摘要:

AbstractA basic problem in the linear elastic analysis is that of finding the vectors of stresses and strains, given a finite element model of a structure and a set of external loads. One purpose of this paper is to show that the problem is a special case of the minimum norm problem for underdetermined systems of linear equations. In this regard, the three conventional structural analysis approaches, i.e. the displacement method, the natural factor formulation and the force method, are unified and interpreted in the framework of the minimum norm problem, which is divided into two approaches—the primal formulation and the dual formulation. Numerical comparisons of several computational procedures capable of solving the minimum norm problem are given from computational efficiency and accuracy points of view. Included in the comparisons are the three conventional structural analysis approaches mentioned above, and several alternative approache

ISSN:0029-5981    

DOI:10.1002/nme.1620200602

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA set of path independent integrals is constructed for the calculation of the generalized stress intensity factors occurring in elastic plates having sharp re‐entrant corners or notches with stress‐free faces and subjected to Mode I, II or III type loading. The Mode I integral is then demonstrated to enjoy a reasonable degree of numerical path independence in a finite element analysis of a test problem having an exact solution. Finally, this integral is used on the same problem in conjunction with a regularizing, finite element, procedure or superposition method. The results indicate that sufficiently accurate estimates of these stress intensity factors for engineering purposes can be achieved with little computational eff

ISSN:0029-5981    

DOI:10.1002/nme.1620200603

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThis paper looks at some well‐known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved. New forms are given of the general three‐parameter method introduced by Zienkiewicz.1Some new one‐step methods are introduced; these are of great practical importance because of the ease with which the size of time step can be ch

ISSN:0029-5981    

DOI:10.1002/nme.1620200604

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA very effective numerical formulation is proposed to solve approximately the problem of steady, fully developed laminar flows of incompressible fluids in straight ducts of arbitrary, simply connected cross‐sections. The method is an application of the discrete singularity technique, with a finite number of singularities located outside the domain concerned. To illustrate the usefulness of the method, some examples of computations are also presente

ISSN:0029-5981    

DOI:10.1002/nme.1620200605

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractIt is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man‐made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained condition

ISSN:0029-5981    

DOI:10.1002/nme.1620200606

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe paper describes an algorithm for generating maximum entropy distributions for probabilistic data. The central moments of the data form constraint equations developed from Jaynes' formalism, which are solved by mathematical programming. Criteria are presented for selecting starting points and scaling parameters, upon which the accuracy and efficiency of the algorithm depends. Results are given of tests in which maximum entropy distributions are generated from the moment information of numerous analytical distributions. They show that four moments are generally required to produce good agreement and that maximum entropy distributions can represent most data populations very well. The notation used in the paper is defined in Appendix I.

ISSN:0029-5981    

DOI:10.1002/nme.1620200607

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed. An implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces. A two‐time level implicit method is used, while Taylor's forward projection method is employed for taking account of the nonlinearities. An iterative method is described which predicts unknown surface conditions. An example is illustrated which is typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitatio

ISSN:0029-5981    

DOI:10.1002/nme.1620200608

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA linear model for the solidification of a dilute binary alloy is presented. In this model the solidus and liquidus curves are linear. As a consequence internal energy depends linearly upon temperature and concentration. The formulation is a generalization of the well‐known enthalpy method to treat a phase change problem involving coupled heat and mass transfer. Both analytic and numerical formulations are given. Results from the latter are presented and compared with an explicit solution of Rubinstein for a Stefan‐like problem posed in a semi‐infinite slab. Some remarks on the behaviour of the explicit solution are

ISSN:0029-5981    

DOI:10.1002/nme.1620200609

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThis is the first in a series of three papers in which we discuss a method for ‘post‐processing’ a finite element solution to obtain high accuracy approximations for displacements, stresses, stress intensity factors, etc. Rather than take the values of these quantities ‘directly’ from the finite element solution, we evaluate certain weighted averages of the solution over the entire region. These yield approximations are of the same order of accuracy as the strain energy. We obtain error estimates, and also present some numerical examples to illustrate the practical effectiveness of the technique. In the third paper of this series we address the matters of adaptive mesh selection anda posteriorierror e

ISSN:0029-5981    

DOI:10.1002/nme.1620200610

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractIn the context of a model problem we describe post‐processing techniques for the calculation of generalized stress intensity factors as well as displacements, stresses, etc., near corner points. We discuss two broad classes of methods, one involving an ‘influence’ function, and the other related to the well‐known energy release principle of fracture mechanics. An error analysis is sketched and two numerical examples are given to illustrate the effectiveness of the tec

ISSN:0029-5981    

DOI:10.1002/nme.1620200611

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY