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  • Articles  (18)
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  • Engineering  (18)
  • 1980-1984
  • 1970-1974  (18)
  • 1950-1954
  • 1974  (13)
  • 1970  (5)
  • 1954
  • 1
    Electronic Resource
    Electronic Resource
    On the numerical solution of a class of problems in a linear first strain-gradient theory of elasticity (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 159-174 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of general discrete models for the analysis of boundary-value problems in the first strain-gradient theory of elasticity. Extensions of the finite element method are constructed for this purpose, and general equations of motion are derived for finite elements of a class of micro-polar materials which are characterized by strain energy functions involving strains and second gradients of strains or displacements. The notion of generalized nodal doublets is introduced. The problem of a composite consisting of a strain-gradient sensitive microlayer embedded between semi-infinite bodies is examined as an example problem. Some of the results are compared with available exact solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020203
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  • 2
    Electronic Resource
    Electronic Resource
    Finite element bending analysis of multilayer plates (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 215-225 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a general quadratic multilayer plate element is presented for the analysis of arbitrarily layered curved plates. In the formulation, each layer of the multilayer plate can have different orthotropic properties and can deform locally. Examples of bending problems are presented which demonstrate the applicability of the formulation.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080203
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  • 3
    Electronic Resource
    Electronic Resource
    The finite element analysis of elasto-plastic materials by use of dislocation dipole systems (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 277-288 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the stress field due to any prescribed continuous distribution of dislocation dipoles can be determined. This technique then forms the basis of a general method of solution of elasto-plastic material problems. The presentation is limited to situations which conform to either plane stress or strain conditions. Some results are obtained for relatively simple geometrical and loading configurations and compared with classical plasticity solutions. Finally, the method is applied to the problem of a circular hole in a finite strip under tension.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080207
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical quadrature used for radiative heat-transfer computations (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 395-401 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Physical reasoning makes it possible to use artificial parameters with numerical quadrature in order to obtain approximate solutions for the Fredholm integral equations associated with radiative heat transfer calculations. With the aid of such parameters, decisions can be made concerning the applicability and usefulness of the numerical quadrature technique.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080215
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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Convergence studies of eigenvalue solutions using two finite plate bending elements (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 99-116 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence rates of eigenvalue solutions using two finite plate bending elements are studied. The elements considered are the well-known 12 degree of freedom, non-conforming rectangular element and the 16 degree of freedom, conforming rectangular element. Three problems are analysed, a square plate simply supported on two opposite sides with the other two sides clamped, simply supported, or free. Closed form, finite element solutions for these problems are obtained by using shifting E-operators.With few exceptions, eigenvalue solutions found with the non-conforming element converge from below the exact answers at an asymptotic rate of n-2, where n is the number of elements on a side. However, since the array size needed for such convergence is very large, little can be said about the convergence rates for practical arrays. The conforming element solutions converge from above at an asymptotic rate of n-4. A comparison of the errors involved in using these two elements shows that the conforming element is far superior to the non-conforming element.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020110
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  • 7
    Electronic Resource
    Electronic Resource
    Discussion of paper by Bruce M. IronsBruce M. Irons, ‘A conforming quartic triangular element for plate bending’, Int. J. num. Meth. Engng, 1, 29-45 (1969). (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 453-454 
    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.1620020311
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  • 8
    Electronic Resource
    Electronic Resource
    Least square-finite element for elasto-static problems. Use of ‘reduced’ integration (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 341-358 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least square based finite element algorithm is developed for some elasto-static problems. In the formulation both stresses and displacements appear as simultaneous variables. In two dimensional (plane) analysis, parabolie isoparametric elements are used. Considerable improvement of performance is obtained with a numerical integration based on 2 × 2 Gauss point distribution over more accurate integration schemes. Reasons for this are presented.The formulation is extended in the section ‘General least square formulation’ to beams and plates with a similar success of ‘reduced’ integration.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080212
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  • 9
    Electronic Resource
    Electronic Resource
    Observations regarding assumed-stress hybrid plate elements (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 513-519 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Edge displacement of assumed-stress hybrid plate elements are commonly chosen as either linear, quadratic or cubic functions of the edge co-ordinate. The present paper examines the effect of this choice on the acceptability, accuracy, and possible zero energy modes of elements based on a linear stress field. It is concluded that triangular elements may be preferable to quadrilaterals, and that linear edge displacements are not desirable.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080307
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  • 10
    Electronic Resource
    Electronic Resource
    The torsional stiffness of prismatic members with sections divisible into rectangles (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 671-675 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of determining the torsional stiffness of a wide range of structural sections, both homogeneous and composite, is presented. Prandtl's stress function along the boundaries of component sections is approximated by finite Fourier series with coefficients chosen to minimize a functional. An example indicates that the stiffness may be determined to acceptable accuracy by the solution of very few equations.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080320
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