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  • Life and Medical Sciences  (716)
  • Engineering
  • 1995-1999
  • 1980-1984
  • 1975-1979  (1,116)
  • 1925-1929
  • 1978  (627)
  • 1976  (489)
Collection
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  • 1995-1999
  • 1980-1984
  • 1975-1979  (1,116)
  • 1925-1929
Year
  • 1
    Electronic Resource
    Electronic Resource
    Calculation of eigenvalues of the Helmholtz equation by an integral equation (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 59-66 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented to calculate the eigenvalues of the Helmholtz equation Δ2ø + k2ø = 0 in a two-dimensional area when ø vanishes on the boundary. The method is based on an integral equation, which can be easily solved numerically. Results obtained for circular and rectangular geometries are also given and compared to the exact values.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100105
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  • 2
    Electronic Resource
    Electronic Resource
    Panel flutter optimization - a refined finite element approach (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 77-91 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the results of an aeroelastic optimization study. In this study the weight of a large aspect ratio panel immersed in high Mach number supersonic flow is minimized subject to the requirement that a critical aeroelastic parameter for flutter be held within specified limits. A refined finite element technique is used to model the panel flutter equilibrium equations, equations which act as constraints on the design search. The optimization mechanism itself is studied and discussed to provide qualitative results which may be useful to the solution of other aeroelastic optimization problems. The numerical results of this investigation are compared to converged numerical results to illustrate finite element accuracy. The results of the study show that the weight savings and material distribution found with an effective finite element model are comparable to those found by more complicated numerical methods.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100107
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  • 3
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100114
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  • 4
    Electronic Resource
    Electronic Resource
    Optimum design of stiffened cylindrical panels with constraint on the frequency in the presence of initial stresses (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 283-299 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the optimum design of stiffened cylindrical panels with weight as the objective function and constraints on the frequencies in the presence of initial stresses, using unconstrained minimization techniques of non-linear mathematical programming problem. The interaction between the buckling constraints and the frequency constraints in the presence of initial stresses are included in the formulation. Loss of load carrying capacity due to imperfection and due to suddenly applied loads are included in the buckling analyses. Results for cylindrical shell are obtained by setting the panel angle to 360 degrees. The relationship between the weight of the cylinder and the panel (a segment of the cylinder) is examined.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100205
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  • 5
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100208
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  • 6
    Electronic Resource
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    Steady and unsteady finite element analysis of incompressible viscous fluid (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 437-456 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element procedures and related illustrative numerical examples for incompressible viscous fluid motion are discussed in this paper. The steady flow problem is solved by the Newton-Raphson method and the perturbation method. By numerical examples, it can be shown that the combined use of the Newton-Raphson method and perturbation method is suitable. For the analysis of unsteady flow, the perturbation method is employed. Assuming that the basic flow is known, unsteady flow is calculated by accumulating the solution of the linearized equation in which the boundary values are varied by small amounts. Steady flows of temperature dependent free convection are also discretized and analyzed by the same procedure as the conventional finite element Galerkin method. For shape functions, quadratic polynomials are used for velocity and temperature, and linear polynomials for pressure. It is to be noted that the selections of shape functions and solution method are the keys to the analysis of highly non-linear fluid flow problems such as those discussed in this paper.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100213
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  • 7
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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 
    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.1620100223
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  • 8
    Electronic Resource
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    The incremental perturbation method for large displacement analysis of elastic-plastic structures (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 503-525 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure of applying the perturbation method is presented for the incremental numerical analysis of materially and combined non-linear problems of discrete and discretized structral systems. Small but finite strain and stress increments are strictly distinguished from the strain rates and stress rates, respectively. It is shown that, by applying the perturbation procedure not only to the non-linear strain-displacement relations and equilibrium equations, but also to the constitutive equations in terms of rate quantities, all the governing equations can be satisfied to any desired accuracy at every instantaneous configuration in between the starting and terminal points of an incremental step. The proposed method provides also means of finding, to a desired accuracy, every point on an equilibrium path of a discrete system at which a new element will start yielding or unloading and possible critical points on the path. The significance of the proposed method is expected to be appreciated particularly in numerical investigations of critical behaviours and post-buckling behaviours.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100303
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  • 9
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    Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 301-343 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of a numerical procedure for solving complex boundary value problems in plane elastostatics. This procedure - the displacement discontinuity method - consists simply of placing N displacement discontinuities of unknown magnitude along the boundaries of the region to be analyzed, then setting up and solving a system of algebraic equations to find the discontinuity values that produce prescribed boundary tractions or displacements. The displacement discontinuity method is in some respects similar to integral equation or ‘influence function’ techniques, and contrasts with finite difference and finite element procedures in that approximations are made only on the boundary contours, and not in the field. The method is illustrated by comparing computed results with the analytical solutions of two boundary value problems: a circular disc subjected to diametral compression, and a circular hole in an infinite plate under a uniaxial stress field. In both cases the numerical results are in excellent agreement with the exact solutions.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100206
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  • 10
    Electronic Resource
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    Finite element method applied to the supersonic flutter of circular cylindrical shells (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 423-435 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the finite element method to the supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression is presented. A circular cylindrical shell element is used. The element stiffness, mass and initial stiffness matrices are given. The element aerodynamic matrix is derived based on a first order high Mach number approximation to the linear potential flow theory. The eigenvalue problem is solved by the QR algorithm. Numerical results are presented and these are compared with analytical solutions and experimental data.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100212
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  • 11
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    A finite element solution program for large structures (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 401-412 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A straightforward and general computer program for assembling and solving (using Gauss elimination technique) widely sparsed finite element matrix equations with very large bandwidth and capable of handling different degrees-of-freedom and variable bandwidth at different nodes, is described herein. The program assembles any type of finite elements having arbitrary number of nodes and each node may have differnt degrees-of-freedom. It requires only a small core memory in the computer, although a fast random access device is also needed. The two very important features of this program are (i) it does not store any zero submatrices within the band and (ii) during the solution of equations all operations dealing with zero submatrices within the band are automatically skipped and thus the savings of a considerable amount of disc storage space and computer time can be effected in many cases. Another feature is that many right hand sides can be handled simultaneously. Hence the program is very economical for structures having widely sparsed matrix equations. A listing of the computer program written in FORTRAN IV for CDC 6400 computer is readily available from the authors, but unfortunately could not be given here because of lack of space. The program is so general that it can be used to solve a wide class of finite element problems without actually having to understand fully the techniques behind it.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100210
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  • 12
    Electronic Resource
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    An ADI procedure suitable for virtual storage systems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 465-470 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Peaceman-Rachford ADI technique is a well-known iterative method for solving large systems of linear equations arising from finite difference methods of solution of partial differntial equations. The present note demonstrates how the algorithm can be conveniently rearranged for computation in a virtual storage system with paging. Timing results are given for a sample problem typical of those encountered in nuclear diffusion computation.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100215
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  • 13
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    Author's reply to the discussion by Watkins (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 472-474 
    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.1620100217
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  • 14
    Electronic Resource
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    Closed form elastic-plastic stiffness matrix for axisymmetric finite elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 59-65 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note presents the closed form equations for the stiffness terms in the elastic-plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl-Reuss flow rule and von-Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120106
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  • 15
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    Certain properties of numerical schemes used to solve the blade-to-blade flow problem (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 85-92 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The compressible potential flow on a blade-to-blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non-linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade-to-blade configurations.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120109
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  • 16
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    Modification to the Suhara-Fukuda method of network generation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 93-99 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note describes improvements to the Suhara-Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are given.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120110
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  • 17
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    Discussion of a paper by E. O. FrindInt. J. num. Meth. Engng, 945-962 (1977). (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 183-185 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120117
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  • 18
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    Masthead (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978) 
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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.1620120201
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  • 19
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    A least squares finite element approach to unsteady gas dynamics (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1-10 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120102
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  • 20
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    Finite element analysis of steady-state elasto-visco-plastic flow by the initial stress-rate method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 47-57 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady-state visco-plastic flows.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120105
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  • 21
