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  • Electronic Resource  (489)
  • 1970-1974  (489)
  • Engineering General  (489)
  • Nuclear reactions
  • 101
    Electronic Resource
    Electronic Resource
    Announcement (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 240-240 
    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.1620070216
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  • 102
    Electronic Resource
    Electronic Resource
    Comparison of some penalty function based optimization procedures for the synthesis of a planar truss (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 155-173 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present investigation examines the multibar truss optimization problem in the context of a general class of unconstrained optimization procedures in conjunction with various types of penalty function transformations. Specifically, the problem is transformed into a series of unconstrained minimization problems using the penalty function techniques of Heaviside and SUMT. These are solved using the methods of Rosenbrock (orthogonal directions), Powell (conjugate directions) and Nelder-Mead (Simplex). This resulted in many cases in substantial improvements being recorded over previously reported data. The paper includes a comparative study of the synthesis based on these procedures.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070206
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  • 103
    Electronic Resource
    Electronic Resource
    Construction of curvilinear co-ordinate systems and applications to mesh generation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 461-477 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Computer-oriented mesh generators, which serve as pre-processors to finite element programs, have recently been developed by several investigators to alleviate the frustration and to reduce the amount of time involved in the tedious manual subdividing of a complex structure into finite elements. Our purpose here is to describe how the techniques of bivariate ‘blending-function’ interpolation, which were originally developed for, and applied to, geometric problems of computer-aided design and numerically controlled machining of free-form surfaces such as automobile exterior panels, can be adapted and applied to the problems of mesh generation for finite element analyses. We concentrate attention on the problem of curvilinearly co-ordinating simply connected planar domains R by constructing invertible maps of the unit square S ≡[0, 1] × [0, 1] onto R. Extensions of the methods described herein to shells in 3-space is straightforward and is illustrated by a practical example taken from the automobile industry. Analogous mesh generators for three-dimensional solids can be developed on the basis of the trivariate ‘blending-function’ formulae found at the end of the second section.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070405
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  • 104
    Electronic Resource
    Electronic Resource
    The efficient finite element analysis of rectangular and skew laminated plates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 309-323 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Various solutions of laminated plates by the finite element method are analysed. An efficient solution of skew (or rectangular) laminated plates with small effect of σz and ∊z stress and strain components is developed. It can be used with an arbitrary number of layer elements (sub-elements) in different plate elements. Some remarks to the possible modification of solution are presented. Numerical examples with a short discussion and conclusions complete the paper.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070308
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  • 105
    Electronic Resource
    Electronic Resource
    A hybrid-element approach to crack problems in plane elasticityPortions of this work were accomplished when the first author served as a visiting professor at the Istituto di Elaborazione dell'Informazione, Consiglio Nazionale delle Ricerche, Pisa, Italy, during the summer of 1972. The completion of this work was supported by the AFOSR under Contract No. F44620-72-C-18. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 297-308 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The hybrid-element concept and the complex variable technique have been adopted for constructing a special super-element to be used jointly with conventional finite elements for the analysis of elastic stress intensity factors for plane cracks. The use of the complex variable technique permits the proper consideration of the stress intensity at the crack tip, and it also leads to very efficient programming. The use of such a super-element in the finite element solution has been shown to be highly accurate when only a very coarse element mesh is used near the crack.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070307
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  • 106
    Electronic Resource
    Electronic Resource
    Finite element technique applied to heat conduction in solids with temperature dependent thermal conductivity (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 345-355 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Consider a solid heat conductor with a non-linear constitutive equation for the heat flux. If the material is anisotropic and inhomogeneous, the heat conduction equation to be satisfied by the temperature field θ(x, t) is, \documentclass{article}\pagestyle{empty}\begin{document}$$ \rho c\frac{{\partial \theta }}{{\partial t}} = {\rm div}({\rm L}(\theta,{\rm x})[{\rm grad}\theta]) + q $$\end{document} Here L(θ, x) [grad θ] is a vector-valued function of θ, x, grad θ which is linear in grad θ, In the present paper, the application of the finite element method to the solution of this class of problems is demonstrated. General discrete models are developed which enable approximate solutions to be obtained for arbitrary three-dimensional regions and the following boundary and initial conditions: (a) prescribed surface temperature, (b) prescribed heat flux at the surface and (c) linear heat transfer at the surface. Numerical examples involve a homogeneous solid with a dimensionless temperature-diffusivity curve of the form κ = κ0(l + σT). The resulting system of non-linear differential equations is integrated numerically.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070311
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  • 107
    Electronic Resource
    Electronic Resource
    Gaussian quadrature formulas for triangles (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 405-408 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several formulas are presented for the numerical integration of a function over a triangular area. The formulas are of the Gaussian type and are fully symmetric with respect to the three vertices of the triangle.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070316
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  • 108
    Electronic Resource
    Electronic Resource
    Anisotropic parametric plate discrete elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 413-425 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A limitation of most plate and shell discrete elements now in use is the shape of their undeformed geometry. Typically, the plan form of these elements is a straight-sided triangle or quadrilateral that linearly approximates the undeformed geometry while often using higher-order polynomials to approximate the deformed geometry. This modelling difference leads to inefficiencies that can be eliminated, as demonstrated by a new parametric discrete element based entirely on bicubic Hermite polynomials. This representation of element geometry corresponds to the bicubic Coon's surface patch widely used in design, which allows a common mathematical model for design and analysis. Consideration is given to automating the generation of these patches. Solutions are presented for several plate bending and plate stretching problems. The solutions are in good agreement with closed-form solutions and photoelastic results in the case of a stress-concentration problem. These data demonstrate that the new parametric discrete element maintains solution accuracy for plates with curved boundaries.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060311
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  • 109
    Electronic Resource
    Electronic Resource
