A Thermomechanically Consistent Constitutive Model for Finite Elastoplastic Deformation

Based on a thermomechanically consistent mechanical model consisting of springs and plastic dashpots, a plastic constitutive equation for large deformation is derived. Then the incremental form of elastoplastic constitutive equation is developed, which can easily be applied to the finite element analysis and other numerical approaches. The method for the determination of the involved material constants is suggested, which is based on the concept of nonstress configuration proposed by Lee. The necking process of a circular bar subjected to large elastoplastic deformation is simulated and the comparison between the analytical and experimental results is quite satisfactory. The developed model does not use the eoncept of a yield surface, which effectively improves the convergence and computation efficiency.     

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.     

A BOUNDARY ELEMENT METHOD FOR THE NEUMANN PROBLEM OF HELMHOLTZ EQUATION BY USE OF A DOUBLE LAYER POTENTIAL IN R~3

This paper presents a new numerical solution for Neumann problem of Helmholtz equation in R~3. The expression of the solution for this problem is obtained by use of a double layer potential and it leads to a Fredholm boundary integral equation of the first kind. Then, the existence and unicity of the integral equation which is equivalent to the boundary value problem are obtained in a suitable Sobolev space. Finally, a variational form which is equivalent to the integral equation is applied to the construction of a finite element method and the error estimate is given.     

THE THREE-DIMENSIONAL CALCULATING MODEL OF INVERSE PROBLEM IN ECG AND A SPECIAL BOUNDRYVALUE PROBTEM

In this paper, the mathematical model and the three-dimensional finite clement formulation of inverse problem in electrocardiography (ECG) under a general inhomogcneous and anisotropic configuration of the torso conductor is focused on. The following points are especially considered: 1. The mathamatical model is described by a differential equation instead of the Fredholm integral equation. 2. A kind of special boundary value problem is defined as ill-posed boundary value problem. 3. A group of finite element formulation, in which the method that treats anisotropic medium, is built up. 4. The calculating method of ill-posed boundary value problem is discussed.     

A BOUNDARY ELEMENT METHOD FOR SOLVING DIRICHLET PROBLEM OF THE HELMHOLTZ EQUATION IN R~2

This paper presents a boundary element method for solving Dirichlet bou-ndary value problem of the Helmholtz equation in R~2.First,the existence andthe uniqueness of an extended solution for the problem are obtained.Then,thesolution is expressed in terms of simple layer potentials,and this expression,which is suitable to the interior as well as the exterior problem,leads to aboundary integral equation of the first kind.Finally,a finite element approachis applied to solve a variational form which is equivalent to the boundaryintegral equation.     

INCREMENTAL FORM OF ENDOCHRONIC CONSTITUTIVE EQUATION AND ITS APPLICATIONS

An incremental formula is derived from integral form of endochronic plastic constitutive equation, which greatly reduces the error caused by the one which was directly obtained from differential form of the constitutive equation. An elastoplastic matrix is then proposed, based on which a stiffness finite element approach is developed. The analysis of the residual stress at the inner skin of an autofrettaged thick-walled cylinder agrees well with the experimental result. The calculated stress-strain fields of a double - edge - notched plate subjected to cyclic zero-to-tension loading are also quite reasonable. The numerical process is steady and quickly convergent, and the developed approach can easily be applied to practical engineering analysis.     

Non-linear finite element analysis based on the spatial catenary cables

According to the elastic catenary theory,this paper derives the spatial catenary cable element from the exact analytical expression,which is used for finite element analysis of the structure.It deduces the precise expression of two-node cable element tangent stiffness matrix and the tension of cable end.The equivalent node load of cable element is expressed by the total load algorithm,and the non-linear equation is solved by double Newdon-rapson method.The proposed non-linear semi-analytical finite element method based on spatial catenary cable element can take full account of the impact of non-linear geometry.The initial configuration and the internal forces on any directional spatial loads can be solved.The example shows that the calculation method is accurate and effective.     

The Initial Value Problem of Nonlinear Evolution Equation

This paper discusses the initial value problem of the nonlinear evolution equation. The uniqueness and stability of the solutions for the problem are proved. It is also obtained that the solution of the problem blows up in a finite time.     

Galerkin Boundary Element Method for Direct Boundary Integral Eqution for Dirichlet Problem of 2-D Laplace Eqation

The direct boundary integral equation of two-dimensional Laplace equation for Dirichlet problem is(con-sidered).It is deduced by Green's formula and the fundamental solution.The most-used numerical method for solving(direct) boundary integral equation is collocation method,and seldom have been used the Galerkin scheme in this case.The direct boundary integral eqution is changed into the variational eqution.Using linear element,it is solved by Galerkin boundary method.In the variational eqution double integrations shall be carried out.The paper presents the analytical formula to calculate the inner integration and the Gaussian quadrature is used for the outer integration. The numerical experimentation proved thefaesibility and the efficiency.     