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    A finite element formulation for large elastic-plastic deformation analysis of polycrystals and some numerical considerations on polycrystalline plasticity (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 101-114 
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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 formulation for large elasto-plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress-strain curves for several proportional loadings, effect of change of loading path on stress-strain curve, subsequent yield loci for uniaxial and equi-biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120111
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  • 22
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    Addendum to the paper ‘finite element analysis of steady-state elasto-visco-plastic flow by the initial stress-rate method’ (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 382-383 
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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.1620120216
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  • 23
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    A 2nd order numerical method for laminar flow at moderate to high Reynolds numbers: Entrance flow in a duct (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 405-414 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120303
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  • 24
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    On least squares approximations to indefinite problems of the mixed type (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 453-469 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The mehod retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency i.e., the resulting matrix system is always symmetric and positive definite,. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120307
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  • 25
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    Finite element methods for an optimal steady-state control problem (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1375-1382 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An optimal steady-state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120906
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  • 26
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    Sensitivity Of matrix eigenvaluesThis work was done while both authors were summer visitors to Argonne National Laboratory in connection with the LINPACK project. (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1367-1373 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A recent paper by Donald Gignac describes some difficulties with a certain matrix eigenvalue problem. This paper shows that the difficulties result from the naturue of the matrix itself. Quantities called condition numbers, which measure the sensitivity of the eigenvalues, are computed, and numerical results given.
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    URL: http://dx.doi.org/10.1002/nme.1620120905
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  • 27
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    Efficient implementation of anisotropic three dimensional boundary-integral equation stress analysis (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1383-1397 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary-integral equation medthod is particularly well suited for solution of stress concentration and elastic fracture mechanics problems. The method was not previously applicable to anisotropic three dimensional problems because no efficient technique existed for calculation of the required point load solution for an infinite body. A technique has been developed to evaluate numerically the anisotropic point load soultions, and used to generate data bases for various materials. An intrpolation technique is used to evaluate the point load solutions efficiently within a higher order boundary-intgral equation code. The effectiveness of the technique is verified by solution of problems involving both uniaxial stress states and stress concentrations.
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    Numerical fourier transformation: Singularity expansions and product integration (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1473-1477 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    ‘Potential energy with iterative correction’… or deterioration, that is the question (Reply by Authors to M. Crisfield's Discussion1 of ‘A Critical Assessment of the simplified Hybrid Displacement Method’2) (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1461-1472 
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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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    A frontal-based solver for frequency analysis (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1659-1666 
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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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    Lumped mass matrices with non-zero inertia for general shell and axisymmetric shell elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1635-1650 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A diagonal lumped mas formulation with non-zero inertia terms is presented for Ahmad's general shell element. The effect of co-ordinate transformation of the mas matrix is demonstrated. Due to arbitray co-ordinate transformation on nodal variables, the diagonal lumped mas matrix becomes a banded matrix of half bandwidth three. It is shown that with some approximations this matrix can be made diagnoal without effecting the results appreciably. Numerical examples are presented to illustrate the accuracy of the formulation. Similar lumped mass matrix formulation is also given for axisymmetric shell elements.
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    A systematic procedure for generating useful conformal mappings (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1651-1657 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A Procedure is presented for generating a class of conformal mappings useful in the formulation of finite-difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly-rectangular domain for a wide variety of partical problems. The introduction of sheared co-ordinates in this computational domain then provides for solution of the problem in a nearly-orthogonal (in fact, nearly-conformal) co-ordinate system, with its boundaries corresponding to co-ordinate lines. The method is based upon the Schwarz-Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.
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    Thin plate semiloof element for structural analysis-including stability and natural vibrations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1667-1676 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents a thin plate element formulated along parallel lines to the general three-dimensional Semiloof shell element. This plate version possesses only one half of the total number of degrees-of-freedom of the shell element and has the advantqage that the formulation of the strains and other terms is very much simplified. The element is first assessed in static situations and then its performance in the solution of eigenvalue problems is considered.
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    Central difference approximations to the heat transport equation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1697-1704 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper analyses the oscillatory nature of central difference approximations to the heat transport equation when convection is the important mechanism of heat transport. The effects of three different boundary conditions, various heat source profiles, the Peclet Number and the parity of the number of meshes on the amplitudes of these oscillations are described. A boundary condition is presented which suppresses the oscillations to insignificant amplitudes in the one-dimensional situation.
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    Upwinding of high order Galerkin methods in conduction-convection problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1764-1771 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Upwinded parabolic and cubic elements are derived on a uniform grid of size h for the finite element Galerkin method applied to the solution of the model conduction-convection problem εu″  -  Ku′ = 0, ε, K 〉 0, subject to the boundary conditions u(0) = 1, u (1) = 0. Extension of the results to more complicated problems is indicated. Finally numerical results are given comparing some of the methods derived for a range of L(=Kh/2ε), the grid Peclet number.
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    Hybrid stress finite element model for non-linear shell problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1819-1839 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present paper describes a hybrid stress finite element formulation for geometrically non-linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger-Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi-field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non-linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton-Raphson iteratioin. Numerical examples presented in the paper include complete snap-through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non-linear shell problems of high complexity.
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    On thick superparametric shell element (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1883-1889 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 3 Ill.
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    Improved three point integration schemes for triangular finite elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1890-1896 
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    Keywords: Engineering ; Engineering General
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    Notes: Symmetric three point quadrature schemes are at present available for triangles for exact integration of polynomials of degree 2. There are other possible symmetries, which provide higher accuracies. Exact integration of polynomials of a higher degree is possible. General formulations are made and a set of three integration points for improved accuracy is given.
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    Announcements (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1898-1900 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Non-linear ordinary differential equations, D. W. Jordan and P. Smith, Oxford University Press (part of Oxford Applied Mathematics and Computing Science Series), 1977. No. of pages: 360. Price:£6.50 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1897-1898 
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    Keywords: Engineering ; Engineering General
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    Structural optimization: A review and some recommendations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 13 (1978), S. 203-228 
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    Keywords: Engineering ; Engineering General
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    Notes: A brief review of the structural optimization literature and a description of the present status of optimization methods are presented. The scope of the review is limited and does not profess to cover the entire literature.Results of the optimization of two structures (by the optimality criteria approach) are presented. There are some conclusions and recommendations for future developments in structural optimization.
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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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    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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    Masthead (1976)
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    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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    URL: http://dx.doi.org/10.1002/nme.1620100201
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    Frontal solution program for unsymmetric matrices (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 379-399 
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    Keywords: Engineering ; Engineering General
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    Notes: A frontal solution program is presented which may be used for the solution of unsymmetric matrix equations arising in certain applications of the finite element method to boundary value problems. Based on the Gaussian elimination algorithm, it has advantages over band matrix methods in that core requirements and computation times may be considerably reduced; furthermore numbering of the finite element mesh may be completed in an arbitrary manner. The program is written in FORTRAN and a glossary of terms is provided.
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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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    Keywords: Engineering ; Engineering General
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    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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    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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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    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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    Isoparametric finite element methods for two-dimensional transport calculations (1976)
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 171-183 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Finite element methods for solving the two-dimensional x-y transport equation are considered. Numerical schemes are defined and tested on some simple practical problems.
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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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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    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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    Letter to the editor (1976)
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 718-719 
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    Keywords: Engineering ; Engineering General
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    Large deformation analysis of plates and cylindrical shells by a mixed finite element method (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 731-746 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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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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    Keywords: Engineering ; Engineering General
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    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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    Reduction scheme for some structural eigenvalue problems by a variational theorem (1976)
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 845-852 
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    Keywords: Engineering ; Engineering General
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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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    On the finite element solution of an exterior boundary value problem (1976)
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    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)
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    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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    A hexagonal finite element with one degree-of-freedom per hexagon (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 958-959 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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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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    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
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    On the optimum shape of fillets in plates subjected to multiple in-plane loading cases (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1007-1019 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The shape of a plate in plane stress is determined, such that the maximum elastic stress corresponding to given loads is minimized. The shape of the boundary is approximated by a series and optimization is carried out by solving a sequence of linearized minimum-maximum problems using linear programming. The optimization problem is extended to include multiple loading cases and geometrical constraints. The stress derivatives are found using analytical expressions for stiffnesses and stiffness derivatives of the finite elements. For the optimum design of a hole in an infinite plate under biaxial stretching the numerical result is compared with an analytical solution. As another example the method is used to optimize the edge shape of a shape of a junction in a web frame.
    Additional Material: 10 Ill.
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    Stiffness matrix for a non-prismatic beam-column element (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1125-1142 
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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 is presented which generates an element stiffness matrix for non-prismatic beam-column members using Newmark's numerical procedure of successive approximations. The resulting element stiffness matrix on element co-ordinates is fond to be in excellent agreement with those available for limiting cases. An approximate stability analysis conducted on the covergence of the numerical scheme shows that the proposed algorithm is stable. The critical buckling loads for various and conditions are computed as part of the computational scheme. A computer program listing in FORTRAN IV is included which will handle essentially and order and/or kind of non-prismaticity of beam elements. The results are presented in the conventional and convenient coefficient format.
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    A hybrid element method for steady linearized free-surface flows (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1153-1175 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is first shown that the two-dimensional linearized ship wave problem can be recast as the sum of a radiation and a diffraction problem for simple harmonic waves. Each problem can be solved by a hybrid element method (HEM) where conventional finite elements are used near the body and analytical solutions are used in the remaining infinite regions (super-elements). Variational principles which incorporate the matching conditions between regular and super-elements as natural conditions are derived. Numerical examples are presented. The theoretical aspects for extending the above ideas to a three-dimensional ship wave problems are also described.
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    A quadrature method for finite intervals (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 708-712 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The quadrature rule for a finite interval obtained by transforming to an infinite range and applying the midpoint rule is examined. It is found that the condition required to make the quadrature exact for a constant integrand imposes severe practical limits. The method is very good for integrands with singularities near the endpoints but ineffective for oscillatory integrands.
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    A computer program for the Chebyshev solution of overdetermined systems of linear equations (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1197-1202 
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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.1620100521
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    A non-conforming element for stress analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1211-1219 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 5 Ill.
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    Computer plotting of stress contours in excavated slopes (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1261-1280 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The contouring of stresses in two-dimensional slopes is done quickly and efficiently by using the computer and an incremental plotter. The computer program developed here interpolates in two directions between centroids of finite elements at which the stresses are given, determines contour line co-ordinates, and plots the contours. This program can be easily modified to plot stresses produced by other two-dimensional finite element analysis programs as long as the arrangement of elements in the mesh is similar.
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    Stress intensity factors in anisotropic plates using singular isoparametric elements (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1281-1287 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A conformable displacement model is presented for the finite element analysis of stress intensity factors in linear elastic fracture mechanics. The method is an extension to anisotropic materials of the one developed by Benzley for isotropic materials. Very good agreement is shown for the case of inclined cracks in an orthotropic plate between finite element results and those obtained by least squares collocation of stress functions.
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    The solution of the three-dimensional Navier-Stokes equations using a new finite difference approach (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1299-1308 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for integrating the three-dimensional Navier-Stokes equations for a viscous, incompressible, laminar duct flow is given. A new method is applied to the derivation of stable, and second order accurate difference representations to the momentum transport and diffusion terms. Numerical examples are given.
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    The elasto-plastic analysis of plates using hybrid finite elements (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1343-1356 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An elasto-plastic plate-bending analysis is developed based on the finite element method and utilizing an assumed-stress hybrid (Pian) element. Plasticity is incorporated using the Prandtl-Reuss relations and isotropic hardening theory together with an incremental residual force technique. Several example solutions are included to demonstrate the ability of this approach in elasto-plastic plate-bending problems.
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    Finite element residual schemes for unconfined flow (1976)
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 1415-1418 
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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 procedure based on residual potential or flow concept is proposed for free surface flow through porous media. A preliminary example is solved by using the proposed procedure.