    Accuracy of the finite element analysis for the elastic plate with a circular hole (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 443-446 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper compares the results obtained by the finite element method with ‘exact’ solutions to a given set of problems. These are the stresses on the boundary of a hole in an infinite plate, the plate being subjected to three different types of loading. Two types of element are used for these plane stress problems, triangular elements with constant strains and tri- angular elements with linearly varying strains. The problems are solved for two different meshes and the results shown are stresses along a radial section and the values derived for stress concentrations against the number of unknowns in each mesh.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060314
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  • 110
    Electronic Resource
    Electronic Resource
    Note on the residual force method - Comment on reference 1 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 446-447 
    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.1620060315
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  • 111
    Electronic Resource
    Electronic Resource
    Finite element analysis of bonded connections (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 450-451 
    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.1620060318
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  • 112
    Electronic Resource
    Electronic Resource
    Numerical control: Mathematics and applications, P. Bézier, Wiley, London, 1972. No. of pages: 240. Price: £4.95 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 456-456 
    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.1620060322
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  • 113
    Electronic Resource
    Electronic Resource
    Mathematical models of synchronous electrical machines (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 459-466 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with developments in mathematical modelling of turbo-generator units for use in the dynamic analysis of electrical power systems. Emphasis is placed on an over-all reduction in computing time, whilst retaining a high order of accuracy of transient response. Accurate linear models are then derived and provide an alternative to the piecemeal formulations hitherto employed in small signal analysis. These equations form a practical basis for the synthesis of optimal control systems for large alternators.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060402
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  • 114
    Electronic Resource
    Electronic Resource
    A new finite element method for analysing symmetrically loaded thin shells of revolution (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 475-487 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An essential feature of finite element methods of analysis for symmetrically loaded shells of revolution is the setting up of equations representing the response of a short ‘ring’ element to edge loading.In this paper the axisymmetric behaviour of a short elastic cylindrical shell element under edge loading is described in a new way by means of a matrix which is a combination of stiffness, flexibility and ‘neutral’ sub-matrices. The coefficients of the matrix are derived direct from the equations of the problem, which involves a trivial amount of work in comparison with conventional methods.The corresponding matrix for a short section of an arbitrary shell of revolution is set up with little additional effort, and its use is described for calculation of edge response coefficients for portions of spherical shells.Finally, the method is used to study by iteration the behaviour of a thin spherical shell of viscous material containing a rigid boss which is loaded radially inwards: changes in meridional profile are followed as deformation proceeds. Results are presented for both linear and non-linear viscous material.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060404
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  • 115
    Electronic Resource
    Electronic Resource
    A new relaxation method for obtaining the lowest eigenvalue and eigenvector of a matrix equation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 511-519 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The matrix eigenvalue problem Hui = λi ui is considered. It is shown that when a new approximate vector v(n+1) to u1 (the eigenvector of the lowest eigenvalue) is computed from the present one v(n) by the relation v(n+1) = (1- αH + βH2) v(n) or v(n+1) = (1- αH + βH2 - γH3) v(n), the convergence rate is at least double that of the gradient method which corresponds to set β = γ = 0. Moreover, by choosing parameters α, β, or γ properly, one can get about three to five times faster convergence rate than that of the latter method, for H having very small γ2-γ1 and very large λN (the largest eigenvalue), further modifications are suggested. The relation with the Richardson method is also discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060407
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  • 116
    Electronic Resource
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    Sector elements for matrix displacement analysis (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 553-563 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three sector elements, two for plane stress problems (PSL and PSN) and one for plate bending problems (BSN), have been developed. Of the three elements, two are based on the natural mode technique. The elements have been applied to typical problems to test their performance.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060411
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  • 117
    Electronic Resource
    Electronic Resource
    A finite element weighted residual solution to one-dimensional field problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 577-585 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The one-dimensional diffusion-convection equation is formulated with the finite element representation employing the Galerkin approach. A linear shape function and two-dimensional triangular and rectangular elements in space and time were used in solving the problem. The results are compared with finite difference solutions as well as the exact solution. As another example, the convective term is set equal to zero and these techniques are applied to the resulting heat equation and similar comparisons are made.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060413
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  • 118
    Electronic Resource
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    A simplified numerical scheme for calculating the flow of a chemically reacting gas (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 595-598 
    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.1620060416
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  • 119
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    Reply to preceding discussion (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 602-602 
    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.1620060419
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  • 120
    Electronic Resource
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    Specification of geometrical parameters for elements with cubic mapping functions (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 94-98 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070108
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  • 121
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    A remark on the ‘Serendipity family’This paper was prepared during a visit to the Istituto di Elaborazione della Informazione - C.N.R in Pisa, Italy. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 98-100 
    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.1620070109
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  • 122
    Electronic Resource
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    Optimized prestressing by linear programming (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 125-136 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of optimizing the prestressing force and the tendon configuration for an indeterminate prestressed structure with prescribed cross-sectional dimensions is formulated in linear programming form, The structure is subjected to multiple load conditions and constraints are related to the structural behaviour and to the tendon configuration.It is shown that the number of behaviour constraints at each point in the structure can be reduced, as they represent parallel hyperplanes in the design space. Necessary conditions for feasible solutions are derived. The method based on transformation of the design variables, is suitable for beams, frames, grids and plates. Its application is illustrated for the case of a prestressed bridge.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070204
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  • 123
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    Erratum (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 242-242 
    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.1620070302
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  • 124
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    A higher-order triangular finite element for the solution of field problems in orthotropic media (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 287-295 
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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 a triangular finite element for the solution of two-dimensional field problems in orthotropic media. The element has nine degrees of freedom, these being the potential and its two derivatives at each node.The ‘stiffness’ matrix is derived analytically so that no further integration is required when computations are performed using the element.The results obtained using the element are compared with the exact mathematical solution of both a temperature distribution and a torsion problem.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070306
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  • 125
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    Transient shell response by numerical time integration (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 273-286 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In using the finite element method to compute a transient response, two choices must be made. First, some form of mass matrix must be decided upon. Either the consistent mass matrix prescribed by the finite element method can be employed or some form of diagonal mass matrix may be introduced. Secondly, some particular time integration procedure must be adopted. The procedures available divide themselves into two classes: the conditionally stable explicit schemes and the unconditionally or conditionally stable implicit schemes. The choices should be guided by both economy and accuracy. Using exact discrete solutions compared to the exact solutions of the differential equations, the results of these choices are displayed. Concrete examples of well-matched methods, as well as ill-matched methods, are identified and demonstrated. In particular, the diagonal mass matrix and the explicit central difference time integration method are shown to be a good combination in terms of accuracy and economy.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070305
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  • 126
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    A curved cubic triangular finite element for potential flow problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 337-344 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A curved cubic triangular element which has as nodal parameters the value of the function and its two derivatives is derived by use of a transformation similar to that used for quadrilateral isoparametric elements. A special form of the element which may be used to satisfy the condition that the function is constant along a boundary is also presented.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620070310
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  • 127
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    The use of analytic surfaces for the design of centrifugal impellers by computer graphicsThis paper is Crown copyright and is reproduced with the permission of the Controller, Her Majesty's Stationery Office. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 137-154 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper shows how analytic surfaces can be used to define the vanes of an impeller of a centrifugal compressor. The analysis has been given of a cubic-linear patch for representing three-dimensional geometries. An example has shown how this type of patch can be successfully used to model the geometry of centrifugal or mixed flow impellers having 'swept back vanes at the outlet.The analysis has been programmed for the Atlas computer at the Computer Aided Design Centre (CADC), Cambridge and set up in such a way that the designer can examine systematically a range of impeller shapes.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070205
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  • 128
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    Reduction of the degrees of freedom in solving dynamic problems by the finite element method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 185-194 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of lowering the order of a matrix equation which describes the dynamics of a finite element model is presented. The finite element with a ‘truncated’ mass matrix is obtained for calculating thin plate vibrations. Such an element has one vibrational degree of freedom at each nodal point. In the case of uniform systems the accuracy provided by the suggested element is no less than that provided by the non-conforming elements, which have three vibrational degrees of freedom at each nodal point, and in some cases it is greater. The finite elements with a ‘truncated’ mass matrix have essential advantages in the study of non-uniform systems.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070208
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    Normal gradient boundary condition in finite difference calculations (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 395-400 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An outline is given of a method for dealing with curved boundaries in finite difference calculations (relaxation or other similar techniques) where the gradient normal to the boundary is specified. Fluid flow calculations using the velocity potential are typical of such problems and the flow round a circular cylinder is computed as an example. The method makes no approximation which is not made in the usual finite difference techniques, therefore accuracy at the boundary is as good as in the remainder of the field.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070314
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  • 130
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    Letter to the editor (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 410-410 
    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.1620070318
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973) 
    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.1620070401
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  • 132
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    Non-linear transient finite element analysis with convected co-ordinates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 255-271 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method is presented for the transient analysis of large-displacement, small-strain problems with material non-linearities. The method employs a convected co-ordinate technique and a direct nodal force computational scheme of considerable efficiency. Detailed formulations are given for a plane, constant strain triangular element and a Euler-Bernoulli beam element. Results are presented for several example problems and compared with experimental data and other numerical solutions.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620070304
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  • 133
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    Direct iteration of ascending natural frequencies of vibration without inversion of the stiffness matrix (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 554-556 
    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.1620070414
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  • 134
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    A discussion of papers by D. B. Spalding and A. K. Runchal (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 560-563 
    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.1620070416
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  • 135
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    On an integration method for solving boundary value problem (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 566-568 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070418
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  • 136
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973) 
    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.1620060401
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  • 137
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    Numerical studies of viscous, incompressible flow through an orifice for arbitrary Reynolds numberFunds for the computations described in this paper were made available by the Research Committee of the Graduate School of the University of Wisconsin. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 489-496 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060405
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  • 138
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    Mass condensation and simultaneous iteration for vibration problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 543-552 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A relationship is developed between mass condensation and simultaneous iteration when used to determine the natural frequencies and vibration modes of large structural systems. A significant factor in the comparison between the methods is the extra versatility and reliability of simultaneous iteration.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060410
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  • 139
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    Spline interpolation techniques for variational methods (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 565-576 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Interpolation techniques are reviewed in the context of the approximation of the solution of boundary value problems. From the variational formulation, the approximation error norm is related to the interpolation error norm.Among global interpolation techniques, bicubic splines and spline-blended are reviewed; among local, Hermite's and ‘serendipity’ polynomials. The corresponding interpolation error norms are computed numerically on two test functions. The methods are compared for accuracy and for number of operations required in the solution of boundary value problems. The conclusion is that spline interpolation is most convenient for regular hyper-elements, while high precision finite elements become convenient for very fine or irregular partition.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060412
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  • 140
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    Numerical computation of antenna patterns near a conducting elliptic cylinder (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 591-594 
    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.1620060415
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  • 141
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    Discussion of a paper‘Comparison between sparse stiffness matrix and substructure methods’, Int. J. num. Meth. Engng, 5, 383-394 (1973). By F. W. Williams (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 601-602 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060418
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  • 142
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    Modal control, B. Porter and T. R. Crossley, Taylor & Francis Ltd., London, 1972. No. of pages: xii + 234. Price: £7.00 nett (cloth) (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 606-607 
    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.1620060421
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  • 143
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    Exact finite element solutions to the Helmholtz equation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 529-542 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For one-, two- and three-dimensional co-ordinate systems finite element matrices for the wave or Helmholtz equation are used to produce a single difference equation holding at any point of a regular mesh. Under homogeneous Dirichlet or Neumann boundary conditions, these equations are solved exactly. The eigenfunctions are the discrete form of sine or cosine functions and the eigenvalues are shown to be in error by a term of + O(h2n) where n is the order of the polynomial approximation of the wave function. The solutions provide the means of testing computer programs against the exact solutions and allow comparison with other difference schemes.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060409
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  • 144
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    Diagonally dominant matrices for the finite element method in hydrology (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 587-591 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method provides a powerful new instrument in the solving of problems of flow in the subsoil by means of a numerical processor. This new technique may be reinforced, without complicating its numerical aspect, by an appropriate choice of the sub-regions into which the original region is divided.In two-dimensional confined flows particular types of triangular meshes may be adopted which ensure the final matrices to be diagonally dominant both in steady-state and transient conditions, in heterogeneous and anisotropic fields. This will allow the utilization of rapidly converging iterative processes in the solution of the final linear systems with a notable saving of processing time.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060414
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  • 145
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    An integration algorithm for hyperbolic systems having non-zero, non-analytic steady-state solutions (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 598-601 
    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.1620060417
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  • 146
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    A computer program to find analytical solutions of second order linear differential equations (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 603-606 
    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.1620060420
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  • 147
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    Numerical methods for unconstrained optimization, Ed. W. Murray, Academic Press, London, 1972. No. of pages: 144. Price: £3.00 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 608-608 
    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.1620060423
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  • 148
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    Non-reacting and equilibrium chemically reacting turbulent boundary-layer flows (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 1-15 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Turbulent boundary-layer flows of non-reacting gases are predicted for both internal (nozzle) and external flows. Effects of favourable pressure gradients on two eddy viscosity models were studied in rocket and hypervelocity wind tunnel flows. Nozzle flows of equilibrium air with stagnation temperatures up to 10,000°K were computed. Predictions of equilibrium nitrogen flows through hypervelocity nozzles were compared with experimental data. A slender spherically blunted cone was studied at 70,000 ft altitude and 19,000 ft/sec in the earth's atmosphere. Comparisons with available experimental data showed good agreement. A computer program was developed and fully documented during this investigation for use by interested individuals.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070102
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  • 149
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    Stability and convergence of streamline curvature flow analysis procedures (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 69-83 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A convergence technique for use with the streamline curvature method of cascade and channel flow is presented which produces stable and rapid convergence for subsonic, transonic and supersonic flow and also in the downstream region where the Kutta-Joukowski condition is applied to a cascade flow. The convergence method is fully two-dimensional in nature, the iterative changes being determined via a model which takes into account the actual streamwise error distribution and the real normal changes in the grid.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070106
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  • 150
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    Modeling and simulatioin in chemical engineering, R. G. E. Franks, Wiley-Interscience, London, 1972. No. of pages: 285. Price: £7.75 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 607-608 
    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.1620060422
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  • 151
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973) 
    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.1620070101
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    Eigenproblem solution by a combined Sturm sequence and inverse iteration techniqueThis paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 17-42 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = λBq with band symmetric A and B, B being also positive definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures.The program may be conveniently utilized for the efficient solution of practical engineering problems including free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070103
