L~∞-Error Estimate of a Nonconfoming Rectangular Plate Element

In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.

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.

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.

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.

Multiresolution Finite Element Method Based on a New Locking-Free Rectangular Mindlin Plate Element

A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

EQUIVALENCE BETWEEN TONG HYBRID PLATE ELEMENT WITH CONSTANT MOMENTS AND NONCONFORMING MORLEY PLATE ELEMENT

在这篇论文中我们证明了董平常力矩杂交板元与非协调Ｍｏｒｌｅｙ板元具有相同的单元刚度矩阵，因此这两个板元是等价的。

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.

On Choices of Stress Modes for Lower Order Quadrilateral Reissner-Mindlin Plate Elements

A kind of stabilized mixed/hybrid scheme for Reissner-Mindlin plates is proposed with conforming isoparametric bilinear interpolations of de?ection/rotations. The choice of shear stress modes is discussed. It is shown by numerical experiments that fulfilling an energy orthogonal condition for stress approximations is crucial to avoiding “shear locking”.

A Generalized Point Conforming Rectangular Plate Element

A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element node, but also satisfy the generalized continuity at the middle point of each element boundary, where the generalized conforming condition is to make the non-conforming residual to be minimum. Numerical results show that the proposed element is more accurate than the ordinary 4-node non-conforming rectangular plate element (ACM element).

Finding an optimization of the plate element of Egyptian research reactor using genetic algorithm

The second Egyptian research reactor ET-RR-2 went critical on the 27th of November 1997.The National Center of Nuclear Safety and Radiation Control (NCNSRC) has the responsibility of the evaluation and assessment of the safety of this reactor.The purpose of this paper is to present an approach to optimization of the fuel element plate. For an efficient search through the solution space we use a multi objective genetic algorithm which allows us to identify a set of Pareto optimal solutions providing the decision maker with the complete spectrum of optimal solutions with respect to the various targets.The aim of this paper is to propose a new approach for optimizing the fuel element plate in the reactor.The fuel element plate is designed with a view to improve reliability and lifetime and it is one of the most important elements during the shut down.In this present paper,we present a conceptual design approach for fuel element plate,in conjunction with a genetic algorithm to obtain a fuel plate that maximizes a fitness value to optimize the safety design of the fuel plate.

SIMULATION OF FABRIC DRAPE USING A THIN PLATE ELEMENT WITH FINITE ROTATION

The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

In the present work,a new class of finite elements(FEs)for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed.By making use of node-by-node variable plate theory assumptions,the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy,in a global/local sense.As a consequence,the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states,and their electro-mechanical coupling present a complex distribution.The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements,because the plate structural theory varies within the finite element itself.In other words,the structural theory of the plate element is a property of the FE node in this present approach,and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes.The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei,which are invariants of the theory approximation order and the modeling technique(Equivalent-Single-Layer,Layer-Wise).In this work,the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories.Several numerical investigations,such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load,boundary conditions,and piezoelectric material polarizations,are carried out to validate and demonstrate the accuracy and efficiency of the present plate element,including comparison with various closed-form and FE solutions from the literature.

SUBSTRUCTURE PRECONDITIONERS FOR NONCONFORMING PLATE ELEMENTS

In this paper, we consider the problem of solving finite element equations of biharmonic Dirichlet problems. We divide the given domain into non-overlapping subdomains, construct a preconditioner for Morley element by substructuring on the basis of a function decomposition for discrete biharmonic functions. The function decomposition is introduced by partitioning these finite element functions into the low and high frequency components through the intergrid transfer operators between coarse mesh and fine mesh, and the conforming interpolation operators. The method leads to a preconditioned system with the condition number bounded by C(1 + log(2) H/h) in the case with interior cross points, and by C in the case without interior cross points, where H is the subdomain size and h is the mesh size. These techniques are applicable to other nonconforming elements and are well suited to a parallel computation.

Adaptive Lagrange finite element methods for high precision vibrations and piezoelectric acoustic wave computations in SMT structures and plates with nano interfaces

This paper discusses the validity of (adaptive) Lagrange generalized plain finite element method (FEM) and plate element method for accurate analysis of acoustic waves in multi-layered piezoelectric structures with tiny interfaces between metal electrodes and surface mounted piezoelectric substrates. We have come to conclusion that the quantitative relationships between the acoustic and electric fields in a piezoelectric structure can be accurately determined through the proposed finite element methods. The higher-order Lagrange FEM proposed for dynamic piezoelectric computation is proved to be very accurate (prescribed relative error 0.02% - 0.04% ) and a great improvement in convergence accuracy over the higher order Mindlin plate element method for piezoelectric structural analysis due to the assumptions and corrections in the plate theories.The converged lagrange finite element methods are compared with the plate element methods and the computedresults are in good agreement with available exact and experimental data. The adaptive Lagrange finite elementmethods and a new FEA computer program developed for macro- and micro-scale analyses are reviewed, and recently extended with great potential to high-precision nano-scale analysis in this paper and the similarities between piezoelectric and seismic wave propagations in layered structures and plates are stressed.

Two-Dimensional Large Deformation Finite Element Analysisfor the Pulling-up of Plate Anchor

Based on mesh regeneration and stress interpolation from an old mesh to a new one, a large deformation finite element model is developed for the study of the behaviour of circular plate anchors subjected to uplift loading. For the deterruination of the distributions of stress components across a clay foundation, the Recovery by Equilibrium in Patches is extended to plastic analyses. ABAQUS, a commercial finite element package, is customized and linked into our program so as to keep automatic and efficient running of large deformation calculation. The quality of stress interpolation is testified by evaluations of Tresca stress and nodal reaction forces. The complete pulling-up processes of plate anchors buried in homogeneous clay arc simulated, and typical pulling force-displacement responses of a deep anchor and a shallow anchor are compared. Different from the results of previous studies, large deformation analysis is of the capability of estimating the breakaway between the anchor bottom and soils. For deep anchors, the variation of mobilized uplift resistance with anchor settlement is composed of three stages, and the initial buried depths of anchors affect the separation embedment slightly. The uplift bearing capacity of deep anchors is usually higher than that of shallow anchors.

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.

STABILIZED FINITE ELEMENT METHODS FOR THE REISSNER-MINDLIN PLATE

A new stabilized finite element method which is different from Hughes and Franco’s (1988) is presented for the Reissner-Mindlin plate model. The least square mesh-dependent residual form of the shear constitute equation is added to the Partial Projection scheme to enhance the stability. Using piecewise polynomials of order k≥1 for the rotations, of order k+1 for the displacement and of order k-1 for the shear, the kth order error-estimates are obtained. Besides, our computing scheme can be also applied to some lower order elements. All error-estimates are obtained independent of the plate thickness, and the stability parameter is an arbitrary positive constant.

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.

TRIANGULAR ELEMENTS FOR REISSNER-MINDLIN PLATE

A general method to construct locking free Reissner-Mindlin plate elements is presented. According to this method the shear strain is replaced by its proper interpolation polynomial, which corresponds to the Kirchoff conditions at the interpolation points as the thickness of plate tends to zero, so the element is locking free. We construct two triangular elements by this method - a 3-node element and a 6-node element. The numerical results are provided.