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    Convergence problems in the asymptotic expansions for the Bessel functions of complex argument (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1404-1406 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of Hankel's asymptotic expansions for the Bessel functions of large complex argument are discussed, and a method is proposed to avoid numerical problems derived from their implementation in computer programs. Whiel the error tolerance cannot in all cases be controlled by the user, excellent results can indeed be obtained with application of the proposed method.
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    Supercritical wing sections II, F. Bauer, P. Garabedian, D. Korn and A. Jameson, Springer-Verlag, Berlin, 1975. No. of pages: 296. Price DM28.00, $11.50 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1427-1427 
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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.1620100625
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    Continuous elements in the finite element method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 11-33 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The discretization of the media at all spatial co-ordinates but one is presented here. This partial discretization leads to continuous finite elements as opposed to fully discrete ones and the problem resolves, for the cases presented here, into a set of linear differential equations rather than algebraic equations. The general problem of first derivative functionals in elastostatics is considered and it is shown, in general, how the continuous finite elements required for the solution may be obtained. Plane states, axisymmetric and three-dimensional continuous elements are obtained to illustrate application to particular cases.Different methods of solution for the set of differential equations are discussed and it is shown that several existing and widely used finite element related techniques are particular cases of this local partial discretization. Three numerical examples are solved to demonstrate the good comparison obtained between the numerical and the exact solutions. The semi-infinite examples included also illustrate the treatment of these types of problems without the use of fictitious boundaries.
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    Some criteria for numerically integrated matrices and quadrature formulas for triangles (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 67-76 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For a wide calss of finite element matrices integrated numerically rather than exactly, a definable number of sampling points is found to be sufficient for keeping their theoretical properties unchanged. A systematic criterion limiting the number of possible point configurations for numerical quadrature formulas on triangles is established. Some new high order formulas are presented. Tables containing optional formulas with respect to minimum number of sampling points and required degrees of accuracy are given. They are arranged so as to assist with selection of suitable quadrature formulas for finite element computer programming.
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    Periodic Galerkin finite element method of tidal flow (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 115-127 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the finite element method of the analysis of tidal flow. Assuming that tidal flow is periodic, the Galerkin approach is employed as the numerical integration procedure in time using a trigonometric function as the interpolation function. The present method has shown to be suitable for computation especially from the point of computing time and numerical stability.
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    The visco-plastic approach to problems of plasticity and creep involving geometric non-linear effects (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 169-181 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The visco-plastic model is used in the context of large displacement (geometrically non-linear) analysis. As the process now involves in numerical computation an updating of relevant stiffness matrices, formulation which is stable and computtionally more efficient. The applications shown demonstrate the applicability of the process to large displacement elasto-plastic shell analysis as well as to problems of creep buckling.
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    Author's reply to R. A. Brockman's discussionInt. J. num. Meth. Engng, 12, 183-185 (1978) of ‘an isoparametric hermitian element for the solution of field problems’ (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 185-186 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120118
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    Erratum (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 194-194 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120202
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    Finite difference approximation of boundary conditions along irregular boundaries (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 229-235 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The approximation of normal derivatives along a curved boundary becomes a major difficulty in obtaining finite difference solutions for irregular regions. A number of authors (for-example, Allen,1 Fox,2 Greenspan3 and Parker and Ma4) have suggested various solutions to this problem. However, most of these suggested methods are fairly cumbersome to use since they require the use of different formulas for various combinations of mesh and boundary geometries. This note shows a different way to approximate a quite general boundary condition along curved boundaries. The method uses a uniformly spaced mesh, is simple, general, relatively easy to program and appears to give accurate results.
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    A partitioned parallel Runge-Kutta method for weakly coupled ordinary differential equations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 267-278 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In many systems it is known a priori, that some states are ony weakly coupled with others. If such systems are solved on parallel processor it is possible to partition the states in such a way that one set of states is assigned to one processor and the other set of weakly coupled states to another. Computations can then be done in parallel. Because of the weak coupling it may not be necessary for information from the two sets to be communicated to each other for many integration steps. This can result in significant cost savings. In this paper, a partitined Runge - Kutta scheme is formulated for use on weakly coupleld systems of ordinary differential equations. An error expression is derived which provides a means for predicting the number of step sizes over which the partitioned formulas can be used in terms of a prespecified error tolerance. Numerical examples are presented both to verify the error expressions and to compare solutions using partitioned and unpartitioned schemes.
