摘要:

AbstractThe paper outlines a numerical procedure for the finite element solution of convective diffusion problems with significant convective terms using conventional (not upwinded) Galerkin methods in connection with ‘boundary‐layer type’ elements. The underlying argument in the sequel is that the poor stability properties of conventional Galerkin methods are caused by the insufficient approximation of eigensolutions. These are located at some sections of the boundary and are only present within a generally very thin layer. Consequently, the identification of these layers and the satisfactory approximation of the eigensolutions are necessary and totally sufficient for a satisfactory solution. In the following we intend to present this procedure, its theoretical background and selected numerical re

ISSN:0029-5981    

DOI:10.1002/nme.1620180203

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractIn this paper we discuss and expand the direct‐iterative method proposed originally by Wilson.1First we introduce several simple numerical examples to illustrate the basic idea of this method before we proceed to prove the convergence of the direct‐iterative method. We then discuss the methods for selecting the transformative matrix (Q) to be used in transforming an ill‐conditioned matrix into a well‐conditioned matrix in the direct‐iterative method. There are two methods used to choose the matrixQ, namely the rigid body movement method and the imaginary element method. From examples 1‐3 we can see that the imaginary element mesh is optional, and the finite element mesh is not necessary. The imaginary element method is a generalization of the mesh refinement method development in Reference 3. Because instead of local rotation angle we only choose displacements of nodes to represent rigid body movement, the rigid body movement method is an improvement of the method in Reference 2. The advantage of these two methods is that, in order to obtain well‐conditioned matrices, only a few changes in the stiffness matrices are required even with general ill‐conditioned stiffness matrices, and then convergency is achieved rapidly under SOR iteration. Finally, the examples for computing each type of the ill‐conditioned matrix in three‐dimensional finite element analysis are presented to demonstrate the effectiveness of the direct‐iterative method in solving the lar

ISSN:0029-5981    

DOI:10.1002/nme.1620180204

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA clearer insight into the ‘shear locking’ phenomenon, which appears in the development ofC0continuous element using shear‐flexible or penalty type formulations, is obtained by a careful study of the Timoshenko beam element. When a penalty type argument is used to degenerate thick elements to thin elements, the various approximations of the shear related energy terms act as different types of constraints and, depending on the formulation, two types of constraints which are classified as true or spurious may emerge. The spurious constraints, where they exist, are responsible for the ‘shear locking’ phenomenon, and its manifestation and elimination is demonstrated in a very simple example. The source of difficulty is shown to be the mathematical operations involved in the various shape function definitions and subsequent integration of functionals. It is seen that formulations that ensure only true constraints in the extreme penalty limit cases display far superior performance in the thick element situation as well, and thus guidelines for the development of efficient elements are drawn. A similar type of behaviour is observed in a shallow curved beam element and here ‘inplane locking’ can be eliminated by selective integration to obtain an improved curved beam element. However, ‘inplane locking’ does not cause a spurious constraint as the error quickly vanishes with the reduction of element size for a reasonable radius of curvature conforming with sha

ISSN:0029-5981    

DOI:10.1002/nme.1620180205

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA mixed variational principle for the limit analysis of rigid‐perfectly plastic continua is discussed, in which the nonlinear yield condition and the associated flow rule appear through a suitably defined ‘penalty’ function. A mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised, affording a complete (static and kinematic) solution. Several results are presented in both structural and soil mechanics, compared with previously available (exact and numerical) solu

ISSN:0029-5981    

DOI:10.1002/nme.1620180206

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe solution of elastostatic bodies in frictionless contact is obtained by an automated direct method which exploits the theory of linear elasticity and circumvents the need for the inclusion of artificial interface elements, mathematical programming techniques or computation of contact pressure. The method is simple and economical to use and can be easily appended to existing numerical schemes such as the finite element method. The formulation and numerical algorithm are presented for body combinations which are independent of relative tangential displacements along the contact surface. The method is illustrated through an elementary example amenable to hand calculation. Numerical results for more realistic problems are given and compared to known solutions. It is concluded that the method provides a powerful means for both the analysis and design of contacting bodies when used in conjunction with a finite element computer program.

ISSN:0029-5981    

DOI:10.1002/nme.1620180207

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA hybrid stress finite element procedure for the solution of bending stress intensity factors of a plate with a through‐the‐thickness crack is presented. Reissner's sixth‐order plate theory including the effects of transverse shear deformation is used. The dominant singular crack tip stress field is embedded in the crack tip singular elements and only regular polynomial functions are assumed in the far field elements. The stress intensity factors can be calculated directly from the crack tip singular stress solution functions. The effects of the plate thickness, the ratio between the crack size and the inplane dimension of the plate, and the singular element size on the stress intensity factor solution are investigated.The effects of the explicit enforcement of traction‐free conditions along crack surfaces, which are the natural boundary conditions in the present hybrid stress finite element model, are also investigated. The numerical results of bending of a plate with a straight central crack compare favourably with analytical solutions. It is also found that the explicit enforcement of traction‐free conditions along crack surfaces is mandatory to obtain meaningful results for the Mode I type of bending stress intensi

ISSN:0029-5981    

DOI:10.1002/nme.1620180208

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractTo reduce the manual work involved in the application of the FEM in practice, preprocessors can be applied for the construction of network structures, which are complicated in generation strategy and do not form any optimum discrete structure. The time necessary for generation can be minimized even more by the application of only one element type within the whole network structure. A technique for the automatic generation of 3D‐network structures with tetrahedron elements is presented in this paper. In this proposed technique, the nodal points of the network structure must be defined manually before the generation procedure, since a random positioning of points is usually undesirable for FEM calculation. The nodal points are connected by a program to a network structure consisting of tetrahedron elements which have optimum form for the numerical computation of the element matrices. After the generation, the element sides forming any part of the boundary surface of the network structure can be automatically identified. If necessary, the network structure can be automatically refine

ISSN:0029-5981    

DOI:10.1002/nme.1620180209

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA finite element stress analysis capability for plane elasticity problems, employing the principle of stationary complementary energy, is developed. Two models are investigated. The first is a 24 d.o.f. rectangular finite element. The second model consists of an 18 d.o.f. triangular element. In order to allow for self‐equilibrating stresses which are continuous within the element, the well‐known Airy stress function ø is used. The function ø is represented by means of quintic Hermitian polynomials within the finite element. The values of the ø function and its derivatives up to order two are used as nodal parameters. For matching the stress function with the prescribed boundary tractions, additional equations are developed considering the force and moment equilibrium equations on the boundary consistent with the assumed stress function. These additional boundary equations are incorporated into the system equations using the Lagrangian multiplier technique. Excellent results are obtained for linear elastic problems even with coarse finite element discretization. Some examples of plane elasticity problems are solved and results co

ISSN:0029-5981    

DOI:10.1002/nme.1620180210

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620180211

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractQuarter‐point elements are used very frequently for fracture mechanics computations, because the quarter‐point technique yields the required singular interpolation without any modification to existing software. This advantage is particularly significant for three‐dimensional stress intensity factor computations because of the difficulty of implementing other techniques. However, in practical 3‐D applications, the crack front is usually curved, and this note proves that a crack front distortion leads to a negative Jacobian in the region surrounding the crack front. The numerical difficulties to be expected depend on the aspect ratio of the e

ISSN:0029-5981    

DOI:10.1002/nme.1620180212

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY