THE 3-D BOUNDARY ELEMENT METHOD OF ROLLER BEARING BY PLATE ELEMENT ANALOGUE

The mill roller bearing is made up of an internal ring, middlerolls and an external ring, the analysis of which is a multi-bodiescontact problem. In this paper, based on the three-dimensionalelastic contact BEM without friction, and using the structuralcharacteristics of roller bearings, middle rolls are de- scribed byelastic plate units of different shapes, which is placed on theinternal ring.

Development of quadrilateral spline thin plate elements using the B-net method

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Numerical Method Based on Compatible Manifold Element for Thin Plate Bending

The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.

AN EXACT ELEMENT METHOD FOR BENDING OF NONHOMOGENEOUS THIN PLATES

In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.

AN EXACT ELEMENT METHOD FOR THE BENDING OF NONHOMOGENEOUS REISSNER’S PLATE

In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional principle, it can he applied to solve nun-positive and positive definite partial differcntial equations with arbitral varutble coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergcnceof displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well, hour numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.

THE STOCHASTIC BOUNDARY ELEMENT METHOD IN STATISTICAL ANALYSIS OF MODERATELY THICK PLATES

In this paper a stochastic boundary element method (SEEM) is developed to analyze moderately thick plates with random material parameters and random thickness. Based on the Taylor series expansion, the boundary integration equations concerning the mean and deviation of the generalized displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random load, so the mean and covariance matrices of unknown generalized boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of generalized displacements and forces at internal points can also be obtained. A numerical example has been worked out with the method proposed and necessary analysis is made for the results.

RATIONAL FINITE ELEMENT METHOD FOR ELASTIC BENDING OF REISSNER PLATES

In this paper; some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements. And therefore the rational FEM, which is perfect combination of the analytic methods and numeric methods, has been presented. This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures. What's more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.

CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM

On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.

A Comparative Study of Stress Recovery Method and Error Estimation of Plate Bending Problem Using DKMQ Element

Recovery by Equilibrium in Patches (REP) is a recovery method introduced by B. Boroomand. This method is using patch as recovery media as is used by Superconvergent Patch Recovery (SPR) which is well known as a good recovery method. In this research, a numerical study of REP implementation is held to estimate error in finite element analysis using DKMQ element. The numerical study is performed with both uniform and adaptive h-type mesh refinement. The result is compared with three other recovery method, i.e. SPR method, averaging method, and projection method.

AN OPTIMAL V-CYCLE MULTIGRID METHOD FOR CONFORMING AND NONCONFORMING PLATE ELEMENTS

In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.

Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges

The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.

VARIATIONAL PRINCIPLES OF PERFORATED THIN PLATES AND FINITE ELEMENT METHOD FOR BUCKLING AND POST-BUCKLING ANALYSIS

On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated,owing to the multiple connexity of the region.

STOCHASTIC BOUNDARY ELEMENT METHOD FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

In this paper, the reliability of orthotropic plate and beams composite structures, which is under the actions of the stochastic loading and stochastic boundary conditions, have been analyzed by stochastic boundary element method. First, the boundary integral equation of orthotropic plate and beams composite structures is given in this paper, and then based on the stochastic boundary element method, the method for reliability analysis of stochastic structures is establishes and formulas for computation of reliability index of orthotropic plate and beams composite structures are obtained. The computed examples show the efficient of the method used in this paper.

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum

The 6061-T651 aluminium alloy is one of the most common aluminium alloys for marine components and general structures. The stress intensity factor (SIF) is an important parameter for estimating the life of the cracked structure. In this paper, the stress intensity factors of a slant-cracked plate, which is made of 6061-T651 aluminum, have been calculated using extended finite element method (XFEM) and finite element method (FEM) in ABAQUS software and the results were compared with theoretical values. Numerical values obtained from these two methods were close to the theoretical values. In simulations of crack growth at different crack angles, the crack propagation angle values were closer to the theoretical values in XFEM method. Also, the accuracy and validity of fatigue crack growth curve were much closer to the theoretical graph in XFEM than the FEM. Therefore, in this paper the capabilities of XFEM were realized in analyzing issues such as cracks.

Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.

Modified Layer-Removal Method for Measurement of Residual Stress in Pre-stretched Aluminium Alloy Plate

Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus, the studies on machining deformation rules induced by residual stresses largely depend on correctly and efficiently measuring the residual stresses of workpieccs. A modified layer-removal method is proposed to measure residual stress by analysing the characteristics of a traditional, layer-removal method. The coefficients of strain release are then deduced according to the simulation results using the finite element method （FEM）. Moreover, the residual stress in a 7075T651 aluminium alloy plate is measured using the proposed method, and the results are then analyzed and compared with the data obtained by the traditional methods. The analysis indicates that the modified layer-removal method is effective and practical for measuring the residual stress distribution in pre-stretched aluminium alloy plates.

INCOMPATIBLE CURVED QUADRILATERAL PLATE BENDING ELEMENT WITH 12-DEGREES OF FREEDOM

This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle. Using this method, the compatibility conditions between element can be treated very easily, if displacements and stress resultants are continuous at nodes between elements. The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed. Numerical examples are given at the end of this paper, which show the excellent precision and efficiency of the new element.

Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method,the stream surface strip element method,for simulating the three-dimensional deformation of plate and strip rolling process was proposed.The rolling deformation zone was divided into a number of stream surface(curved surface)strip elements along metal flow traces,and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation.The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve,of which the lateral distributions were expressed as the third-power spline function,and the altitudinal distributions were fitted in the quadratic curve.From the flow theory of plastic mechanics,the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed.Compared with the streamline strip element method proposed by the first author of this paper,the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction,and realizes the precise three-dimensional analysis and computation.The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.