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    A starting algorithm for the numerical simulation of two-phase flow problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 319-329 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The diferential equations governing two-phase flow through a porous medium are derived and the space discretization is carried out by the Galerkin finite element method. An examination of the eigenvalues of the resulting system follows in order to decide on a suitable stability criterion to be satisfied by the time-stepping algorithm. A class of time-stepping schemes is introduced and their behaviour when applied to a specific problem is analyzed. The aim is to achieve an adequate modelling of the water-oil interface and to preserve reasonable values of the capillary pressure. A technique to clustering the mesh around the interface is used to improved the modelling, and a boundary condition based on the relative mobilities of the two fiuids is imposed to enable the program to calculate the water-oil ratio after breakthrough. The effect of lumping the mass matrix is then examined with a view to reducting the surge in the values obtained for the capillary pressure. Finally an optimum method is suggested for use as a starting algorithm for more sophisticated time-stepping schemes.
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    Finite elements in geomechanics, Ed. by G. Gudehus, Wiley, Chichester, 1977. No. of pages: 573. Price: £17, $32.50 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 384-384 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620120217
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    A finite element method for Burgers' equation in hydrodynamics (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 415-428 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Finite Element Method using rectangular elements is applied to solve Burgers' non-linear equation in one space dimension. The non-linear algebraic equations thus obtained are solved by an iteration which is equivalent to the generalized Newton method. Numerical experiments indicate that the order of accuracy is equal to 2. In two space dimensions, the method is more efficient than other methods we have tested.
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    The indirect design of fluid channels using a global variational method with trial functions not satisfying the prescribed boundary conditions: II cupling method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 471-477 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A global variational method (GVM) not requiring the boundary conditions to be incorporated in the trial functions is described. The method is outlined for a linear differential equation and the extensions necessary to handle the non-linear problem of the indirect design of a compressible fluid channel described. The method requires a suitable estimate of a parameter, but the results obtained for the non-linear problem indicate that the actual value of this parameter is not critical (provided that a sufficeintly large number of trial functions is used). Comparisons are made with the results from an alternative GVM approach described in Davies and Hendry.1
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    The generalized problem of confined seepage (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 479-486 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of confined seepage of water under a hydraulic structure, through a porous medium, is considered in an appropriate abstract space. Existence and uniqueness of the solution are proved. The numerical solution is derived by means of the finite element method. An error estimate is given. A sample problems in included.
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    Letters to the editor (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1485-1486 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Announcements (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1487-1488 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Special topics volumes (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1491-1491 
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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.1620121002
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    Erratum (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1492-1492 
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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.1620121003
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  • 90
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    An iterative algorithm to build continuous stress and displacement solutions (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1493-1506 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative algorithm is presented: it builds a continuous stress and displacement solution starting from the solution of a classical displacement finite element analysis. The modified solution satisfies the virtual work principle, and is much better than the starting solution. The algorithm is very easily included in existing programs. A number of examples shows the efficiency of the method.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121004
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  • 91
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    The shear deformation of profiled metal sheeting (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1507-1541 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the stressed-skin analysis of metal structures it is vital to have a simple yet accurate treatment of the shear deformation of profiled metal sheeting. A suitable theory is developed in this paper for the two important cases of sheeting fastened to the supporting structure through every and alternate troughs of the corrugations. Various practical factors are taken into account. The results of an extensive series of numerical investigations are presented as a simple equation and a set of tables.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121005
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  • 92
