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  • Engineering
  • 1970-1974  (54)
  • 1970  (54)
  • 1
    Electronic Resource
    Electronic Resource
    A conforming triangular finite element plate bending solution (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 259-264 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A conforming plate bending solution using simple polynomial deflection functions of third-degree inside each triangular element is presented. In order to avoid normal slope discontinuities along the sides of the elements, the plate displacement parameters are subjected to ‘slope continuity conditions’ acting as constraints to the minimum potential energy problem. This is then solved by the classical method of Lagrange introducing multipliers as new auxiliary variables. If a special variational formulation of the problem is used, it can be shown that the Lagrangean multipliers are generalized stress parameters. The suggested solution is therefore basically a ‘mixed’ solution, the unknown variables of the problem being both displacement and stress parameters. Several numerical results are presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020211
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  • 2
    Electronic Resource
    Electronic Resource
    A curved element approximation in the analysis of axi-symmetric thin shells (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 459-476 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness equation is derived for curved elements of orthotropic axi-symmetric thin shells, and equivalent applied loads are found for shells subjected to initial strains, applied surface loads and body forces. The Lure approximation of thin shells and displacement field approximation by polynomials of arbitrary degree are included in the formulae derived.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020402
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  • 3
    Electronic Resource
    Electronic Resource
    A direct numerical method for the solution of field problems (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 117-131 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for the analysis of field problems is described. The algorithm is based upon the generalized Betti-Maxwell theorem. Using a set of known solutions to problems with similar boundary conditions produces a set of ‘integral’ equations for the required solution. Using any convenient numerical integration formula reduces the problem to the solution of a set of simultaneous algebraic equations. The accuracy of the solution depends upon the accuracy of the integration formula as applied to the problem under consideration and is independent of the known auxiliary solutions. The method is described in detail as applied to harmonic problems.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020111
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  • 4
    Electronic Resource
    Electronic Resource
    A finite element application of the modified Rayleigh-Ritz methodCrown Copyright, reproduced with the permission of the Controller, Her Majesty's Stationery Office. (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 85-98 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Considerable attention has been devoted in the literature on numerical methods towards securing energy convergence of solutions for, say, linearly elastic plate bending problems. Although energy convergence is necessary it by no means follows that the derived bending moments and shearing forces converge uniformly at a given point and it is this kind of feature which the engineer is really seeking.This question is examined in the context of a problem which is of particular interest to the civil engineering field and concerns the bending of a square plate under uniformly distributed load; the plate has simply supported edges and contains a central square hole with free edges. The solution to this multiply connected and mixed boundary value problem is obtained through a recently developed modification to the Rayleigh-Ritz method which has very general application and renders the solution mathematically valid up to the internal corner points where the bending moments are singular. Use is made of triangular equilibrium finite elements in conjunction with continuous eigenfunctions. Although it is already known that the order (i.e. the eigenvalue) of the singularity at the internal corners is available by inspection, it is an interesting feature of the present solution that a good approximation to the amplitude is also obtained by an inspection of the finite element results.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020109
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  • 5
    Electronic Resource
    Electronic Resource
    A frontal solution program for finite element analysis (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 5-32 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The program given here assembles and solves symmetric positive-definite equations as met in finite element applications. The technique is more involved than the standard band-matrix algorithms, but it is more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes. Artifices are included to improve efficiency when there are many right hand sides, as in automated design. The organization of the program is described with reference to diagrams, full notation, specimen input data and supplementary comments on the ASA FORTRAN print-out.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020104
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  • 6
    Electronic Resource
    Electronic Resource
    A gradient computational procedure for the solution of large problems arising from the finite element discretization method (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 477-494 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational procedure based on gradient iterative techniques is proposed for the solution of large problems to which the finite element method is applicable. In linear problems the procedure can be used either for solving the set of algebraic equations or for the complete inversion of the matrix of coefficients. Special attention is focused on the practical aspects of the procedure concerning its realization on the digital computer.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020403
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  • 7
    Electronic Resource
    Electronic Resource
    A multidata method of approximate Laplace transform inversion (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 207-219 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A newly developed numerical Laplace transform inversion technique is described. A derivation of the method, termed the ‘multidata method’, is presented along with a description of a similar collocation method. Similarities and differences between the two numerical methods are described and discussed. Results of parameter studies of both methods are presented which demonstrate the sensitivity to error displayed by the collocation method and the magnitude of the improvement in accuracy obtainable with the multidata method as compared with the collocation method, especially when errors exist in the function to be inverted.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020206
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  • 8
    Electronic Resource
    Electronic Resource
    A numerical solution for the symmetric melting of spheres (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 175-188 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the solution of the radially symmetric heat conduction problem in a melting sphere. The method employs the embedding technique; this permits the solution to be written in the form of an ordinary integro-differential equation which is readily solved numerically by means of a forward integration scheme. The accuracy of the method is briefly discussed and numerical results for both constant and variable heat inputs are presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020204
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  • 9
    Electronic Resource
    Electronic Resource
    A simple matrix-vector handling scheme for three-dimensional and shell analysis (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 509-522 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple program carrying out various vector operations in two- or three-dimensional spaces is presented. The listings are given in A.S.A. FORTRAN IV. The program is of particular application in various forms of three-dimensional and shell analysis as it can create and transform locally orthogonal co-ordinates, etc. While these applications motivated its design, it is of very general use one such application is illustrated by applying the program to general perspective projection.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020405
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  • 10
    Electronic Resource
    Electronic Resource
    An application of the finite element technique to boundary value problems of potential flow (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 243-252 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This report summarizes an experimental application of the finite element approach to two-dimensional inviscid fluid flow.The method results in a matrix equation relating the vector of velocities at the nodal points with the vector of singularities. The singularities, which are concentrated at the nodes, consist of a source and a vortex.On solution of this equation (defining the flow in the region), boundary conditions must te stipulated. This usually involves setting the internal singularities to zero and making certain modifications ro those lying on the boundary of the region.Some results of the application to a particular problem are included in the paper.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020209
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