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  • 1
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Quadratic isoparametric elements which embody the inverse square root singularity are used in the calculation of stress intensity factors of elastic fracture mechanics. Examples of the plane eight noded isoparametric element show that it has the same singularity as other special crack tip elements, and still includes the constant strain and rigid body motion modes. Application to three-dimensional analysis is also explored. Stress intensity factors are calculated for mechanical and thermal loads for a number of plane strain and three-dimensional problems.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100103
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  • 2
    Electronic Resource
    Electronic Resource
    An Extended Matrix Transfer Method with an automatic root search capability (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 67-76 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An ‘Extended Matrix Transfer Method’ is presented which has an automatic root search capability that can be guaranteed to determine all the roots of the problem with the exception of those roots lying within prescribed tolerance bandwidths.The power and generality of the method is demonstrated by application to a specially synthesized problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100106
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  • 3
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The equations for the meridional through-flow in a turbomachine are formulated as a quasi-harmonic non-linear equation. This equation is then solved iteratively by the finite element method and in order to obtain convergence an under-relaxation factor has to be introduced. Comparisons with experimental results in single and multistage axial compressors show very good agreement. The finite element method is thus shown to be an efficient tool for this type of problem.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100108
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  • 4
    Electronic Resource
    Electronic Resource
    Theory and examples of partial approximation in the finite element method (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 115-122 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents theory and examples of partial approximation as a modification of the displacement method in the finite element analysis. This method requires different shape functions for different terms in the potential energy expression to curtail the processes in the standard displacement method. Explanation of the theory is given by use of a simple example for Poisson's equation. It can also be effectively utilized to give mathematical foundation to some finite element models based on physical reasonings, such as Melosh's rectangular element for plate bending and beam element approximation of circular arches.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100109
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  • 5
    Electronic Resource
    Electronic Resource
    The calculation of branch flows in a directed network (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 123-131 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a procedure for the calculation of branch flows in a directed network in which the node-to-node flows are prescribed.The node-to-node paths of the network are enumerated using a combinatorial process. Procedures based on the path list are used to allocate the node-to-node flows to the alternative paths of the network according to Wardrop's first principle. The calculation, although necessarily iterative, is rapidly convergent.The method has been implemented as a computer program and the results obtained for a typical network are discussed.A linear relationship between branch potential and branch flow has been used, but the method can be extended to piece-wise linear and non-linear relationships.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100110
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  • 6
    Electronic Resource
    Electronic Resource
    Sequential interpolation functions (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 133-143 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper it is shown how to achieve special interpolation functions that can be applied to the finite element method, least squares methods or other related numerical techniques. We call these functions sequential interpolation functions since one of the main characteristics of this technique refers to the fact that the refinement of the solution does not require the redefinition of the interpolation funtions used in a previous step, as the case for instance in the FEM.The present theory and the FEM using an isoparametric element were compared for a plane stress problem. The results show that both have the same degree of accuracy. The choice of the sequential interpolation functions is easier than those used in the finite element formulation and the computer time was reduced by about 50 per cent.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100111
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  • 7
    Electronic Resource
    Electronic Resource
    Technical note: Horizontally curved beam finite element including warping (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1397-1403 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100618
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  • 8
    Electronic Resource
    Electronic Resource
    A new finite element scheme for instability analysis of thin shells (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 145-170 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a new finite element scheme for the analysis of instability phenomena of arbitrary thin shells. A computationally efficient procedure is proposed for calculating the non-linear stiffness and tangential stiffness matrices for a doubly-curved quadrilateral element defined by co-ordinate lines. The essential feature is the explicit addition of the non-linear terms into the rigid-body motion of the element. Thus the non-linear and tangential element stiffness matrices can easily be generated by transforming the generalized element stiffness matrix for linear analysis, and the non-linear terms of these matrices are separated into a number of component terms multiplied by the rigid-body rotations. These component terms can be stored permanently and used to calculate efficiently the non-linear and tangential stiffness matrices at each iteration. Illustrative examples are presented which confirm the validity of the present approach in the analysis of instability phenomena of thin plates and shells.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100112
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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problems associated with the stress analysis of structures subjected to body force loading due to compound motion are outlined. An economic method for calculating equivalent nodal loading, for use in a finite element displacement analysis, is proposed in which the element discretization and consistent mass matrices are used to advantage. The relevant equations, relating to the rigid body dynamics of compound motion, are appended in matrix notation. Validity of the method is demonstrated by an analysis of the stresses, due to gyroscopic and centrifugal forces, in an aero engine blade model.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100115
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  • 11
    Electronic Resource
    Electronic Resource
    Domain mappings for the numerical solution of partial differential equations (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 211-223 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Independent variable transformations of partial differential equations are examined with regard to their use in numerical solutions. Systems of first order and second order partial differential equations in conservative and nonconservative form are considered. These general equations are transformed using generalized mapping functions and important computational features of the transformed equations are discussed. Examples of mappings which regularize domains are given involving various types of partial differential equations. These mappings are of particular importance in finite difference approximations because of the ease with which a mesh can be adapted to regions formed by co-ordinate lines.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100116
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  • 12
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Alternative finite difference formulations for elliptic equations on skew nets are investigated for suitability for rapid convergence of S.O.R. iterations. In dealing with the differential equation directly, diagonal dominance is a key property for convergence theorems. Mixed derivatives boundary conditions threatens this property, but formulas are presented which protect it as long as the net skewness is not too severe. Test calculations are reported showing convergence for these formulas to be as good as that of optimal S.O.R. theory, whereas other more direct formulas give a very inferior performance.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100117
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  • 13
    Electronic Resource
    Electronic Resource
    Announcement and call for papers (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 238-240 
    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.1620100120
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  • 14
    Electronic Resource
    Electronic Resource
    Discussion of paper by R. D. Henshell and K. G. Shaw (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 235-237 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100119
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  • 15
    Electronic Resource
    Electronic Resource
    An algorithm for minimal degree linear Chebyshev approximation on a discrete set (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 619-635 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm for computing a linear Chebyshev approximation to a function defined on a finite set of points is presented. The method requires the accuracy of the approximation to be specified, and determines the least degree approximation which achieves this accuracy. The algorithm is based upon the simplex method of linear programming. A FORTRAN program is supplied in the Appendix.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100311
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  • 16
    Electronic Resource
    Electronic Resource
    A simultaneous iteration algorithm for symmetric eigenvalue problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 647-663 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A FORTRAN IV algorithm is presented for determining sets of dominant eigenvalues and corresponding eigenvectors of symmetric matrices. It is also extended to the solution of the equations of natural vibration of a structure for which symmetric stiffness and mass matrices are available. The matrices are stored and processed in variable bandwidth form, thus enabling advantage to be gained from sparseness in the equations. Some of the procedures may also be used to solve symmetric positive definite equations such as those arising from the static analysis of structures loaded within the elastic range.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100313
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  • 17
    Electronic Resource
    Electronic Resource
    Mathematical model and boundary conditions in stress analysis relating to steam turbine rotors, under transient operating conditions (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 345-360 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An appropriate mathematical model for calculation of thermoelastic stress in steam turbine rotors, under transient operating conditions, is developed in the framework of so called uncoupled quasi-static theory. The numerical analysis has been carried out by means of the finite element code ANGUS, the accuracy of which has been evaluated by comparing it with an analytical solution given by one of the authors in Reference 2. It has been shown that, with an appropriate choice of thermal and elastic boundary conditions, it is possible to carry out stress transient analysis considering only a segment of the hottest zone of high or intermediate pressure body of rotors. The paper includes a comparison study of the influence of two types of thermal boundary conditions in the labyrinth glands.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100207
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  • 18
    Electronic Resource
    Electronic Resource
    A thick finite strip solution for static, free vibration and stability problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 665-678 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite strip method for the analysis of plate bending problems is described. This method, which takes into account the effects of transverse shear deformation, is applied to the static analysis of a curved plate and then to the free vibration and stability of thick and thin plates.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100314
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  • 19
    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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  • 20
    Electronic Resource
    Electronic Resource
    An iterative penalty function method in structural analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 413-421 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative solution process combined with the penalty function method employed in constrained variational priciples is described. As an example of the use of the method an axi-symmetric plate with the complementary energy formulation is considered.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100211
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  • 21
    Electronic Resource
    Electronic Resource