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    A computational technique-for the efficient handling of large matrices (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 85-93 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is well known that the finite element method leads to large square symmetric matrices which are highly banded. Even if only the half bandwidth is stored it is easy to saturate the computer storage; this is because the half bandwidth contains a large amount of zeros. This paper discusses an alternative approach where a small rectangular section of the full bandwidth is stored, this method leading to a significant reduction in storage requirements.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620070107
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  • 154
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    Computational considerations in non-linear diffusion (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 103-116 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of non-linear diffusion problems is considered from the computational view- point. The advantage of various aspects of the problem solution are considered toward enhancing the computational understanding of the system. First is the analytical solution to the reduced linear case which acts as an error check on the numerical solutions as well as providing a base for a perturbation theory approach. Next are two different numerical solutions which are utilized to generate solution redundancy. These are based upon the method of differential quadrature and the method of finite differences.The application to non-linear transient slab diffusion with a general reservoir boundary condition is shown as an example of the various methods.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070202
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  • 155
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    A matrix technique for constructing slip-line field solutions to a class of plane strain plasticity problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 357-378 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure is described for solving plane strain rigid perfect-plasticity problems which lead to linear integral equations. The problem of finding the initial characteristic (slip-line), from which the complete field can be constructed, is reduced to a simple matrix inversion. Although the form of this matrix will depend on the particular problem concerned, it will be expressible in terms of a few fundamental matrices which occur in all problems of this type. The properties of these basic matrices and FORTRAN subroutines for assimilating them and for performing the corresponding linear transformations are given in detail. In illustration the procedure is applied to a drawing and to a strip rolling problem.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620070312
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  • 156
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    On convergence of Newton's method for load flow problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 325-336 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Kantorovich theorem is virtually the only known sufficiency condition for convergence of Newton's method on a set of non-linear equations. The theorem gives very conservative bounds and is difficult to apply. In this paper the power system load flow problem is solved by Newton's method, and a sufficiency condition for the convergence of the iterations on this particular problem is given. The criterion relates to a condition number defined on the Jacobian matrix associated with the non-linear equations. Computational feasibility is considered and the merits of its use are discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070309
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  • 157
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    Finite element analysis of Supersonic panel flutter (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 379-394 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070313
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    Some comments on the equation block solver (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 227-228 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070212
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  • 159
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    Note on a modified Conjugate Gradient Method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 228-232 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mr. Bruce Irons recently1 proposed a modification of the Conjugate Gradient Method. This note shows that if the matrix of the original set of equations is symmetric this method will have the same terminal property as the usual Conjugate Gradient Method except for a particular case when it will not converge at all. If the matrix is not symmetric we cannot deduce the usual terminal property.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070213
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973) 
    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.1620070301
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    Finite element stress formulation for wave propagation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 441-459 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a variational principle due to Gurtin, for linear elastodynamics, a finite element method in terms of stresses is developed for wave propagation problems. The finite element equations are simultaneous integral equations in time, with the peculiarity that they are equivalent to simultaneous linear differential equations with zero initial conditions. Written as differential equations, the finite element equations are of the form \documentclass{article}\pagestyle{empty}\begin{document}$$ [H]\{ s\} + [Q]\{ \mathop s\limits^{..} \} = \{ q(t)\} $$\end{document} where [H] is a symmetric positive-semidefinite matrix, [Q] is a symmetric positive-definite matrix and the stresses are represented by {s̈}. This is, of course, the same form as the equations for the displacement formulation.As a demonstration of the validity of the formulation numerical results are compared with a solution for a triangular-shaped strip load applied to an elastic half-space as a ramp function of time. This solution is obtained by numerical integration of the exact solution for Lamb's problem of a line load suddenly applied to a half-space. The agreement is found to be generally very good. As a further example, the case of a plate subject to uniform tension on two ends and containing a hole in the centre is presented. The results are found to be reasonable in that the characteristic stress concentration occurs near the hole, and away from the hole the results are similar to the solution for an infinitely wide plate.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620070404
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    On a combined sturm sequence and inverse iteration technique for eigenproblem solution of spinning structuresThis paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 509-518 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an efficient numerical algorithm for the accurate computation of specific eigenvalues and related vectors of spinning structures. The Sturm sequence technique is first applied to isolate the required roots, which are then individually located by an inverse iteration technique adopting an efficient matrix formulation specially developed for this purpose. The associated digital computer procedure is numerically stable, which also fully exploits the banded form of relevant matrices. Furthermore, the algorithm proves to be much faster than other related existing procedures.A computer program, based on the current algorithm, has been developed in FORTRAN V for the JPL UNIVAC 1108 computer. Numerical results for representative structures, computed by the program, are also presented in detail. Extensive applications of the program are envisaged in the attitude control of spacecraft and in the natural frequency analysis of spinning structures, discretized by the finite element method.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070409
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    Author's reply to a recent discussion1. Solution of eigenvalue problems by sturm sequence methodK. K. Gupta, ‘Solution of eigenvalue problems by Sturm sequence method’, Int. J. num. Meth. Engng, 4, 379-404 (1972). (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 553-554 
    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.1620070413
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    An inhomogeneous, tapered finite element (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 568-570 
    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.1620070419
