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  • AERODYNAMICS  (2,111)
  • Engineering
  • 1975-1979  (3,056)
  • 1925-1929  (1)
  • 1
    Electronic Resource
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    Masthead (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090101
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  • 2
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    A mixed finite element method for bending of plates (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 1-15 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple mixed finite element method is developed. The finite element is a rectangular triangle and rectangle. In the element the deflections are assumed to be simple four-element polynomials, bending moments, Mx and My with a partially linear distribution, and a constant, Mxy, expressed in terms of the node deflections. The element matrix is of the order of 8 × 8. It is derived in a common engineering way. The unknowns are the deflections at the nodes and mid-diagonal, the two moments at the end of the diagonal and the two moments on the cathetus. The results obtained by this method show good convergence and an improvement in the accuracy of the moments as well as in the deflections, compared with results obtained by similar methods, such as those of Herrmann.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090102
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  • 3
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    Finite element buckling analysis of homogeneous and sandwich plates (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 39-50 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element buckling analyses of plates are performed by means of quardrilateral elements having 12 degrees-of-freedom. It is found that if the plate is capable of appreciable transverse shear deformation, initial-stress stiffness matrices that represent the lateral dispalcement by cubic polynomials do not yield convergence to correct results. An initial-stress stiffness that works satisfactorily for both homogeneous and sandwich plates is formulated. A Fortran listing of the associated subroutine is provided.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090104
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  • 4
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    Finite difference analysis for laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 17-38 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of a finite difference analysis are presented for the problem of incompressible laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers, the boundary conditions of one wall being isothermal and the other wall adiabatic. This corresponds to the fundamental solution of the third kind according to the four fundamental solutions classified by Reynolds, Lundberg and McCuen1.Firstly, the hydrodynamic entry length problem, based on the boundary layer simplifications of the Navier-Stokes equations, was solved by means of an extension of the linearized finite difference scheme used previously by Bodia and Osterle2 to solve a similar problem between parallel plates. The energy equation is then solved, using the velocity profiles previously obtained, by means of an implicit finite difference technique.The accuracy of the numerical solution was checked by comparing results for the annulus of radius ratio 0.25 with the avaiable solution of Shumway and McEligot3.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090103
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  • 5
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    Effect of shear deformations and rotary inertia on optimum beam frequencies (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 51-62 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Accounting for shear deformations and rotary inertia effects, necessary condition for optimum fundamental frequency of a vibrating beam of constant volume and with a given distribution of non-structural mass, is obtained through the calculus of variations. Minimum cross-section of the beam is controlled by the introduction of an inequality constraint. A finite element displacement formulation is then used in an iterativve manner to arrive at the optimum fundamental frequency and the corresponding material distribution for the discretized beam models with various boundary conditions. A comparison is then made with the corresponding results of an Euler beam.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090105
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  • 6
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    Cubic spline Galerkin approximations to parabolic systems with coupled non-linear boundary conditionsThis work was supported by the Rockwell International IR and D Interdivisional Technology Program under the sponsorship of the Mathematics and Statistics Technological Panel. (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 63-71 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a practical implementation of the Galerkin finite element procedure for solving systems of parabolic partial differential equations with non-linear boundary conditions. This technique consists of finding an approximation in the form of a finite sum of cubic B-splines, which yield high-order accurate results, and consequently, solutions can be developed with remarkable precision and speed up to the steady state region where conventional finite difference methods often fail. In addition, the choice of mesh width and nodal spacing can be automatically determined for a predictor-corrector routine, thereby relieving the engineer of a great deal of ‘guess work’ that is normally characteristic of solving such problems.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090106
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  • 7
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    On computations involving stiffness matrices stored in rectangular form (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 250-252 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090120
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  • 8
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    A note on the cylindrical shell finite element (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 245-250 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090119
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  • 9
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    The method of moments and its optimization (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 337-351 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of moments is a semidiscrete numerical method for solving partial differential equations. The method approximates the solution of a partial differential equation by a finite sum of products of two functions. One function in the product is an unknown function of a single variable and the other function (moment function) is a prescribed function in the remaining variables. Using variational technique we obtain a finite system of boundary value problems of ordinary differential equations for the unknown functions.The main goal of this paper is the study of the theoretical background and numerical effectiveness of the method of moments for solving linear partial differential equations on rectangular-like domains.The mathematical formulation of the method together with error estimates and the theory of optimal moment functions are given. If for the one-dimensional moment functions piecewise polynomials of degree K are used then finite element type error bounds are obtained for the approximate solution in two dimensions.We also consider the numerical implementation of the method through the factorization method and efficient initial value methods. Several numerical examples showing the efficiency of the method are presented.
    Additional Material: 5 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620090206
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  • 10
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    An iterative improvement for non-conforming bending elementsCrown copyright. Any views expressed in this article are not necessarily those of the Department of the Environment. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged. This is the first publication of this article but since the author is a British Civil Servant his work is covered by Crown copyright. Reproduced by permission of Her Britannic Majesty's Stationery Office. (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 641-648 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is described whereby the formulation for non-conforming bending elements includes the work dissipated across the inter-element boundaries. For the examples considered, this correction is shown to lead to a significant improvement in accuracy at little extra cost. Since the solution procedure is based on an iterative technique, the method would be particularly suitable if applied to non-linear problems.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090311
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  • 11
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    A comparison of time marching schemes for the transient heat conduction equation (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 679-689 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the phenomenon of ‘noise’ which is common in most time-dependent problems. The emphasis is on the achievable accuracy that is obtained with various time-stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank-Nicolson scheme with a simple averaging process is superior to the other methods investigated.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090314
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  • 12
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    Solution of stiff boundary value problems by orthogonal collocation (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 691-699 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The utility of the method of orthogonal collocation for solving stiff boundary value problems is investigated. To this end, the method is applied to a number of very stiff problems from the engineering and applied mathematics literature. The examples include both linear and non-linear problems defined on both finite and infinite intervals, a singular perturbation problem, and an inherently unstable problem. The examples demonstrate the usefulness of the method for a wide variety of stiff problems, as well as some of its limitations.
    Additional Material: 6 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620090315
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  • 13
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    Optimum design of continuous thin-walled beams (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 711-720 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090317
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  • 14
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    Difference operator for variable stiffness plates (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 701-709 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A symmetric central finite difference operator is derived for the small deflection analysis of transversely loaded, ‘thin’, elastic plates, whose stiffnesses vary as functions of the in-plane co-ordinates. The operator is written here in Cartesian co-ordinates for a square mesh, but the same technique can also be used to construct an operator for a rectangular mesh.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090316
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  • 15
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    Crack tip finite elements are unnecessaryOne of the journal editors and the referees of this paper had differing views on the title of this paper. The authors have left it in its original form to sitmulate discussion. (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 495-507 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090302
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  • 16
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    Optimal frequency-weight computations for a disc (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 509-533 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the computational aspects of an earlier analytical study1,2 of the problem of maximizing a linear combination of the natural frequencies of vibration of a turbine disc idealization subject to weight and fabrication constraints. The problem was formulated as an optimal control problem and solutions to the adjoint equations of the Pontryagin formalism obtained using perturbation techniques. These techniques transformed the problem to a non-linear program. This paper gives detailed computational solutions to the non-linear program which is characterized by pockets of relative optima. In addition, the dual problem of minimizing the weight subject to a frequency constraint is considered within the optimal control framework. The duality results are confirmed computationally for the two non-linear programs.A description of some practical procedures for improving the convergence characteristics of these highly non-linear programs is included.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090303
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  • 17
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    Non-linear dynamic analysis of axisymmetric shells (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 535-550 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Incremental equations of motion are derived from a Lagrangian variational formulation for the large displacement elastic-plastic and elastic-viscoplastic dynamic analysis of deformable bodies. The material constitutive behaviour is described in terms of the symmetric Piola-Kirchhoff stress and Lagrangian strain tensors. Degenerate isoparametric elements, permitting relaxation of the Kirchhoff-Love hypothesis, are used in a finite element formulation specialized for the analysis of shells of revolution subjected to axisymmetric loading. The linearized incremental equations of motion are solved using direct integration procedures, with added accuracy obtained from application of equilibrium correction at each step. The effectiveness of the numerical techniques is illustrated by the dynamic response analyses carried out on a shallow spherical cap subjected to uniform external step pressure loadings.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090304
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  • 18
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    A finite element method for the general solution of ordinary differential equations (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 551-561 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method is developed by which it is possible to obtain the general solution of an ordinary differential equation directly. The procedure consists of approximating the differential equation with a rectangular matrix equation and of solving the latter equation by using generalized matrix inversion. It is shown in the paper that the homogeneous and inhomogeneous solutions of the two systems correspond and that the approximate solutions produced form the complete general solution of the original differential equation.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090305
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  • 19
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    A Fortran program to generate finite difference formulas (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 581-599 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A discretization process is described by which it is possible to generate finite difference formulas for arbitrary linear two-dimensional partial differential equations. The process is based on a novel approach to finite difference analysis in which differential operators are approximated by rectangular matrices. In this approach, the discrete form of a complicated operator is obtained by performing simple numerical operations on elementary matrix factors. The analysis is augmented by a listing of a computer program based on the method for the automatic generation of finite difference formulas.
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620090307
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  • 20
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    Alternate hybrid stress finite element models (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 601-615 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Alternate hybrid stress finite element models in which the internal equilibrium equations are satisfied on the average only, while the equilibrium equations along the interelement boundaries and the static boundary conditions are adhered to exactly a priori, are developed. The variational principle and the corresponding finite element formulation, which allows the standard direct stiffness method of structural analysis to be used, are discussed. Triangular elements for a moderately thick plate and a doubly-curved shallow thin shell are developed. Kinematic displacement modes, convergence criteria and bounds for the direct flexibility-influence coefficient are examined.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620090308
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  • 21
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    Linear equality constraints in finite element approximationThis paper was presented at the Seventh U.S. National Congress of Applied Mechanics, University of Colorado, 3-7 June, 1974. (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 563-580 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The typical numerical problem associated with finite element approximations is a quadratic programming problem with linear equality constraints. When nodal variables are employed, the coefficient matrix of the constraint equations, [A], acquires a block-diagonal structure. The transformation from polynomial coefficients to nodal variables involves finding a basis for [A] and computing its inverse.Simultaneous satisfaction of completeness and C1 (or higher) continuity requirements establishes linear relationships among the nodal variables and precludes inversion of the basis by exclusively element-level operations.Linear dependencies among the constraint equations and among the nodal variables can be evaluated by the simplex method. The computational procedure is outlined.
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    URL: http://dx.doi.org/10.1002/nme.1620090306
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  • 22
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    On the use of isoparametric finite elements in linear fracture mechanicsAfter submitting this paper, the author has learned of an independent development reporting a similar approach for 2-D problems, see R. D. Henshell, ‘Crack tip finite elements are unnecessary’, Int. J. num. Meth. Engng, 9, 495-507 (1975). (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 25-37 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Quadratic isoparametric elements which embody the inverse square root singularity are used in the calculation of stress intensity factors of elastic fracture mechanics. Examples of the plane eight noded isoparametric element show that it has the same singularity as other special crack tip elements, and still includes the constant strain and rigid body motion modes. Application to three-dimensional analysis is also explored. Stress intensity factors are calculated for mechanical and thermal loads for a number of plane strain and three-dimensional problems.
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    URL: http://dx.doi.org/10.1002/nme.1620100103
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  • 23
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    An Extended Matrix Transfer Method with an automatic root search capability (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 67-76 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An ‘Extended Matrix Transfer Method’ is presented which has an automatic root search capability that can be guaranteed to determine all the roots of the problem with the exception of those roots lying within prescribed tolerance bandwidths.The power and generality of the method is demonstrated by application to a specially synthesized problem.
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    URL: http://dx.doi.org/10.1002/nme.1620100106
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  • 24
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    A finite element method for the axisymmetric flow computation in a turbomachine (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 93-113 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The equations for the meridional through-flow in a turbomachine are formulated as a quasi-harmonic non-linear equation. This equation is then solved iteratively by the finite element method and in order to obtain convergence an under-relaxation factor has to be introduced. Comparisons with experimental results in single and multistage axial compressors show very good agreement. The finite element method is thus shown to be an efficient tool for this type of problem.
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    URL: http://dx.doi.org/10.1002/nme.1620100108
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  • 25
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    Theory and examples of partial approximation in the finite element method (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 115-122 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents theory and examples of partial approximation as a modification of the displacement method in the finite element analysis. This method requires different shape functions for different terms in the potential energy expression to curtail the processes in the standard displacement method. Explanation of the theory is given by use of a simple example for Poisson's equation. It can also be effectively utilized to give mathematical foundation to some finite element models based on physical reasonings, such as Melosh's rectangular element for plate bending and beam element approximation of circular arches.
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    URL: http://dx.doi.org/10.1002/nme.1620100109
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  • 26
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    The calculation of branch flows in a directed network (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 123-131 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a procedure for the calculation of branch flows in a directed network in which the node-to-node flows are prescribed.The node-to-node paths of the network are enumerated using a combinatorial process. Procedures based on the path list are used to allocate the node-to-node flows to the alternative paths of the network according to Wardrop's first principle. The calculation, although necessarily iterative, is rapidly convergent.The method has been implemented as a computer program and the results obtained for a typical network are discussed.A linear relationship between branch potential and branch flow has been used, but the method can be extended to piece-wise linear and non-linear relationships.
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    URL: http://dx.doi.org/10.1002/nme.1620100110
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    Sequential interpolation functions (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 133-143 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper it is shown how to achieve special interpolation functions that can be applied to the finite element method, least squares methods or other related numerical techniques. We call these functions sequential interpolation functions since one of the main characteristics of this technique refers to the fact that the refinement of the solution does not require the redefinition of the interpolation funtions used in a previous step, as the case for instance in the FEM.The present theory and the FEM using an isoparametric element were compared for a plane stress problem. The results show that both have the same degree of accuracy. The choice of the sequential interpolation functions is easier than those used in the finite element formulation and the computer time was reduced by about 50 per cent.
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    Technical note: Horizontally curved beam finite element including warping (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1397-1403 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100618
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    A new finite element scheme for instability analysis of thin shells (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 145-170 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a new finite element scheme for the analysis of instability phenomena of arbitrary thin shells. A computationally efficient procedure is proposed for calculating the non-linear stiffness and tangential stiffness matrices for a doubly-curved quadrilateral element defined by co-ordinate lines. The essential feature is the explicit addition of the non-linear terms into the rigid-body motion of the element. Thus the non-linear and tangential element stiffness matrices can easily be generated by transforming the generalized element stiffness matrix for linear analysis, and the non-linear terms of these matrices are separated into a number of component terms multiplied by the rigid-body rotations. These component terms can be stored permanently and used to calculate efficiently the non-linear and tangential stiffness matrices at each iteration. Illustrative examples are presented which confirm the validity of the present approach in the analysis of instability phenomena of thin plates and shells.
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    URL: http://dx.doi.org/10.1002/nme.1620100112
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    A computer solution for two-dimensional fluid-particle flows (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 185-196 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer solution for two-dimensional fluid-particle flows using the cellular approach is presented. The euqations describing the flow of the continuous (fluid) phase are formulated using stream function, vorticity and enthalpy as the dependent variables. The effect of the disperse (particle) phase on the continous phase is represented by vorticity and energy sources in each cell. To illustrate the capability of the solution scheme, the flow of gas laden with hot particles issuing into a sudden expansion is analysed.
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    Inertia loading in finite element analysis of structures subject to compound motion (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 197-209 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problems associated with the stress analysis of structures subjected to body force loading due to compound motion are outlined. An economic method for calculating equivalent nodal loading, for use in a finite element displacement analysis, is proposed in which the element discretization and consistent mass matrices are used to advantage. The relevant equations, relating to the rigid body dynamics of compound motion, are appended in matrix notation. Validity of the method is demonstrated by an analysis of the stresses, due to gyroscopic and centrifugal forces, in an aero engine blade model.
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    Domain mappings for the numerical solution of partial differential equations (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 211-223 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Independent variable transformations of partial differential equations are examined with regard to their use in numerical solutions. Systems of first order and second order partial differential equations in conservative and nonconservative form are considered. These general equations are transformed using generalized mapping functions and important computational features of the transformed equations are discussed. Examples of mappings which regularize domains are given involving various types of partial differential equations. These mappings are of particular importance in finite difference approximations because of the ease with which a mesh can be adapted to regions formed by co-ordinate lines.
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    Diagonal dominance and S.O.R. performance with skew nets (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 225-230 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Alternative finite difference formulations for elliptic equations on skew nets are investigated for suitability for rapid convergence of S.O.R. iterations. In dealing with the differential equation directly, diagonal dominance is a key property for convergence theorems. Mixed derivatives boundary conditions threatens this property, but formulas are presented which protect it as long as the net skewness is not too severe. Test calculations are reported showing convergence for these formulas to be as good as that of optimal S.O.R. theory, whereas other more direct formulas give a very inferior performance.
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    Announcement and call for papers (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 238-240 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620100120
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    Discussion of paper by R. D. Henshell and K. G. Shaw (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 235-237 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 85-98 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid-side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the (1/r) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results.The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.
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    Solution of a complex quadratic eigenvalue problem (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 99-106 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complex quadratic eigenvalue problem of order n (n = 20, 30, 40,…) encountered in an investigation of pipe flow was reduced to that of computing the eigenvalues of either a real or a complex matrix of order 2n, depending on the linearization technique used. To get satisfactory results using the CDC 6000 series computer, double-precision versions of certain widely used and highly regarded eigenvalue subroutines were required. Although the modified subroutines used for the real matrix computations required less core than those used for the complex matrix, the calculation time was not significantly faster than that for the complex matrix. The use of ‘balancing’ subroutines merits further investigation.
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    Integration of triangular finite elements containing corrective rational functions (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 107-114 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Rational corrective functions are often supplemented to complete polynomials in order to create conforming triangular finite elements for plate bending. Although such elements containing complete polynomials of degree 3 or 4 have long been known, conforming triangular elements for plate bending, which contain complete polynomials of arbitrary degree p ≤ 5 and new corrective rational functions, have been given only recently.Integration of rational functions usually requires numerical quadrature. It is shown here that these new corrective rational functions fall into two classes. For those in one class, explicit closed form integration formulas are available. For those in the other class, integration can be performed very efficiently by summing series whose general term is O(kd) for large k, where d ≤ 5. These formulas also apply to the older third and fourth order elements.
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    An ‘upwind’ finite element scheme for two-dimensional convective transport equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 131-143 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 13 Ill.
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    A unidimensional convergence test for matrix iterative processes applied to Strapdown Navigation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 115-130 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The investigation of the convergence properties of matrix iterative processes usually involves test matrices of high order. This fact may prohibit an analytic approach to the problem. In this paper a method is presented which converts the multidimensional test procedure into a scalar one. The method is presented in conjunction with the problem of matrix orthogonalization which exists in Strapdown Inertial Navigation. Three examples are presented in which the convergence of matrix orthogonalization techniques is investigated. The examples demonstrate the use of the unidimensional convergence test in determining the order of the processes and in finding sufficient conditions for convergence. Numerical results are presented.
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    An algorithm for minimal degree linear Chebyshev approximation on a discrete set (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 619-635 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An algorithm for computing a linear Chebyshev approximation to a function defined on a finite set of points is presented. The method requires the accuracy of the approximation to be specified, and determines the least degree approximation which achieves this accuracy. The algorithm is based upon the simplex method of linear programming. A FORTRAN program is supplied in the Appendix.
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    A simultaneous iteration algorithm for symmetric eigenvalue problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 647-663 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A FORTRAN IV algorithm is presented for determining sets of dominant eigenvalues and corresponding eigenvectors of symmetric matrices. It is also extended to the solution of the equations of natural vibration of a structure for which symmetric stiffness and mass matrices are available. The matrices are stored and processed in variable bandwidth form, thus enabling advantage to be gained from sparseness in the equations. Some of the procedures may also be used to solve symmetric positive definite equations such as those arising from the static analysis of structures loaded within the elastic range.
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    Mathematical model and boundary conditions in stress analysis relating to steam turbine rotors, under transient operating conditions (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 345-360 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An appropriate mathematical model for calculation of thermoelastic stress in steam turbine rotors, under transient operating conditions, is developed in the framework of so called uncoupled quasi-static theory. The numerical analysis has been carried out by means of the finite element code ANGUS, the accuracy of which has been evaluated by comparing it with an analytical solution given by one of the authors in Reference 2. It has been shown that, with an appropriate choice of thermal and elastic boundary conditions, it is possible to carry out stress transient analysis considering only a segment of the hottest zone of high or intermediate pressure body of rotors. The paper includes a comparison study of the influence of two types of thermal boundary conditions in the labyrinth glands.
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    A thick finite strip solution for static, free vibration and stability problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 665-678 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite strip method for the analysis of plate bending problems is described. This method, which takes into account the effects of transverse shear deformation, is applied to the static analysis of a curved plate and then to the free vibration and stability of thick and thin plates.
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    Multivariable approach to the finite difference solution of elasto-plastic problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 361-377 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The solutions of plane elasto-plastic problems usually use one or two field variables - namely a stress functions or the displacements. The use of three, four or five field variables is investigated and it is concluded that the three stresses from the best basis for a multivariable approach. Attempts to solve the governing equations with an initial value technique were exhaustively tried and discarded in preference to a boundary value or elliptical technique. The problem solved to check the method is that of a hole in plane strain uniaxial tension. Effective plastic strain distributions are plotted, along with stress and strain concentration data and distributions of the mean to effective stress ratio. Comparison is made between solutions produced using incremental and deformation theories.
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    An iterative penalty function method in structural analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 413-421 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An iterative solution process combined with the penalty function method employed in constrained variational priciples is described. As an example of the use of the method an axi-symmetric plate with the complementary energy formulation is considered.
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    Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 231-246 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Based on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees-of-freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.
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    Finite element solutions of the non-self-adjoint convective-dispersion equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 269-287 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Finite element formulations based on the Galerkin and variational principles have been developed for the self-adjoint and non-self-adjoint problems represented respectively by the flow and convective-dispersion equations in the cylindrical polar system of co-ordinates. The formulation based on the variational principle is shown to be restricted to dispersion-dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.
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    A Block-Stodola eigensolution technique for large algebraic systems with non-symmetrical matrices (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 247-267 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Block-Stodola eigensolution method is presented for large algebraic eigensystems of the form AU = λBU where A is real but non-symmetric. The steps in this method parallel those of a previous technique for the case when both A and B were real and symmetric. The essence of the technique is simultaneous iteration using a group of trial vectors instead of only one vector as is the case in the classical Stodola-Vianello iteration method. The problem is then transformed into a subspace where a direct solution of the reduced algebraic eigenvalue problem is sought. The main advantage is the significant reduction of computational effort in extracting a subset of eigenvalues and corresponding eigenvectors. Theorems from linear algebra serve to underlie the basis of the present technique. Complex eigendata that emerge during iteration can be handled without doubling the size of the problem. Higher order eigenvalue problems are reducible to first order form for which this technique is applicable. The treatment of the quadratic eigenvalue problem illustrates the details of this extension.
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    Rubber covered rolls - the thermoviscoelastic problem. A finite element solution (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 767-785 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The coupled thermomechanical behaviour of a layer of thermorheologically simple material bonded to a uniformly rotating rigid cylinder and indented by another rigid cylinder is studied by the finite element method. The various approximations necessary to reduce the problem to one of tractable size and the computational methods used are discussed in some detail. The complete thermal, deformation and stress fields may be computed. Some results, computed for a grid using ‘rectangular’ elements, presented graphically include the temperature distribution, the stress distribution near the bond surface, the contact pressure distribution and the asymmetric surface deformation of the rubberlike layer.
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    An automatic node relabelling scheme for minimizing a matrix or network bandwidth (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 787-797 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automatic algorithm is presented for reducing the bandwidth of symmetric sparse connectivity matrices. The procedure takes an arbitrary input sequence and creates an optimal bandwidth for complex network systems by renumbering the node labels. Thus, considerable improvement for computer storage and time is achieved in the solution of the systems.A large number of examples is presented to demonstrate the reliability and the efficiency of the method.
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    A Poisson equation solver for rectangular or annular regions (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 799-807 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A FORTRAN subroutine is presented which solves the system of simultaneous linear equations associated with the finite difference representation of the Poisson equation for rectangular or annular regions. The code is arranged to require minimum storage, and all possible operations involving known zeros and ones are suppressed. Single subscripting is employed to minimize execution time.
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    Efficient least squares finite elements for two-dimensional laminar boundary layer analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 809-825 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the formulations of essentially one-dimensional least squares and Galerkin-least squares finite elements for the numerical solution of two-dimensional laminar boundary layer equations. An iterative technique to cope with the non-linearity of the boundary layer equations, in conjunction with the least squares finite element method, is proposed. Through exhaustive numerical investigations in the retarded flow over a plate, flow past a circular cylinder, the flow past an elliptic cylinder, the accuracy and applicability of the proposed method are demonstrated.
