A NEW QUADRILATERAL NONCONFORMING MODEL AND ITS CONVERGENCE

This paper presents a new quadrilateral nonconforming finite element.We deal with itsconvergence by using generalized patch test.The error on stresses and displacements areobtained and numerical computations for plane elastic problems are given.     

A STUDY ON YIELD AND FLOW OF ORTHOTROPIC MATERIALS

On the assumption that the yield criterion of orthotropic materials is isomorphic withHuber-Mises criterion of isotropic materials,we put forward a dimensionless stress yieldcriterion,and obtained the associated plastic flow law.Using experimental stress-straincurves in various simple stress states,generalized effective stress-strain formulae may bederived correspondingly in various forms.     

A CLASS OF WILSON ARBITRARY QUADRILATERAL ELEMENTS FOR AN AXISYMMETRIC PROBLEM

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A STUDY ON DEFORMATION CHARACTERISTIC OF ULTRA HIGH STRENGTH STEEL AND ITS FRACTURE

A new shape on the load and elongation curve of ultra highstrength structural steel in tension is measured by means of theadvanced physical methods.A method of calculating true stress-true strain is found in accordance with the whole load-elongationcurve.The calculation results show that during the period of de-formation,whether prior to or after the maximum load,all arestaged power hardening.The method of calculating hardening index is finally studied for discussion.     

A COMPARATIVE STUDY OF THE OPENING AND CLOSING PROCESS OF TWO TYPES OF MECHANICAL HEART VALVES USING ALE FINITE ELEMENT METHOD

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ON THE COMPACTNESS OF QUASI-CONFORMING ELEMENT SPACES AND THE CONVERGENCE OF QUASI-CONFORMING ELEMENT METHOD

In this paper, the compactness of quasi-conforming element spaces and theconvergence of quasi-conforming element method are discussed The well-known Rellichcompactness theorem is generalized to the sequences of quasi-conforming element spaceswith certain properties. and the generalized Poincare inequality.The generalized Friedrichsinequality and the generalized inequality of Poincare-Friedrichs are proved true for them.The error estimates are also given. It is shown that the quasi-conforming element method isconvergent if the quasi-conforming element spaces have the approximability and the strongcontinuity, and satisfy the rank condition of element and pass the test IPT As practicalexamples, 6-paramenter. 9-paramenter, 12-paramenter, 15-parameter, 18-parameter and21-paramenter quasi-conforming elements are shown to be convergent, and theirL~(2‘2)(Ω)-errors are O(h_τ)、 O(h_τ)、O(h_τ~2)、O(h_τ~2), O(h_τ~3), and O(h_τ~4) respectively.     

MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

ON SOLVING HIGH-ORDER SOLUTIONS OF CHIEN’S PERTURBATION METHOD TO STUDY CONVERGENCE BY COMPUTER

In this paper, we have obtained the analytical formula of arbitrary n-th order perturbation solution which perturbation parameter is central deflection for circular thin plate under a concentrated load by means of its integral equation. All unkown constants of every perturbation solution can be determined by computer. Hence higher order perturbation solution is obtained. Based on the solution of higher order perturbation, asymptotical property and suitable interval of Chien’s perturbation method are also discussed.     

STUDY ON TENSILE FAILURE MECHANISM AND HYBRID EFFECT OF INTRAPLY HYBRID COMPOSITES

The random critical-core model is adapted to investigate the tensile failure mech-anism and hybrid effect of unidirectionally arrayed hybrid composites with alternating low andhigh elongation fibers.By utilizing the model in conjunction with the results of the stress con-centration analysis in which the interfacial damage between fiber and matrix is considered,amicroscopic statistical analysis of both the first failure and ultimate failure of hybrids is per-formed.The variations of the first failure strain,the ultimate failure strain and the hybrid effectas the interfacial shear strength are obtained quantitatively.The concept of the hybrid effect forstrains has been clarified.The present results are compared with available experiment data anda reasonable agreement is found between the analytical predictions and the experimental results.     

ON THE CONVERGENCE OF ELASTOPLASTIC BOUNDARY ELEMENT ANALYSIS

Iterative process is a main componertt of boundary element method in plasticity. In this paper, the convergence of elastoplastic boundary element analysis has been discussed in detail and studied theoretically.     