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    On finite element integration in natural co-ordinates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 574-575 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Integration formulas for polynomial expressions in terms of natural co-ordinates are extensively quoted without proof in standard references on finite element theory. A derivation of these relations is presented and their application is extended to non-integral exponents.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620070421
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    On the generalization of equicofactor matrices (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 491-496 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Eguicofactor properties of the entities occurring in electric networks and discrete elastic systems extend beyond the present definition of such entities. For instance, the zero-sum property of these matrices is, in fact, a particular version of a broader definition. The generalization is accomplished in using higher order submatrices as opposed to scalars (submatrices of order 1) in the present literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070407
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    Further discrete variable results for a panel flutter optimization problem (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 537-543 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical solutions are presented for the problem of minimum weight design of a thin one-dimensiona simply-supported, solid panel in compression with one side exposed to a parallel high supersonic air flow. The flutter speed is held fixed, and a minimum thickness constraint is imposed. In addition, a multiplier technique is incorporated into the discrete variable minimization process to improve the convergence speed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070411
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  • 168
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    Optimum laminate design for strength and stiffness (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 519-536 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for minimum weight optimum design of symmetric fibre-composite laminates subject to multiple in-plane loading conditions which takes into account membrane stiffness requirements and strength limitations. The problem is cast as a non-linear mathematical programming problem in which the thicknesses of material placed at preassigned orientation angles are treated as the only design variables. The non-linear programming formulation is transformed into a sequence of linear programs employing an adaptation of the method of inscribed hyperspheres in which only critical and near critical constraints are considered at each stage in the procedure. Example applications illustrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070410
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973) 
    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.1620050301
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    Stochastic shakedown analysis of concrete slabs (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 303-309 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of lower bound plastic analysis of axisymmetric slabs for shakedown conditions is described which permits inclusion of stochastic parameters. All solutions are obtained numerically using a mathematical programming approach. Results are for concreteslabs.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050302
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    Computational procedures for the maximum likelihood parameters of the gamma and beta distributions (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 327-336 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational procedure is presented for calculating the maximum likelihood sampled parameters for the gamma and beta distributions. The procedure employed is both computationally efficient and easy to use. In order to facilitate immediate application, a self-contained FORTRAN IV computer code has been included to carry out the necessary operations.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050304
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    A finite element, linear programming methods for the limit analysis of thin plates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 311-325 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite elements having linear moment distributions and use of linearized yield criteria allow one to determine lower bounds to the collapse load of thin plates as solutions of linear programs.The method is quite general and rigorously meets the requirement of the lower bound theorem of limit analysis for concentrated or line load distributions. Ways of treating distributed surface loads are also discussed and tested.Actual bounds are computed for a variety of plate problems governed by Tresca yield criterion and compared with previous solution obtained from higher order stress elements and non-linear optimization techniques. The comparison shows that the present method can yield accurate bounds with considerably shorter computer times and relatively small number of elements. Additional tests show that numerical convergence to the limit loads is assured by suitable refinement of the mesh pattern.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050303
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    Design parameter variation and structural response (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 337-349 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general power series method is developed to aid in obtaining changes in the response variable due to changes in design parameters. The approach is considered for eigenvalue problems and systems of simultaneous equations which may represent static, dynamic and stability response problems. Particular emphasis is placed upon the eigenvalue problem and techniques for improving the calculations form the power series are suggested utilizing modified Rayleigh quotient expressions. Each of the methods proposed is treated computationally by the formulation of a finite element solution of column elastic stability. Investigations of solution accuracy versus percentage variation in element stiffness, whether the method underestimates or overestimates the changes, and the required number of eigenvalue solutions are presented.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050305
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    A finite element tensor approach to plate buckling and postbuckling (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 351-365 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A practical finite element method is presented for geometrically non-linear (von Kármán) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stage of non-linearity.Several different triangular elements are used in explicitly the required tensors. Buckling and post-buckling solutions are outlined and demonstrated by numerical examples.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050306
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    The finite element method in domains with curved boundaries (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 367-373 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For boundary value problems of the second order in two variables, there are proposed elements suitable for use along the curved part of the boundary. Numerical results show a considerable improvement of accuracy.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050307
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    The quadratic programming approach to the finite element method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 375-381 
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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 approximation technique is described in which the potential energy function is minimized subject to liner constraints. The constraints require satisfaction of all kinematic boundary conditions and interelement continuity conditions. An example, indicating the efficiency of the proposed method, is presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050308
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    Comparison between sparse stiffness matrix and sub-structure methods (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 383-394 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recent publications have emphasized the advantages of the sparseness of the over-all stiffness matrix of a structure. An alternative to setting up the over-all stiffness matrix is to use sub-structures. The main purpose of this paper is to show that there is equivalence between these two approaches when rows are not interchanged. It follows that a sparse matrix method can never be more efficient than the sub-structure method, if a suitable choice of sub-structures is assumed. However when identical sub-structures are contained within a structure the repetition can be utilized by the sub-structure method. In such cases the sub-structure method will often be quicker than the best sparse matrix solution.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050309