    Rubber covered rolls - the thermoviscoelastic problem. A finite element solution (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 767-785 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The coupled thermomechanical behaviour of a layer of thermorheologically simple material bonded to a uniformly rotating rigid cylinder and indented by another rigid cylinder is studied by the finite element method. The various approximations necessary to reduce the problem to one of tractable size and the computational methods used are discussed in some detail. The complete thermal, deformation and stress fields may be computed. Some results, computed for a grid using ‘rectangular’ elements, presented graphically include the temperature distribution, the stress distribution near the bond surface, the contact pressure distribution and the asymmetric surface deformation of the rubberlike layer.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100405
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  • 22
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automatic algorithm is presented for reducing the bandwidth of symmetric sparse connectivity matrices. The procedure takes an arbitrary input sequence and creates an optimal bandwidth for complex network systems by renumbering the node labels. Thus, considerable improvement for computer storage and time is achieved in the solution of the systems.A large number of examples is presented to demonstrate the reliability and the efficiency of the method.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100406
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  • 23
    Electronic Resource
    Electronic Resource
    A Poisson equation solver for rectangular or annular regions (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 799-807 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A FORTRAN subroutine is presented which solves the system of simultaneous linear equations associated with the finite difference representation of the Poisson equation for rectangular or annular regions. The code is arranged to require minimum storage, and all possible operations involving known zeros and ones are suppressed. Single subscripting is employed to minimize execution time.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100407
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  • 24
    Electronic Resource
    Electronic Resource
    Efficient least squares finite elements for two-dimensional laminar boundary layer analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 809-825 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the formulations of essentially one-dimensional least squares and Galerkin-least squares finite elements for the numerical solution of two-dimensional laminar boundary layer equations. An iterative technique to cope with the non-linearity of the boundary layer equations, in conjunction with the least squares finite element method, is proposed. Through exhaustive numerical investigations in the retarded flow over a plate, flow past a circular cylinder, the flow past an elliptic cylinder, the accuracy and applicability of the proposed method are demonstrated.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100408
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  • 25
    Electronic Resource
    Electronic Resource
    A simple finite-difference modification for improving accuracy near a corner in heat flow problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 827-832 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100409
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  • 26
    Electronic Resource
    Electronic Resource
    Reduction scheme for some structural eigenvalue problems by a variational theorem (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 845-852 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100411
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  • 27
    Electronic Resource
    Electronic Resource
    Splines and variational methods, M. Prenter, Wiley, New York, 1975. £10.75 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 487-487 
    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.1620100222
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  • 28
    Electronic Resource
    Electronic Resource
    Linear and non-linear waves, G. B. Whitham, Wiley, New York. Price: £12.15. 636 pages (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 488-488 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100223
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  • 29
    Electronic Resource
    Electronic Resource
    Masthead (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976) 
    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.1620100301
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    Definition of programming languages by interpreting automata, Alexander Ollengren, Academic Press, Price £9.00 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 488-488 
    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.1620100224
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  • 31
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    Numerical quadrature and two-dimensional radiative heat transfer (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 491-502 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Four methods of numerically integrating a two-variable integral equation, which is used to describe non-dimensional radiosity in a diffuse grey cavity, are presented. Physical reasoning is used to organize the successful method for obtaining physically plausible solutions.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100302
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  • 32
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    Transformation of elliptic partial differential equations for solving two-dimensional boundary value problems in fluid flow (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 527-533 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is possible to transform elliptic partial differential equations to exchange the dependent with one of the independent variables. The Laplace equation for a stream function ‘Ψ’ over the X and Y co-ordinate system, for example, can be transformed into a relationship expressing the Y position of streamlines in terms of strem function Ψ and X.Although the resulting new partial differential equation is much more complex it is much more convenient to use in a computer. An irregular Y boundary becomes, with the new relationship, merely the boundary values assigned to the outer streamlines and the computer always need only deal with a rectangular array. The resulting answer is in the form of the position of streamlines which is the information directly required for plotting flow maps.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100304
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    On the relationship between the finite element and finite difference methods (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 893-923 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The integral equations which arise from application of the Galerkin-finite element scheme to the convective diffusion equation are examined to illustrate how this method represents differential equations. The formulae obtained are effectively spatial averages of standard finite difference equations written at a node. The truncation error in the finite element solution at a node is obtained for various nodal configurations.
