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  • Engineering  (10)
  • Wiley-Blackwell  (10)
  • Annual Reviews
  • Springer
  • 1980-1984
  • 1975-1979  (10)
  • 1950-1954
  • 1975  (10)
  • 1
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a practical implementation of the Galerkin finite element procedure for solving systems of parabolic partial differential equations with non-linear boundary conditions. This technique consists of finding an approximation in the form of a finite sum of cubic B-splines, which yield high-order accurate results, and consequently, solutions can be developed with remarkable precision and speed up to the steady state region where conventional finite difference methods often fail. In addition, the choice of mesh width and nodal spacing can be automatically determined for a predictor-corrector routine, thereby relieving the engineer of a great deal of ‘guess work’ that is normally characteristic of solving such problems.
    Additional Material: 3 Tab.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 259-270 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of approximations to the matrix linear differential equation is presented. The approximations range, in accuracy, from the simplest forward difference scheme to the exact solution. The infinite series defining the exponential matrix is used to ascertain the accuracy of the various approximations. A clear distinction is made between approximations to the system equations and the forcing function, with the forcing term being represented by a piecewise linear function. Special application is given to the equations arising in structural dynamics of the form For these structural dynamic equations, the measure of the energy of the system is used to analyse the stability of the numerical approximations.
    Additional Material: 3 Tab.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 209-218 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Advances in technology and interest in limit state design have made the inclusion of non-linear effects, such as elasto-plastic behaviour, desirable in the analysis of many structures. Improvements in solution algorithms coupled with parallel developments in high speed digital computers have now made the practical solution of such problems possible. The paper presents numerical solutions to three-dimensional elasto-plastic problems illustrating the applicability of isoparametric elements and the order of computation times involved.
    Additional Material: 6 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 39-50 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element buckling analyses of plates are performed by means of quardrilateral elements having 12 degrees-of-freedom. It is found that if the plate is capable of appreciable transverse shear deformation, initial-stress stiffness matrices that represent the lateral dispalcement by cubic polynomials do not yield convergence to correct results. An initial-stress stiffness that works satisfactorily for both homogeneous and sandwich plates is formulated. A Fortran listing of the associated subroutine is provided.
    Additional Material: 4 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 325-336 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a thermal-structural deformation vector for an anisotropic quadrilateral membrane element. The elastic properties of the element are based on linear stress assumptions and were developed by Robinson1. A general bilinear temperature field within the element is chosen in order to obtain a thermal deformation capability for the element commensurate with its elastic capability. A pseudo shear term is developed to account for part of the thermal deformation. The element is suitable for finite element analysis of advanced aircraft structures under elevated temperature environments and is particularly well suited for analysis of regions with severe temperature gradients such as occur in the vicinity of local heat sources and sinks. An example problem is included to demonstrate the behaviour of the element.
    Additional Material: 7 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 297-323 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a program which has given excellent results for uniform approximation of functions by polynomials, rational functions, generalized polynomials, and generalized rational functions. The algorithm is described in detail and several examples are discussed. The approximation is done over a finite point set, which is commonly a set of real numbers or points in the plane (in the latter case we are doing what is often known as surface fitting). Input to and output from the program is in tabular form. The method used is a linear programming approach known as the differential correction algorithm, which has been shown by several authors to always converge in theory (quadratically in some situations). In practice, we have obtained convergence in nearly every case, and quadratic convergence in most cases. The program can also be used for simultaneous approximation of several functions.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 415-432 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Details are given of a finite element scheme for the determination of the elastic buckling loads of thin flat plates of arbitrary shape under general kinematic and traction boundary conditions. The buckling loads are calculated using a triangular finite element with corner connections which is based on a previously derived variational principle combining both stresses and displacements. Numerical solutions are presented to a number of example problems, including plates with reinforcing members, and comparisons are made, where possible, with results from the finite element analyses of other authors and with exact or classical Rayleigh-Ritz solutions.
    Additional Material: 5 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 649-667 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for solving structural design problems that allows a continuous distribution of material along structural elements is presented. The method is an extension of the generalized steepest descent method presented in Reference 1. Inequality constraints on design variables, displacement, natural frequency, and buckling are explicitly treated and a minimum weight cost function is employed. A steepest descent method for boundary-value state equations is developed and a computational algorithm is given. Several example problems in minimum weight structural design are solved and compared with results obtained by discretization techniques.
    Additional Material: 6 Ill.
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  • 9
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.
    Additional Material: 13 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 938-943 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A comparison is made of the Crandall and Crank-Nicolson methods applied to a transient heat conduction problem with a convective boundary layer on its surface for a range of values of Nusselt modulus and Fourier modulus. A new equation is derived to handle the convective boundary condition. For reasonable accuracy requirements the Crank-Nicolson method gives superior performance with respect to accuracy.
    Additional Material: 6 Ill.
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