Influence of Pile-soil Dynamic Interaction for the Structure Elastio-plastic Deformation

It is necessary to analysis the structure elastoplastic deformation subjected to rare seismic action and the present methods are mostly based on the rigid foundation assumption, which give rise to the method considering the soilstructure dynamic interaction. Adopting the plan pile-soil-structure elastoplastic finite element models, the influence of soil- structure interaction for the structure elastoplastic deformation in the horizontal earthquake has been analyzed. Through analysing we found, considering interaction, the muhilayer-frame elastoplastic displacement was discounted, elastic displacement was minished in the weakness layer and the possibility of break was reduced. The elastoplastic deformation computed by the Code is conservative.     

Mixed Finite Element Formulation of the Linear Biphasic Theory for Soft Tissues

The behavior of soft tissues of human musculoskeletal system can be describedwith the biphasic model based on a continuum theory of mktures. This paper. using Galerkin weight-ed residual method.obtains a mixed finite element formulation for the linear biphasic model of smalldeformation. and. in turn. gives out the iterative scheme solving the system equations. The results ofnumerical analysis for the constrained compression problem are consistent with those obtained bytheory. which illustrates the correctnas and feasibility of the derived mixed finite element formula-tion. concludingly. this formulation provides an effective means of numerical analysis for the motfonmechanism of human articulating joints.     

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.     

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.     

The Non-Linear Finite Element Analysis of Cable Structures Based on Four-Node Isoparametric Curved Element

In this paper,based on the geometric nonlinear behavior of cable structures,a finite element method with four-node isoparametric element was presented,the third order polynomial was used as displacement functions and initial curve of the element.By means of the principle of virtual work and the updated Lagrangian method,the authors derived the finite element equations,and solved them by Newton-Raphson method.The proposed model leads to high precision and can meet the engineering requirements.The model presented in this paper can be applied in the analysis of long-span tension structures,such as cable structures,cable domes and so forth.     

对偶性与特大增量步算法在复杂平面框架中的应用

特大增量步算法（LIM）是一种基于力法和广义逆矩阵理论的迭代算法,在简单桁架和刚架非线性初步应用中,达到相同计算精度下有同等甚至超过位移有限元的计算效率。针对工程中的复杂杆系结构,利用平衡与协调的对偶性,探讨LIM在复杂平面框架结构中的应用,建立了平面框架结构的LIM基本方程,提出了针对典型支座约束以及组合结点的处理方法。该处理方法的线弹性问题算例表明,与位移有限元相比具有至少同等的精度和相当的计算效率。在支座本身不考虑塑性的情况下,该处理方法同样适用于弹塑性问题,为LIM在复杂杆系结构的弹塑性分析中奠定了基础。     

About the Synthesis Method of Planar Multilink Mechanisms Based on Genetic Algorithm

This paper discusses the method of synthesizing planar multilink mechanisms based on GA. The pivotal technology is coding, creating population, account fitness, genetic operation and defining population size. This method does not require initial mechanisms and can search for plural appropriate mechanisms simultaneously. It is efficient about the non-linear problem. As an example, configuration of 4-bar planar mechanisms is decided in a practical application. It can be used the synthesis of 6-bar or more bar planar mechanisms as well.     

Nonlinear Stiffness Matrices of Plane Beam Element Including Initial Stress and Strain Item

There were often happened cases for beam elements with initial stress or initial strain while the geometrically nonlinear analysis was performed for the plane structure. The deduction of stiffness matrices was awfully difficult because the nonlinear stiffness matrices included node displacement vectors and extensive matrix operations. Based on the nonlinear geometric equation of plane beam element and general elastic relationship of stress-strain including initial stress and initial strain,the tangent stiffness matrix was derived. All explicit formula of stiffness matrices including initial stress and strain item have been developed by use of the MATLAB Mathematical Tools. The results are of great significance to the nonlinear finite element programming for plane beam elements.     

SCALAR LOCALLY UNIQUE SOLUTIONS OF VECTOR VARIATIONAL INEQUALITY

This paper first deds with the relations of solutions of vector variational inequality and vector optimization problem. Then, K-T Necessary and sufficient conditions are proved. Finally, scalar locally unique solution is introduced. Under certain conditions,the exitence of scalar locally unique solution of vector variational inequality is proved.