On the error estimate of h-convergence in quadrilateral elements

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A 17-node quadrilateral spline finite element using the triangular area coordinates

Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.     

计算叶片力学特性的三维8节点非协调有限单元法

针对叶片结构几何形状复杂的特点，建立了能进行叶片力学特性分析的三维8节点非协调有限单元模型。该模型采用了几何非线性和线弹性模式，来考虑叶片径向刚度远大于弯曲刚度而引起的在不同转速下初应力对叶片的作用，能够正确反映叶片的弯曲和扭转耦合振动模态、叶片组的切向和轴向振动模态以及它的应力状态。根据质量等效和力等效的原理，导出了在非协调单元中计算单元变形能时，记入附加的内部自由度，而计算单元的动能、体积力、表面力、以及阻尼力所做的虚功时，不记入附加的内部自由度，这是不同于目前一些文献中的提法。最后，通过实例计算验证了该模型的正确性。     

非协调四结点平面等参位移元新列式方法

本文导出一种等参协调元位移函数的新的表示方法,在此基础上建立起了构造等参非协调元的新方法。作为实例,构造出两个可以给出单刚显式的四结点平面非协调新单元。     

Introducing new cracked finite elements and a method for SIF calculation of cracks

Two different types of 8-node cracked quadrilateral finite element are presented for fracture applications. The first element contains a central crack and the other one includes an edge crack. The introduced elements are applicable in 2D problems. The crack is not physically modeled within the element, but instead, its effects on the stiffness matrix are taken into account by utilizing linear fracture mechanics laws. Furthermore, a simple and practical procedure is proposed for calculation of stress intensity factor (SIF) by employing proposed cracked elements. Several numerical examples are presented to evaluate the capabilities of the proposed elements and procedure.     

An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks

The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors (SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole (a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.     

一个不闭锁和抗畸变的四边形厚板元

构造一个彻底消除剪切闭锁现象并且对网格畸变不敏感的四边形厚薄板通用单元RPAQ。在方法上有三个特点：第一,在厚板挠度和转角的试函数中,采用了合理匹配方案,从而在源头上彻底消除了剪切闭锁现象;第二,采用四边形面积坐标,以代替通常的等参坐标,从而使网格畸变时仍然保持高精度;第三,采用广义协调元做法,使协调条件的采用灵活多样,并保证单元的收敛性。进行了一系列数值例题测试,表明单元RPAQ能自动消除闭锁现象,在由薄板到厚板的不同情况下,在各种网格畸变的情况下,都能体现出良好的精度和数值稳定性。     

A cubic quadrilateral spline element with concave shapes

Basic requirement for applying isoparametric element is that the element has to be convex and no violent distortion is allowed. In this paper, a cubic quadrilateral spline element with 12 nodes has been developed using the triangular area coordinates and the B-net method, which can exactly model the cubic field for quadrilateral element with both convex and concave shapes. Neither mapping nor coordinate transformation is required and the spline element can obtain high accuracy solutions and insensitive to mesh distortions.     

带旋转自由度C^0类任意四边形板（壳）单元

基于Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｉｌｉｎ板弯曲理论和Ｖｏｎ－Ｋａｒｍａｎ大挠度理论,采用单元域内和边界位移插值一致性的概念,将四节点等参弯曲单元与Ａｌｌｍａｎ膜变形二次插值模式相结合,对层合板壳的大挠度分析提供了一种实用的带旋转自由度的四节点Ｃ＾０类板单元。大量算例表明：该单元对板壳结构的线性强度、稳定性和后屈曲分析都表现出良好的收敛性和足够的工程精度。     

A class of Wilson arbitrary quadrilateral elements for an axisymmetric problem

A class of modified Wilson arbitrary quadrilateral nonconforming elements for an axisymmetric problem is proposed. Their convergence is proven by means of the strong patch test. The structure of this finite element class is investigated. Thus a general method of axisymmetric nonconforming elements with convergence properties is presented. Project supported by the Foundation of the Chinese Ministry of Machine-Building Industry