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    A simple finite-difference modification for improving accuracy near a corner in heat flow problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 827-832 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100409
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    Reduction scheme for some structural eigenvalue problems by a variational theorem (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 845-852 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An accurate reduction scheme for structural eigenvalue problems is deduced from a variational theorem in which the displacement, velocity and/or momentum fields are taken to be independent.
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    Splines and variational methods, M. Prenter, Wiley, New York, 1975. £10.75 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 487-487 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620100222
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    Linear and non-linear waves, G. B. Whitham, Wiley, New York. Price: £12.15. 636 pages (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 488-488 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100223
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    Masthead (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100301
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    Definition of programming languages by interpreting automata, Alexander Ollengren, Academic Press, Price £9.00 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 488-488 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100224
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    Numerical quadrature and two-dimensional radiative heat transfer (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 491-502 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Four methods of numerically integrating a two-variable integral equation, which is used to describe non-dimensional radiosity in a diffuse grey cavity, are presented. Physical reasoning is used to organize the successful method for obtaining physically plausible solutions.
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    Transformation of elliptic partial differential equations for solving two-dimensional boundary value problems in fluid flow (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 527-533 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: It is possible to transform elliptic partial differential equations to exchange the dependent with one of the independent variables. The Laplace equation for a stream function ‘Ψ’ over the X and Y co-ordinate system, for example, can be transformed into a relationship expressing the Y position of streamlines in terms of strem function Ψ and X.Although the resulting new partial differential equation is much more complex it is much more convenient to use in a computer. An irregular Y boundary becomes, with the new relationship, merely the boundary values assigned to the outer streamlines and the computer always need only deal with a rectangular array. The resulting answer is in the form of the position of streamlines which is the information directly required for plotting flow maps.
    Additional Material: 2 Ill.
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    On the relationship between the finite element and finite difference methods (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 893-923 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The integral equations which arise from application of the Galerkin-finite element scheme to the convective diffusion equation are examined to illustrate how this method represents differential equations. The formulae obtained are effectively spatial averages of standard finite difference equations written at a node. The truncation error in the finite element solution at a node is obtained for various nodal configurations.
    Additional Material: 9 Tab.
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    On the construction of conforming rectangular plate elements (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 925-933 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620100417
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    On the finite element solution of an exterior boundary value problem (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 885-891 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper compares three methods for dealing with an exterior boundary value problem by the Finite Element Method, one of which involves using an infinite element. The methods are illustrated by application to the problem of ground water flow round a tunnel with permeable invert. The use of a special trial function with a variable parameter in the infinite element gives a particularly efficient method of solution.
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    Subspace iteration accelrated by using Chebyshev polynomials for eigenvalue problems with symmetric matrices (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 935-944 
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    Keywords: Engineering ; Engineering General
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    Notes: Bathe's algorithm of subspace iteration for the solution of the eigenvalue problem with symmetric matrices is improved by incorporating an acceleration technique using Chebyshev polynomials. This method of acceleration is particularly effective for this kind of iteration. The rate of convergence of the iteration scheme presented is considerably improved when compared with the original one, and satisfactory rates of convergence can be obtained for a wider range of eigenvalues.
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    Fuller Obituary on Professor B. Fraeijs de Veubeke (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 407-407 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620110221
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    Efficient large scale non-linear transient analysis by finite elements (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 579-596 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 11 Ill.
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    Artificial adjustment of element stiffness with a particular reference to plate bending (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 945-949 
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    Keywords: Engineering ; Engineering General
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    Notes: A finite element may satisfy all convergence requirements and work well except for being too stiff or too flexible when the mesh is coarse. Here we discuss a technique for softening or stiffening such elements, provided that they have internal degrees-of-freedom. The technique is applied to a previously derived plate element, and the element is found to be much improved.
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    A numerical method for the solution of certain classes of nonlinear Volterra integro-differential and integral equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 431-438 
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    Notes: A direct numerical method is presented for the solution of classes of non-linear, singular Volterra integral and integro-differential equations of the types where y is the unknown and the Fs and Gs are given but to a large extent arbitrary functions of their arguments. The adaptation of the method to other equations, in particular with different kernels, is immediate.
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    An attenuation-free upwind difference formula for analogue computation of charge flow in semiconductorsThis work was supported by GEC Telecommunications Limited. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 439-445 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The first order partial differential equations of charge flow are commonly differenced in the space co-ordinate, with a view to analogue computation of the resulting ordinary differential equations in time. Defects of orthodox difference formulae are identified. In particular: (a) reversed waves and stability problems arise from central differences and (b) first order errors and a ‘pseudo-viscous’ dispersion effect with accompanying false attenuation results from upwind differences. These difficulties are particularly serious in view of the coarse differencing required for practical analogue computation. A much superior formula is presented which is entirely free of attenuation and is easily implemented. Various other desirable features are reported.
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    Comment on hybrid finite elementsBritish Crown Copyright Reserved. Reproduced by permission of the Controller, Her Majesty's Stationery Office. (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 968-973 
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    Keywords: Engineering ; Engineering General
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    Notes: It is shown that an apparently sound selection of trial functions can give rise to hybrid elements with rank deficient stiffness matrices and unused interior fields. An account is given of modifications which overcome these problems for a particular plate bending element.