    Additional Material: 9 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100416
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    On the construction of conforming rectangular plate elements (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 925-933 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100417
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  • 35
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    On the finite element solution of an exterior boundary value problem (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 885-891 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100415
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  • 36
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    Subspace iteration accelrated by using Chebyshev polynomials for eigenvalue problems with symmetric matrices (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 935-944 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100418
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    Efficient large scale non-linear transient analysis by finite elements (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 579-596 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100308
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  • 38
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    Artificial adjustment of element stiffness with a particular reference to plate bending (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 945-949 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element may satisfy all convergence requirements and work well except for being too stiff or too flexible when the mesh is coarse. Here we discuss a technique for softening or stiffening such elements, provided that they have internal degrees-of-freedom. The technique is applied to a previously derived plate element, and the element is found to be much improved.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100419
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  • 39
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100425
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  • 40
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    Inners and stability of dynamic systems, E. I. Jury, Wiley, London, 1974. No. of pages: 308. Price: £9.70 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 975-975 
    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.1620100428
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  • 41
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    Computational mechanics, vol. 461 of lecture notes in mathematics, edited by J. T. Oden (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 976-976 
    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.1620100429
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  • 42
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    Thermodynamics and thermophysical properties of combustion products. Vol. II: Oxygen-based propellants (translated from Russian). V. E. Alemasov et al. Keter Publishing House, Jerusalem Ltd., Price: £14.95 (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 975-975 
    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.1620100427
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  • 43
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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 
    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.1620100430
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    Masthead (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976) 
    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.1620100501
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  • 45
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    An iterative technique for fitting exponentials (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 979-990 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interative method to fit the function \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[y = \sum\nolimits_i^n { = 1} a_i e^{lix}\] $\end{document} to data is considered. The technique used is that of inversion of a linear differential operator with constant coefficients. This method reproduces the parameters for mathematically precise data and gives satisfactory results when the data are affected by random errors.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620100502
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  • 46
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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 
    Details
    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.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100505
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  • 47
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    Computing three-dimensional free surface flows (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1143-1152 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element techniques are developed for the analysis of high-speed three-dimensional free surface flows within the context of potential flow theory. The primary dependent variable is the velocity potential, which is approximated as a quadratic within each isoparametric element. An iterative approach is used to seek the initially unknown free surface location.A high-speed fluid jet issuing through an orifice plate into a transvese gravity field is examined to illustrate features of the approach. Convergence of the solutions is very good at a Froude number of 3-53 but deteriorates as F nears unity.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100513
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  • 48
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    Beam-column element for inelastic analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1177-1178 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100515
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  • 49
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    On reduced integration in solid isoparametric elements when used in shells with membrane modes (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1179-1182 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100516
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  • 50
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    The generation of elements with singularities (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1249-1259 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure is given for generating two-dimensional conforming singularity elements from standard conforming elements. Three new elements with 0(r-p) derivative singularities are introduced. The technique is based on the use of elements defined by numerically integrated shape functions. Special quadrature rules are suggested for triangular elements. The degeneration of these elements to crack tip elements and the direct evaluation near the singularity of element quantities, such as the stress intensity factors, is discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100605
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    Computation of the feedback vector for single-input linear multivariable systems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1411-1414 
    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.1620100621
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    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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    Finite element large deflection analysis of shallow shells (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 39-58 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation is presented to study the non-linear buckling of arbitrary shallow elastic thin shells with general boundary conditions and subjected to conservative pressure loading. Pre and post buckling behaviour of a large number of shallow and semi deep doubly curved shells is studied in detail. Unsymmetrical bifurcation paths of a shallow spherical shell subjected to uniform inward pressure are also investigated.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100104