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    Solution techniques for non-linear finite element problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1677-1696 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a classification of mathematical commonly encountered in connection with solution of non-linear finite element problems. The principal methods for numerical solution of the non-linear equations are surveyed and discussed. Special emphasis is placed upon the description of an automatic load incrementation procedure with equilibrium iterations. It is shown how this algorithm can be adapted for solving problems involving instabilities, snap-through and snap-back. A simple scalar quantity denoted the current stiffness parameter is suggested; this parameter is used to characterize the overall behaviour of non-linear problems. It can also be used as a steering parameter in the solution process. The use of the present technique is illustrated by several examples.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121106
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    An accurate method of dynamic condensation in structural analysis (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1705-1715 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new and efficient method of dynamic condensation is presented. It reduces the order of dynamic matrices without intoroducing further approximation by representing the passive co-ordinates in terms of the active ones exactly. The resulting frequency dependent eigenvalue problem is solved by a combined technique of Sturm sequence and subspace iteration. Examples are given for a space frame and a substructure problem. Results are compared to the complete solution.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121108
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    Blended infinite elements for paraboblic boundary value problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1841-1851 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A common method for numerically approximating two-point parabolic boundary value problems of the form ut = L[u]+f(u) defined of the semi-infinite strip S = [0, 1]×[0, ∞] is to first discretize the spatial operator in the differential equation and then solve for the time evolution. Such an approach typically involves solving a system of algebriaic equations at a sequence of time steps. In this paper we take a different approach and subdivide S into a collection of semi-infinite substrips Si = [xi, xi+1]×[0, ∞], and use blending function techniques to derive finite parameter functions ei(x, t) defined on Si. Spectral matching methods are used in deriving ei to ensure that (u - ei) can be made small on Si. Galerkin's method, with associated integration sover the entire space-time domain S, is then used to generate approximations to u(x, t) based upon the so defined infinite element (ei, Si). Approximations are hence found for all (x, t) in S by solving one well structed system of algebraic equations. We apply the method to several linear and non-linear problms.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121206
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    Calculation of optimum feedback gains for output constrained regulators (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1873-1878 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new and a simple algorithm for approximate calculation of optimal output-constrained feedback regulators is presented. computational simplicity is achieved by using properties of weakly coupled linear systems. The algorithm has been shown to be very effective in solving high dimensional control problems.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121208
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    On a problem arising from the derivation of finite element matrics using Reissener's principle (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1879-1882 
    Details
    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.1620121209
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    Limit analysis of structures formed from rigid blocks (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1853-1871 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a technique previously developed for the analysis of rigid-plastic structural frames is adapted to provide a formal procedure for finding the limit load of any structure formed from rigid blocks. In this procedure the load factor is maximized subject to the euilibrium equations of the structure and linear constraints imposed by criteria of failure at the block interfaces.In part I of the paper it is assumed that the limiting shear force associated with sliding at a block interface is independent of the normal component of force across the interface. This assumption means that the normality rule is satisfied, so that the upper- and lower-bound theorems of classical limit analysis apply. This part includes a description of computer program for the collapse analysis of masonry arches with joints incapable of carrying tension.In part II the limit on the Shear force at a block interface is assumed to be that associated with Coulomb friction. It is not difficult to extend the computational algorithm described in part I to deal with this situation. However, the failure mechanism computed by the algorithm will not necessarily satisfy the normality rule. The corresponding limit load may therefore be an over-estimate of the true failure load, even though it is computed by a lower-bound (equilibrium) approach. A criterion is established for testing the validity of a failure load computed in these circumstances.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121207
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    Numerische methoden der mechanik, J. Dankert. Festigkeits- und Schwingungsberechnung mittels elektronischer Rechentechnik, 162 illustrations. 318 pages. 1977. ISBN 3-211-81439-6. Paperback S338,DM 49 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1897-1897 
    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.1620121212
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    Masthead (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 13 (1978) 
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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.1620130101
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  • 100
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    Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 13 (1978), S. 1-16 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents an introduction to two general approaches used in the soluation of coupled structures and fluid systems in which effects of large scale flow are excluded. In the first approach, the Lagrangian, the fluid is simply treated as a ‘solid’ with a negligible shear modulus. In the second method, Eulerian, a single pressure variable is used in the fluid.The numerical problems posed, discretization methods used and possible simplifications are discussed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620130102
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