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    Inners and stability of dynamic systems, E. I. Jury, Wiley, London, 1974. No. of pages: 308. Price: £9.70 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 975-975 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620100428
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    Computational mechanics, vol. 461 of lecture notes in mathematics, edited by J. T. Oden (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 976-976 
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    Keywords: Engineering ; Engineering General
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    Thermodynamics and thermophysical properties of combustion products. Vol. II: Oxygen-based propellants (translated from Russian). V. E. Alemasov et al. Keter Publishing House, Jerusalem Ltd., Price: £14.95 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 975-975 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Linear differential equations with periodic coefficients, 2 volumes, V. A. Yakubovich and V. M. Starzhinskii, Wiley, New York, 1975. No. of pages: 839. Price: £20.60 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 976-976 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    An iterative technique for fitting exponentials (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 979-990 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An interative method to fit the function \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[y = \sum\nolimits_i^n { = 1} a_i e^{lix}\] $\end{document} to data is considered. The technique used is that of inversion of a linear differential operator with constant coefficients. This method reproduces the parameters for mathematically precise data and gives satisfactory results when the data are affected by random errors.
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    A mathematical programming method for the inelastic analysis of reinforced concrete frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1137-1154 
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    Keywords: Engineering ; Engineering General
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    Notes: A mathematical programming method is presented for solving problems of (i) determining the moments and rotations and (ii) determining the safety factor of reinforced concrete frames. The proposed method is essentially a reformulation of those developed by De Donato and Maier. However, the reformulation results in a new mathematical programming model for which an efficient algorithm is developed. The advantage of the proposed method is mainly computational; in fact it requires roughly one half computer time and storage space as compared with those De Donato and Maier employ to solve the same problem.
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    Drying-induced stresses in porous bodies (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1175-1184 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 7 Ill.
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    Nodal grafting for crack propagation studies (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1185-1187 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A simple, efficient method for propagating cracks through a finite element mesh is presented: nodes, borrowed from other points in the mesh, are ‘grafted’ along the advancing crack front. The method requires neither an increase in bandwidth nor a mesh regeneration. It can be easily implemented in any existing program using iso(sub)parametric elements of at least quadratic order.
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    A review of least-squares methods for solving partial differential equations (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1021-1046 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Continuous (integral) and discrete (point-matching) least-squares methods are presented for linear and non-linear problems in boundary-value, eigenvalue, and initial-value form. The history is traced, and important theoretical and practical results are summarized. A comprehensive sample of the literature is presented, indexed to show type of application, version of least squares used, and results of comparison studies. The advantages of least-squares methods are discussed, including convenience in formulation and error evaluation, generality of mixed and local (finite element) versions, and performance that is competitive with other methods.
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    A heuristic for root isolationThis work was supported by the National Science Foundation under grant ENG75-10234. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 598-603 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A heuristic for isolating the real roots of an equation involving a continuous function over a specified region is presented. Root isolation strategies are well known for polynomial and rational functions; however, there have been no really effective root isolation strategies for transcendental functions. For a transcendental function and a given interval, there has been no way to decide the existence of roots within the interval unless the function changed sign at the endpoints or unless evaluations were performed within the interval. This paper presents a new decision procedure using only interval endpoints. The methodology developed does not guarantee to detect real roots in an interval; however, the technique will effectively indicate real roots in a given interval unless the behaviour of the function is quite erratic.
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    Comment on ‘optimal stress locations in finite element models’ (1977)
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 604-604 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620110317
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    Optimization of non-unimodal systems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1235-1250 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Two direct search algorithms for the optimization of non-unimodal systems are presented. One method is interior in nature by using boundary relaxation with pseudo one-dimensional search in the feasible region; the other one is an exterior method which allows the violation of constraints followed by the use of a penalty function to drive the search back into the feasible region. These two methods are usually capable of leaving local optima to reach a better solution if such exists. The application of the proposed approaches to several non-unimodal systems shows that they are better than the existing methods. The proposed methods are also attractive because of the ease of programming and the high probability of reaching the global optimum.
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    Computer program for solution of large, sparse, unsymmetric systems of linear equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1251-1259 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A computer program is presented for in-core solution of a large, sparse, unsymmetric, unbanded system of linear equations. The program employs two partially packed arrays (one for storing non-zero elements, and one for column identifications). Used as the pivotal row is the row with the minimum number of non-zero elements. To avoid instability, the pivot is the largest absolute element in the pivotal row. The method was tested on a system of equations encountered in field application of the three-dimensional Galerkin finite element solution of flow and mass transport through porous media. Performance is compared with that of available alternatives.
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    The steady state response of geometrically non-linear shallow arches (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1261-1269 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The non-linear steady state response of structures with curvature is investigated through the expository example of a shallow circular arch. A consistent mass finite element formulation is employed to derive the governing non-linear differential equations.These equations are solved by assuming a single mode expansion reducing the governing equations to the single degree-of-freedom Duffing's equation with a quadratic term. The non-symmetric amplitude-frequency curve is derived and compared with results previously obtained by direct integration of the equations of motion.