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    Masthead (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976) 
    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.1620100601
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  • 55
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    PFVIBAT - a computer program for plane frame vibration analysis by an exact method (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1221-1231 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The described program PFVIBAT uses the exact displacement method to perform free and forced vibration analysis entirely within the differential equation theory of beams thus avoiding assumed modes and lumped masses. The frame may contain rigid bodies. Clamped, hinged, guided and rolling connections are allowed for. Consideration of rotatory inertia, shear deformation and second-order bending moments and shear forces as caused by static axial load is optional. Eigenfrequencies and modal masses are calculated with an accuracy that may be specified. Displacement and moment modes are plotted. Transient vibrations are studied.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100603
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    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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    Masthead (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976) 
    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.1620100201
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    Enumeration of networks (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 230-235 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of previous workers relating the number of internal and external vertices in a two-dimensional network to the number of elements of one given geometry are generalized to cover elements of any geometry (not necessarily convex) and any number of edge nodes, which may be vertex nodses of adjacent elements.It is shown that a relationship between the number of elements and number of vertices (nodes) alone exists only on a surface (plane or otherwise) and therefore cannot be extended to three-dimensional networks.In three-dimensions, the number of elements with any number of edges and vertices is related to the number of internal and external edges and vertices, is related to the number of internal and external edges and vertices, enclosed by a surface which may be non-simple, (i.e. of topological genus greater than zero).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100118
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    Optimal stress locations in finite element models (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 243-251 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The existence of optimal points for calculating accurate stresses within finite element models is discussed. A method for locating such points is proposed and applied to several popular finite elements.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100202
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    Transmission-line matrix solution of waveguides with dielectric losses (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 253-262 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The transmission-line matrix method is a time-domain numerical method for solving wave problems. This paper describes how a minor change in the computer program for loss-free dielectrics extends the method to include dielectric losses. Results are given in terms of the wave impedance of a waveguide with losses, and also in terms of power decay due to losses in the dielectric of a resonant cavity.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100203
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    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.
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    URL: http://dx.doi.org/10.1002/nme.1620100205
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    A simple cubic displacement element for plate bendingBritish Crown Copyright, reproduced with the 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. 263-281 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Early attempts to construct a triangular finite element for plate bending problems from a compatible cubic displacement field are not entirely satisfactory. The present paper shows how an accurate plate element can be achieved using independent cubic polynomial assumptions for the internal and boundary displacements in conjunction with a modified potential energy principle. This approach yields a simple algebraic formulation with favourable connection quantities at the element vertices which will appeal to practical users of the conventional finite element displacement method. Moreover, in Appendix I it is shown that the cubic element is identical to a previous hybrid stress element with linear internal bending and twisting moments and cubic boundary displacements. The stresses obtained from the former hybrid finite element solution therefore satisfy the strain compatibility conditions exactly. This remarkable result has an important significance in the theory of hybrid finite elements.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100204
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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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    On a numerical solution of the supersonic panel flutter eigenproblem (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 637-645 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automated digital computer procedure is presented in this paper which enables efficient solution of the eigenvalue problem associated with the supersonic panel flutter phenomena. The step-by-step incremental solution procedure is based on an inverse iteration technique which effectively utilizes solution results from the previous step in determining such results during the current solution step. Also, the computations are limited to the determination of a few specific roots only, which are expected to contain the flutter mode, and this is achieved at each step without having to compute any other root.The structural discretization achieved by the finite element method yields highly banded stiffness, mass, and aerodynamic matrices; the aerodynamic matrix evaluated by the linearized piston theory is real but unsymmetric in nature. The solution algorithm presented in this paper fully exploits the banded form of the associated matrices, and the resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most efficient and economical when compared to existing procedures of such analysis. Numerical results are presented for a two-dimensional panel flutter problem.
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620100312
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100209
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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 
    Details
    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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    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.
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    URL: http://dx.doi.org/10.1002/nme.1620100212
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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 
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    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.