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    Flow of compressible fluid in porous elastic media (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 419-442 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for flow of fluid in a porous elastic media has been derived from a Gurtin type variational principle. Biot's field equations for porous media have been used in which the constitutive relations include the compressibility of the fluid. It has been shown that by proper choice of the form of the compressibility of the fluid as a function of the state variables, this option of the formulation can be used to treat the partially saturated soil. The method is general with respect to geometry, boundary conditions and material properties. Finally, the results of a series of examples have been presented and compared with exact results to demonstrate accuracy and applicability.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050311
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    Free vibration analysis of spinning structural systems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 395-418 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents an efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems. Important applications of the present work are envisaged in the natural frequency analysis of spinning structures discretized by the finite element technique, and in the determination of transfer function associated with the dynamic blocks of control systems of spacecraft utilizing gas jets or reaction wheels for attitude control, as well as of spin-stabilized and dual-spin-stabilized satellites.The validity of the Sturm sequence property is first established for the related matrix formulation involving Hermitian and real symmetric, positive-definite matrices, both being usually of highly banded configuration. A numerically stable algorithm based on the Sturm sequence method is then developed which fully exploits the banded form of the associated matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be extremely fast and economical in comparison to other existing methods of such analysis. Numerical results are presented for spinning bent cantilever beam and the solar arrays of SKYLAB, the earth-orbiting space station proposed by NASA.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050310
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    The treatment of natural boundary conditions in the finite element and finite difference methods (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 443-446 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To isolate the relative accuracy in the numerical approximation of the natural boundary conditions, a plane- stress example is presented for which the field equations using finite element and finite difference methods are identical. For this example, and by implication a wider class of problem, it is demonstrated that by using conventional practice in both methods the implicit representation of the natural boundary conditions in the finite element gives rise to a lower numerical accuracy than that in the less convenient explicit satisfaction of these boundary conditions in finite difference method.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050312
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    A compact Fortran sequence for limit analysis (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 446-449 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note presents a FORTRAN sequence for solving a particular case of the ‘bounded variables’ problem.1 It is this problem, rather than the standard linear programming problem, which appears when systematic matrix methods are applied to the rigid-plastic collapse analysis of a plane frame or truss The method uses considerably less storage than a standard simplex approach, and produces the collapse mode as a by-product of the calculation. The sequence is part of a complete program for the plastic collapse analysis of frameworks, details of which may be obtained from the author.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050313
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    Announcement (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 452-452 
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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.1620050315
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973) 
    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.1620050401
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    An iterative procedure for the oscillatory laminar boundary layer (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 449-452 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of small sinusoidal oscillations imposed on a stagnation point flow is considered. This leads to an ordinary differential equation which, in the high frequency limit, has a simple solution. An iterative method (involving a linear integral operator) is developed, starting from this basic solution. This scheme, performed numerically, is ‘under-relaxed’ and this renders it applicable to as wide a frequency range as possible: convergence criteria are discussed in terms of the relaxation parameter. The streamwise velocity profiles computed are compared with those given by an independent method.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050314
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    Finite element stress field solution of the problem of saint venant torsion (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 455-458 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some finite element solutions for the Saint Venant torsion problem accounting for orthotropy, inhomogeneity and multiply connected sections are presented. The Prandtl stress function formulation is used. The stresses, torsional stiffness and warping function are calculated. On the basis of various approximations using higher order elements the choice of ‘the best’ element is discussed.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050402
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    Pure moment loading of axisymmetric finite element models (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 459-463 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of loading axisymmetric finite element models by application of a uniform circumferentially distributed moment is presented herein. Operationally, this is accomplished by changing the radius of curvature of some reference point in the axisymmetric model. The radius change gives rise to hoop strains, which are used in an ‘initial strain’ method to actually load the model. The resulting pure axisymmetric moment is computed by integrating the hoop stresses thus generated over a cross-sectional cut through the axisymmetric model. For non-linear problems, the procedure just described can be performed incrementally. Several numerical examples are presented herein to illustrate the method, such as bending of a curved bar, sharp folding of a thin sheet and bending of a toroidal tube until the cross-section is flattened.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050403
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    Axisymmetric triangular finite elements for the scalar helmholtz equation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 481-497 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for solving Laplace's, Poisson's and Helmholtz's equations in the axisymmetric case is developed. Complete polynomial functions of arbitrarily high order are used as basis functions. Each triangular element is described by a matrix equation involving cotangents of the vertex angles, the vertex co-ordinates and the triangle area, as well as certain universal numeric matrices. The method of obtaining these matrices is given in detail. The matrices depend only on the polynomial order; values of all matrices to sixth order inclusive have been computed. Important properties of the matrices are discussed and simple example problems are presented.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050405
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    Rolling and impact on a linearly viscoelastic slabPresented at the 6th U.S. National Congress of Applied Mechanics, 15-19 June 1970, Boston, Massachusetts. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 465-479 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of viscoelastic contact stress analysis introduced in an earlier paper10 is developed further to treat two problems: the steady-state rolling of a cylinder and axisymmetric impact of a sphere. The procedure is equally applicable to a medium of infinite depth (half-space) or to a slab of finite thickness. The analysis is based on the computation of a set of viscoeiastic influence coefficients. To find the pressure distribution on the instantaneous contact surface, point matching is used. In the rolling problem, a study is made of such phenomena as critical speed and the effect of medium thickness through a comparison with existing results. The impact problem is solved in an iterative scheme of successive approximations. An example is presented for the study of typical impact parameters.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050404