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    URL: http://dx.doi.org/10.1002/nme.1620110807
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    A hybrid stiffness matrix for orthotropic sandwich plates with thick faces (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1291-1306 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stiffness matrix is derived for a rectangular orthotropic sandwich plate element with thick faces by the assumed stress hybrid approach.It will be demonstrated that an independent polynomial can be used for the internal forces of the sandwich plate by the membrane theory (assumption of thin faces) and also for the additional moments and shear forces of the faces.The boundary displacements are approached solutions of the homogeneous differential equation of a sandwich beam.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110809
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    Temperature load on thick curved shell elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1329-1333 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Temperature load on a shell is usually represented as initial strains in the tangent plane directions of the shell, since strains in shell surface normal directions are neglected. It is shown, however, that this simplification may give rise to significant errors for thick curved shell elements. A procedure to overcome this problem is presented. In particular the eight-node subparametric thick shell element is considered.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110811
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    A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1340-1342 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral equation method is presented for the numerical calculation of the eigenvalues of the scalar Helmholtz equation. By using a particular solution instead of Green's function, the calculations could be simplified due to the elimination of complex numbers.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110813
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    Announcement & call for papers (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1344-1344 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110816
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    Computing three-dimensional free surface flows (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1143-1152 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element techniques are developed for the analysis of high-speed three-dimensional free surface flows within the context of potential flow theory. The primary dependent variable is the velocity potential, which is approximated as a quadratic within each isoparametric element. An iterative approach is used to seek the initially unknown free surface location.A high-speed fluid jet issuing through an orifice plate into a transvese gravity field is examined to illustrate features of the approach. Convergence of the solutions is very good at a Froude number of 3-53 but deteriorates as F nears unity.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100513
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    Beam-column element for inelastic analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1177-1178 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100515
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    On reduced integration in solid isoparametric elements when used in shells with membrane modes (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1179-1182 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100516
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  • 94
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    Substructured macro elements based on locally blended interpolation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1405-1421 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we describe a new class of locally refined macro finite elements which are especially amenable to the use of substructuring techniques for the efficient solution of the resulting idealization. The tools and guidelines illustrated by the examples of modelling crack tips, point load singularities and singularities at re-entrant corners should enable an analyst to construct other such blended macro elements specifically tailored to his particular class of problems. The use of such substructured macro elements in finite element calculations permits substantial reduction in the manual effort of data preparation and the computational cost of numerical solution.
    Additional Material: 18 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110906
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    A numerical method for two-dimensional Navier-Stokes equation by multi-point finite differences (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1439-1454 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme with a high degree of accuracy has been developed for the full Navier-Stokes equations. The method utilizes the multi-mesh points for space and time derivatives in order to improve the truncation error. Whereas the existing numerical method employing the finite difference scheme, e.g. the explicit, pure implicit, Crank-Nicolson, and DuFort-Frankel schemes, has the truncation errors of the order (Δx)2, Δx being the spatial mesh length, the one for the present method is generally of the order (Δx)3. A numerical example is shown for a natural convection flow in a square box and the results are compared with those of Cormack et al. One order of magnitude reduction of the computing time for a constant degree of accuracy was attained for the two-dimensional problems. Furthermore, a two order of magnitude reduction is to be expected when the method is applied for the three-dimensional Navier-Stokes equations.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110908
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    The generation of elements with singularities (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1249-1259 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure is given for generating two-dimensional conforming singularity elements from standard conforming elements. Three new elements with 0(r-p) derivative singularities are introduced. The technique is based on the use of elements defined by numerically integrated shape functions. Special quadrature rules are suggested for triangular elements. The degeneration of these elements to crack tip elements and the direct evaluation near the singularity of element quantities, such as the stress intensity factors, is discussed.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100605
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    The numerical solution from measurement data of linear integral equations of the first kind (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 729-740 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem considered in this paper is the solution of the Volterra integral equation of the first kind for the input function where we are given the impulse response or kernel and discrete, noise contaminated, observed values of the output function. The present method, introduced here, is based on assuming a multipolynomial form for the input function. Using the integral equation and the least squares method, the coefficients of all the terms in these polynomials are found simultaneously, in order to avoid bias toward any subset of the data. The solution is obtained in such a way that successive polynomials are continuous in function value and derivative at the points of juncture. Thus a smoothed estimate of the input function is generated. The development of the algorithm is presented and applied to two illustrative problems. Possible improvements and extensions of the method are also discussed.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110409
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    Masthead (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111001
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    Analyse numérique des inéquations variationelles (in French), R. Glowinski, J. L. Lions and R. Trémolieres, Dunod, Paris, 1976. No. of pages: 558. price: 390FF (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1486-1486 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110914
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    The influence of the choice of connectors in the finite element methodPresented at the ‘Meeting on Mathematical Aspects of Finite Element methods’, 10-12 December, 1975 in Rome. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1491-1505 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The patch test is interpreted from a variational point of view. This leads to the conclusion that non-conforming (or non-stress diffusive) displacement (stress) models can be considered as special hybrid models. A simple choice of mixed connectors is proposed that satisfy a priori the patch test for any assumed displacement or stress field. Finally some numerical examples are given of finite elements that do not pass the patch test but still exhibit convergence in practical applications.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620111002
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