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    URL: http://dx.doi.org/10.1002/nme.1620100213
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    Comparison of curve fitting techniques (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 457-463 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Various methods of curve fitting used in solving aero-thermodynamic problems of turbomachines have been compared. The first and second derivatives predicted by using orthogonal polynomial fits are much more accurate than those obtained by using spline fits (with different boundary conditions) and method of least squares.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100214
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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 
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    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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    A comment on Gopalacharyulu's 24 node element (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 471-472 
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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.1620100216
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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 
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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.1620100217
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    A further discussion of a paper by K. K. Gupta (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 474-475 
    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.1620100218
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    Announcement and call for papers (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 484-487 
    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.1620100221
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    On the numerical solution of phase change problems in transient non-linear heat conduction (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 833-844 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite difference solution for the transient non-linear heat conduction with phase change in a finite slab is proposed. A two-time level implicit method is used while Taylor's forward projection method is employed for taking into account the non-linearities. The stability due to the boundary conditions at the moving front is verified. The numerical solution is compared with the analytical solutions and found to be in close agreement.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100410
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    Numerical techniques in probabilistic load flow problems (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 853-860 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes numerical techniques which have been developed in order to solve the load flow problem of a power system network probabilistically instead of using normal deterministic methods. The aim in the development of these techniques has been to reduce the computational time and storage commensurate with maintaining a high degree of accuracy.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100412
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    The analysis of rotational shells using a curved ring element and the mixed variational formulation (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 861-872 
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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 for the analysis of rotational shells using a mixed variational formulation is proposed. The element has arbitrary curvature in the meridional plane, its geometry being given by the values of the axial and radial co-ordinates, slope and meridional curvature at the nodal circles. A linear variation in the thickness was included in the formulation as was an orthotropic material. Test cases of flat plates and spherical shells indicate that a high degree of accuracy is obtainable with relatively small number of elements.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100413
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    A numerical model for the simulation of two-dimensional convective-dispersion in shallow estuaries (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 873-883 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical model for describing two-dimensional convective-dispersive processes in tidally influenced shallow bays in given. The model uses a multi-stage implicit technique with finite difference formulation, for solving the basic mass balance equation for a conservative constituent. The basic inputs to this model consist of instantaneous tidal velocities and depths obtained from an operational tidal hydrodynamic model.The sensitivity of the output concentrations to the variation of dispersion coefficients is investigated. Application of the model to a practical situation is demonstrated by considering Galveston Bay. Texas, U.S.A. The transport model is operated to generate results which are compared with measurements from dye release studies made in a physical model of Galveston Bay.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100414
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    Design of efficient stiffened shells of revolution (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 535-549 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100305
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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 
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    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.
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    URL: http://dx.doi.org/10.1002/nme.1620100303
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    A degenerate solid element for linear fracture analysis of plate bending and general shells (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 551-564 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general curved element of arbitrary shape for both thick and thin shells is proposed for the linear fracture analysis of a through crack in a shell or a plate. The element is derived from a degenerate 20-noded solid isoparametric element using reduced integration technique. The 1/√(r) singularity of the strains is obtained by the same procedure proposed earlier for two- and three-dimensional problems,1,2 viz. by placing the mid-side nodes near the crack at the quarter points.Several illustrated examples ranging from classical solutions to practical problems are given to assess the accuracy of solution attainable.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100306
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    Non-linear programming - gradient projection via orthogonalization (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 950-953 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Large scale non-linear programming problems with non-linear constraints are of practical concern in the areas of process control and system design. Although advances in computer technology address these problems, more efficient algorithms are needed. An algorithm currently used is Rosen's Gradient Projection Method. This note presents an alternative technique of performing the steps for finding the projected gradient used in Rosen's method, a technique that gives equivalent results with fewer computations.
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    URL: http://dx.doi.org/10.1002/nme.1620100420
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    Remarks on a method for solving second order differential equations (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 964-967 
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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.1620100424
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    Difference schemes for second order hyperbolic equations (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 960-964 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Implicit difference methods for the wave equation in two space variables have been discussed with the help of a stability diagram. The difference methods of intermediate accuracy 0(h4+k2) have been determined. A method of order of accuracy 0(h2+k2) with minimum truncation error has also been found.
