGNETIC SEPARATION

In this paper, an analytical solution,approximate solution of initial retention, steady-state solution and numerical solution of separator equations of high gradient magnetic separation are discussed. A backward-vave method used to improve the steady-state solution and Treanor-four order Taylor numerical method are suggested for magnetic separator equations and are compared with experimental results.     

The Elimination of Deformation Coupling in Thin Wall Composite Material Rod with Closed Section

Under the condition that normal stress and shear stress are coupled in constitutive equations,a set of displacements which depend on geometric and physical properties of a thin wall rod is specially designated to minimize the coupling of basic deformations in control equations,and general forms to describe self balance system of internal forces are proposed with the model given by the present paper.     

Approximate Estimate of Lateral Deflection for Rigid Frame and Frame-Shear Wall Structure Systems

This paper expounds the engineering significance of deliberating a method of approximate calculation,and has a discussion on lateral deflection of frame and frame_shear wall structures.     

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.     

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.     

Neumann Series Solution of Newmark Method and Its Convergence for Solving Dynamic Equations

The convergence of Newmark Neumann series method for solving dynamic equations is discussed.Conditions of convergence and the estimating expressions of approximate solution and error for the series solution are also given.     

Asymptotic Attractors of the Nonlinear Evolution Equation in Bounded Domain

The basic principle of infinite-dimensional dynamic system is to try to reduce the original infinite-dimensional system to an infinite-dimensional system. However,due to the unknown structure of the reduced system, it is difficult to describe its dynamical behaviour. To overcome this difficulty, the idea of approximate inertial manifolds is introduced, for NSE, the existence of AIM was studied, it is shown that the global attractor lies within a neighborhood of the graph of an Lipschitz function by the squeezing property. In this paper, by constructing a finite dimensional solution sequence, we will prove that it tends to the global attractor, theoretically, this provides a metod of constructing the asymptotic attractors, theoretically, this provides a method of constructing the asymptotic attractors for the evolution equations.     

A Study of Ultimate Loading Capacity of Eccentric Compressed Timber Column

In this paper, ultimate loading capacity of eccentric compressed timber column and elastic-plastic behaviour of the material of the cross section are considered.An approximate theoretic method dealing with the maximum mid-span deflection of the column when breaking is advanced.As a result, a formula calculating failure deflection of the rectangular cross section is derived. The results of theoretic calculation are well coincident with those of tests.     

Optimization Method of Turbine Impeller''s Stress and Deformation Calculation

Taking into the feature of computer computing method, using Stress solution of elasticity theory and according to different method of solving of system of second order ordinary differential equations , this article provides two numerical value computing method as for the stress and deformation of the turbine impeller which is within the scope of elasticity . One combines the initial value computing method of system of ordinary differential equations (Runge-Kutta Method) with optimization method, another combines the boundary value computing method of system of ordinary differential equations difference method-with optimization method and three points interpolation method . The proposed method can eliminate the deficiencies of Secondary Calculation method and is particularly suited for programmable computer-based solution . The sample show that results gotten by two methods is nearly equal to the precise results,so they are practicable. They completes the quick and precise calculating of stress and deformation . They have some general meaning , large commonality and the project employing value.     

Effects of Thorax Muscle Fiber on Body Surface Potentials

A numerical method calculating the forward problem of electrocardiogram (ECG) has been presented. By using this method, the torso part including anisotropic muscle layers has been discretized by means of the finite element method (FEM). The rest of torso have been divided into the surface elements by the boundary element method (BEM). The effects of the skelltel muscle layers over thorax wall, have been discussed in terms of a three-dimensional torso models.     

NONLINEAR ANALYSIS OF LAMINATED ANGLE-PLY PLATE USING A HIGHER-ORDER SHEAR DEFORMATION THEORY

A higher-order shear deformation theory is used to analyse nonlinear bending of symmetrically laminated angle-ply rectangular plates. The nonlinear governing differential equations are solved here by using perturbation method. Numerical rerults are presented graphically for vairous parameters of laminated plate. The present solutions are compared with those obtained using the classical plate theory. A lot of significient conclusions are obtained.     

K近邻的自适应谱聚类快速算法

利用时域递归展开算法对墙体内热湿耦合传递方程进行求解。以木板为例,应用该算法进行了热湿耦合传递的分析计算,在时间域和空间域上分别运用递归展开法和控制容积法进行离散,从而得到递归形式的线性方程组,运用MATLAB软件对这一过程进行求解。计算结果与有限差分算法、解析解计算结果以及实验数据吻合良好,表明该算法能够用于求解多孔介质热湿耦合传递模型。时间步长的改变对计算结果影响较小,可通过增加时间步长方法来减少工作量。     

The edge element method in the forward problem of magnetic inductiontomography with homogeneous sinusoidal magnetic excitation

The edge finite element method and the imaging visualization have been studied in the forward problem of magnetic induction tomography MIT with homogeneous sinusoidal magnetic excitation. The definite equations of the forward problem were established using the electric field intensity as the vector variable. The edge FE method for solving the definite equations was introduced in detail and realized as the MATLAB program. In order to realize the visualization of MIT in imaging the intracranial hemorrhage, a real human brain finite element model was created with the human head MRI data. On the basis of this model, we realized the 3D visualization of MIT imaging in MATLAB. The research results demonstrated the validity of the definite equations and the edge FE method in calculating the forward problem. And the 3D visualization of MIT imaging with real human brain model established a foundation for the application study of MIT in imaging intracranial hemorrhage.     

A Study on Wall Velocity Distribution Law in Mould for C C Billets

In view of liquid steel flow in mould for C C alloy steel billets,the flow velocityof fluid in the different zones in the vicinity of vertical wall on condition of four hole nozzle hassystematically been measured by Laser Doppler Anemometre(LDA).At the same time,according tothe logarithmic wall law,logarithm ic wall law equations near by differen t wall zones and ex-periemental constan ts have been derived by regression method,The velocity distriution law near bywall in mould is obtained.