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    Inversion of prony series characterization for viscoelastic stress analysis (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 499-502 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is common in numerical viscoelastic stress analysis to represent the material functions as Prony series.1 Often series representations for creep function representations are available (for example, see Reference 2) and the stress analysis method requires a relaxation function representation. This paper describes an efficient and reliable method to numerically perform the inversion. An example is given for the inversion and a subsequent re-inversion indicates the accuracy of the method.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050406
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  • 190
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    Numerical solution of mixed boundary value problems using numerical green's functions (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 517-521 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for obtaining the Green's functions for Poisson's equation with mixed boundary conditions is presented. The Green's functions thus obtained are then employed to rapidly obtain numerical solutions of the above equation by matrix multiplication, with subsequent considerable savings in machine time.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050408
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  • 191
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    On the generalization of stress function procedure for dynamic analysis of plates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 523-542 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Southwell's stress functions, hitherto used for static analysis of plate flexure problems, are generalized for use in the dynamic analysis of plates. Four finite element models for plate analysis are formed using stress functions. These are used in the numerical calculation of the natural frequencies for some plate problems and the results are compared with alternative solutions.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050409
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    Experiment versus analysis: Computational techniques for the description of static material responseThis work was supported by the United States Atomic Energy Commission. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 503-515 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical basis is presented for the determination of material properties from arbitrarily shaped experimental specimens. The experimental method is derived from an application of numerical boundary value problem solutions to the specimen stress analysis and from the application of a least squares criterion to the comparison of analytical and experimental deformations.Material properties are determined mathematically from the solution to a non-linear set of equations, in which the non-linearity is a function of the specimen type, number of data points and the quality of recorded data. Several solution techniques, based on either direct iteration or function minimization are examined in terms of the parameters affecting convergence.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050407
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  • 193
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    Large deflection analysis of plates and shallow shells using the finite element method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 543-556 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to stability and large deflection analysis of plates and shallow shells. Based on the von Karman strain expressions for plates and the Marguerre shallow shell theory, equilibrium and incremental equations for a non-linear analysis by finite elements is developed. Great emphasis is placed on the specific matrix formulation, thereby obtaining a highly efficient method that is well suited to modern electronic computer analysis. A doubly curved, non-linear quadrilateral element is developed. The versatility and efficiency of the present method is illustrated by several examples including large deflection and post shear-buckling behaviour of plates and snap-through of shallow shells.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050410
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  • 194
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    Realization of two-dimensional state space digital filters (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 565-571 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a realization procedure for two-dimensional digital filters. The novel procedure evolves from a state space description of the analog filter function and a method of discretization. Examples are presented to illustrate the method proposed. A discussion of small computer implementation of the two-dimensional digital filter is also included.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050412
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    Convergence of the solution for the far scattered field of a conducting cylinder of arbitrary cross-sectionThe research for this paper was supported by the Department of Electrical Engineering at the University of Manitoba. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 557-564 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Convergence of the solution for the far scattered field of a conducting cylinder of arbitrary cross-section is investigated by studying the scattering of a transverse magnetic field by a conducting triangular prism. It is shown that the convergence of the solution depends mainly on the physical size of the cross-section and not on the form of the current distribution on the prism.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050411
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    A self-adjusting grid for finite-difference programsThis research was conducted under the McDonnell Douglas Independent Research and Development Program. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 585-587 
    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.1620050414
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  • 197
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    A comparison of first and second order axially symmetric finite elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 573-583 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An attempt is made to evaluate the relative merits of first and second order triangular elements in axially symmetric elastostatic stress analysis. The presented results should be of value to those requiring comparison data. Typical stresses, displacements and computer times are presented for three specific numerical examples. Where available, the elasticity solution is used to evaluate the accuracy of computed results. Comparisons indicate that for the same nodal point configuration, the second order solutions are generally better than the corresponding first order solutions, even though the latter involve many more elements. Furthermore, the second order elements may lead to improved results even when fewer nodal points are used. Finally, computer times seem to be higher for the first order solutions and the numerical effort required to obtain comparable accuracy is much greater for the first order solutions.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050413
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  • 198
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    A further modification to Ahmad's shell element (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 588-589 
    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.1620050415
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  • 199
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    On the inverse of matrices with nearly equal elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 589-591 
    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.1620050416
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    Advances in computational methods in structural mechanics and design, J. T. Oden, R. W. Clough and Y. Yamamoto, Editors, University of Alabama at Huntsville Press, 1972. No. of pages: 789. price: $10.00 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 591-592 
    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.1620050417
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