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    URL: http://dx.doi.org/10.1002/nme.1620100423
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    Author's reply to a recent discussion (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 974-974 
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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.1620100426
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    Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 991-1005 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The field equations of three-dimensional elastostatics are transformed to boundary integral equations. The elastic body is divided into subregions, and the surface and interfaces are represented by quadrilateral and triangular elements with quadratic variation of geometry and linear, quadratic or cubic variation of displacement and traction with respect to intrinsic co-ordinates. The integral equation is discretized for each subregion, and a system of banded form obtained. For the integration of kernel-shape function products, Gaussian quadrature formulae are chosen according to upper bounds for error in terms of derivatives of the integrands. Use of the integral formulation is illustrated by the analysis of a prestressed concrete nuclear reactor pressure vessel.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620100503
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620100504
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    Derivatives and their error bounds in second order problems by finite element (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1065-1075 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A previous paper by the authors presented a finite element technique for computing accurate and bounded solutions at arbitrary points in second order mixed boundary value problems. The technique is extended herein to the computation of accurate and bounded derivatives at arbitrary interior points. Numerical results are presented to illustrate both the strengths and limitations to the method.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100508
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  • 89
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    A finite element Galerkin formulation and its numerical performance (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1077-1095 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element Galerkin formulation admitting non-homogenous boundary conditions and discontinuous approximants is derived from a variational principle. The procedure results in matrix equations explicitly allowing for jump discontinuties across interelement boundaries. As an illustration, a specialization of the procedure similar to a reduced integration technique is used to solve several problems in elastostatics. The improvement in accuracy in comparison with conventional methods is remarkable.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100509
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  • 90
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    Optimum structural design with stability constraints (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1097-1114 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an optimization method based on optimality criterion for minimum weight of structures with stability requirements. A recurrence relation is derived and the method is explained in the context of the displacement method of finite element analysis. The incipient buckling of the structure is determined by a linear eigenvalue solution. The method is programmed for trusses and frames. Illustrative problems are given to show the applicability of the method of design of structures with a large number of design variables.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100510
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  • 91
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100512
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  • 92
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    A new method of integration over polynomal finite element boundaries (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1115-1124 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this note we are developing integration techniques for triangular regions in which one side is curved. Specifically, we are considering (a) general polynomial boundaries and (b) various combinations of elliptical boundaries. Integration is performed over all of these explicitly.One definite and considerable improvement achieved is the introduction of a new method of integration over polynomial type boundaries. This new method is not only exact for polynomials or other analytic functions, but also reduces the computing time considerably; for example, if for a sixth order polynomial the number of operations necessary (using previously available methods) to perform the integration was n, the method introduced here requires a number proportional to n1/6. Furthermore, coding time is also reduced considerably. It may be of value to mention that the availability of the results presented here could obviate the need for the use of isoparametric elements in some regions with curved boundaries.For completeness, explicit integration formulas for elliptic shaped regions are also listed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100511
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  • 93
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    A discussion on optimization of an alkylation process (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1187-1190 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100518
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  • 94
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    A note on optimization of an alkylation process (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1191-1193 
    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.1620100519
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  • 95
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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 
    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.1620100521
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  • 96
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    Numerical solution of Fredholm integral equations with a logarithmic singularity (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1202-1207 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Generalized quadrature is used for the numerical solution of two Fredholm integral equations which occur in electrostatics and aerodynamics.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100522
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  • 97
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100602
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  • 98
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    Automatic generation of triangular grid: I - subdivision of a general polygon into convex subregions. II - triangulation of convex polygonsWork reported here is drawn from the thesis of the author, supervised by Dr M. J. M. Bernal and submitted in partial fulfilment of the requirements for the degree of PhD at the University of London. (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1329-1342 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: One of the integral parts of any finite element procedure is the subdivision of a finite dimensional region into a finite number of non-overlapping subregions. An algorithm for subdivision of 2-dimensional polygons into triangular subregions is presented here. The algorithm consists conceptually of two steps. In the first step the region is subdivided into convex subregions; In the second step the convex subregions are further subdivided into triangular elements.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100612
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  • 99
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    Sensitivity of inelastic response to numerical integration of strain energy (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1369-1377 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross-section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the non-linear transient responses of a beam with solid cross-section and that of a thin-walled beam on elastic supports under impulsive loads are examined.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100615
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  • 100
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    Finite element methods for second order differential equations with significant first derivatives (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1389-1396 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Galerkin finite element methods based on symmetric pyramid basis functions give poor accuracy when applied to second order elliptic equations with large coefficients of the first order terms. This is particularly so when the mesh size is such that oscillations are present in the numerical solution. In the present note asymmetric linear and quadratic basis functions are introduced and shown to overcome this difficulty in an appropriate two point boundary value problem. In particular symmetric quadratic basis functions are oscillation free and highly accurate for a working range of mesh sizes.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100617
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