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  • Engineering General  (30)
  • Wiley-Blackwell  (30)
  • American Association for the Advancement of Science
  • PANGAEA
  • 1975-1979  (30)
  • 1810-1819
  • 1978  (20)
  • 1975  (10)
Collection
Keywords
Publisher
  • Wiley-Blackwell  (30)
  • American Association for the Advancement of Science
  • PANGAEA
Years
  • 1975-1979  (30)
  • 1810-1819
Year
  • 1
    Electronic Resource
    Electronic Resource
    Solution of non-linear differential equations by discrete least squares (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 597-612 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general-purpose technique has been developed for solving non-linear partial differential equations. A set of approximating functions with undetermined parameters is used to evaluate the differential equation and boundary conditions at discrete points, forming a set of residuals to be minimized. The parameters which minimize the sum of squared residuals are determined by a non-linear least-squares minimization technique. Initial value problems are solved by integrating the equations with respect to time at the fitting points by a predictor-corrector algorithm. The resulting formulation is independent of the form of the problem and the approximating functions, so that a broad class of problems may be solved with a single computer program. The technique is applied to several boundary and initial value problems in one and two spatial dimensions. The tecnique is applied to several boundary and initial value problems in one and two spatial dimensions.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120405
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  • 2
    Electronic Resource
    Electronic Resource
    Cubic spline Galerkin approximations to parabolic systems with coupled non-linear boundary conditionsThis work was supported by the Rockwell International IR and D Interdivisional Technology Program under the sponsorship of the Mathematics and Statistics Technological Panel. (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 63-71 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090106
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  • 3
    Electronic Resource
    Electronic Resource
    The direct numerical integration of linear matrix differential equations using pade approximations (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 259-270 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090202
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  • 4
    Electronic Resource
    Electronic Resource
    Three-dimensional elasto-plastic finite element analysis (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 209-218 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090115
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  • 5
    Electronic Resource
    Electronic Resource
    Modification to the Suhara-Fukuda method of network generation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 93-99 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note describes improvements to the Suhara-Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are given.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120110
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  • 6
    Electronic Resource
    Electronic Resource
    On least squares approximations to indefinite problems of the mixed type (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 453-469 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The mehod retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency i.e., the resulting matrix system is always symmetric and positive definite,. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120307
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  • 7
    Electronic Resource
    Electronic Resource
    A systematic procedure for generating useful conformal mappings (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1651-1657 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Procedure is presented for generating a class of conformal mappings useful in the formulation of finite-difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly-rectangular domain for a wide variety of partical problems. The introduction of sheared co-ordinates in this computational domain then provides for solution of the problem in a nearly-orthogonal (in fact, nearly-conformal) co-ordinate system, with its boundaries corresponding to co-ordinate lines. The method is based upon the Schwarz-Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121103
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  • 8
    Electronic Resource
    Electronic Resource
    Thin plate semiloof element for structural analysis-including stability and natural vibrations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1667-1676 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a thin plate element formulated along parallel lines to the general three-dimensional Semiloof shell element. This plate version possesses only one half of the total number of degrees-of-freedom of the shell element and has the advantqage that the formulation of the strains and other terms is very much simplified. The element is first assessed in static situations and then its performance in the solution of eigenvalue problems is considered.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121105
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  • 9
    Electronic Resource
    Electronic Resource
    Finite element buckling analysis of homogeneous and sandwich plates (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 39-50 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090104
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  • 10
    Electronic Resource
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    Thermal deformation vector for a bilinear temperature distribution in an anisotropic quadrilateral membrane element (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 325-336 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090205
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