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  • Engineering General  (9,884)
  • Wiley-Blackwell  (9,884)
  • Annual Reviews
  • Oxford University Press
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  • Wiley-Blackwell  (9,884)
  • Annual Reviews
  • Oxford University Press
  • Periodicals Archive Online (PAO)
  • Springer Nature
Years
  • 101
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    Electronic Resource
    Numerical solution of dynamical systems by direct application of Hamilton's principle (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 207-216 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method is described which allows a direct derivation of a set of first-order finite difference equations to numerically compute the motion of any conservative or non-conservative dynamic system with a finite number of degrees of freedom. The derivation of the method is based on an application of Lagrangian multipliers to a functional form of Hamilton's equations, and reduces the work required to obtain the most desirable form for numerical integration from the standpoint of computational efficiency and accuracy. For systems with many degrees of freedom, the required matrix inversions produce first derivatives of the co-ordinates, instead of second derivatives, thus eliminating a potential source of error in numerical integration. Two examples are given to illustrate the method.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040207
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  • 102
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    A lumped parameter element for the analysis of hyperbolic paraboloid shells (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 235-249 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the derivation of the stiffness matrix for a lumped parameter hyperbolic paraboloid shell element. This element is used to obtain solutions to hyperbolic paraboloid shells with various edge conditions. Numerical example for three types of support conditions (a simple support, a clamped edge and a shell supported by concentric edge beams) are presented. To illustrate the applicability of the method, the results obtained by the lumped parameter element are compared with those obtained by well-known methods of analysis such as the variational procedure, the finite difference and the finite element method.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040209
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  • 103
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    Convergence of eigenvalue solution in conforming plate bending finite elements (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 217-234 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence proof of plate eigenvalue solution from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem in to a corresponding isoperimetric variational problem. A conforming thick, plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620040208
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  • 104
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    Numerical solution of a separtated viscous flow problem by a non-uniform finite-difference net (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 251-260 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two-dimensional stagnation point flow of a viscous fluid is modified by the introduction of a thin plate placed symmetrically at the stagnation point. Separation of the boundary layer results in back flow near the plate even at small Reynolds numbers. The Navier-Stokes equations governing the flow are replaced by finite differences using unequal net spacing which is finer in the boundary layer. The choice of finite differences guarantees convergence of the iterative procedures used. Only those relaxation parameters, which are necessary to obtain convergence and also to make the method computationally efficient, have been used. Numerical results for Reynolds numbers 9, 100 and 400 are obtained.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620040210
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  • 105
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    Mixed finite element method for axisymmetric shells (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 261-277 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed variational formulation is used as basis for developing a mixed finite element method for axisymmetric shell. The independent unknowns of the method are the axial and radial displacement components, the rotation of the normal to the middle surface and the meridional bending stress couple. The basic element is a frustrum of curved meridian. General advantages of the mixed method are presented, one of which is the possibility of using piece-wise linear functions of the meridional arclength to represent the basic unknowns. Test results are presented for plate bending, transverse shear deformation, membrane behaviour, edge-zone bending, bending near the junction of two shells, convergence of the method and accuracy of middle surface curvature interpolation. Shell geometries considered are cylindrical, conical, spherical and ellipsoidal. Good results are obtained which should increase interest in the relatively less known and less tested mixed method as compared to the stiffness method.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620040211
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  • 106
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    Numerical approximation of one-dimensional consolidation (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 279-287 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized finite difference scheme is developed to represent the one-dimensional consolidation process. The difference equations are derived from integral balance equations which represent the soil as a mixture of two constituents. No restrictions are placed on the soil constitutive properties or stratigraphy. An approach to stability analysis for the scheme is outlined, and an example problem is presented.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620040212
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  • 107
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    Propagation of transient pules from a spherical cavity in a viscoelastic medium (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 289-299 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of an impulsively applied pressure acting on the surface of a spherical cavity in a linear viscoelastic medium is solved by an approximate inversion of the Fourier transform. The method can be applied to general models of viscoelasticity described by the Boltzmann superposition principle, with relaxation or creep functions given analytically or numerically in the time or the frequency domain.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040213
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  • 108
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    A note on the estimation of critical damping in dynamic relaxation (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 301-303 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new way of estimating critical damping in dynamic relaxation is proposed using the concept of a mass-dependant load vector, a postulate concerning vibrations and Rayleigh's principle. The method should be particularly appealing in those not uncommon circumstances where the actual loads are approximately proportional to the masses for then the computer time required in evaluating the various constants would actually be a part of the problem-solving time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040214
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  • 109
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    Dynamic probabilistic system, R. A. Howard, Wiley, New York. Vol. 1, No. of pages: 576. Price: £7·90. Vol. 2, No. of pages: 1108. Price: £8·75 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 303-304 
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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.1620040215
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  • 110
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    Masthead (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972) 
    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.1620040301
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  • 111
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    Linear algebra, vol. 2, handbook for automatic computation, J. H. Wilkinson and C. Reinsch (Editors), Springer-Verlag, Berlin, Heidelberg and New York, 1971. No. of pages: 439. Price: $19.80 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 304-304 
    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.1620040216
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  • 112
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    An iterative approach to strucural optimizationResearch sponsored by the Air force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract F33615-69-C-1826. (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 331-336 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative procedure of structural optimization is discussed that combines finite element analysis with the use of explicit optimality conditions. The procedure is illustrated by examples concerning sandwich beams with constraints on the deflection at a specified section, the maximum deflection or the sum of the maximum deflection in all spans of a continuous beam. The examples suggest that, starting from a uniform beam, by far the greatest saving in weight is obtained in the first two or three iterations.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620040303
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  • 113
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    The finite element method applied to ideal gaseous mixtures (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), 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: The finite element technique is extended to an ideal gaseous mixture to study diffusion of several gaseous species in a carrier gas under various geometries and flow conditions. This is accomplished by obtaining the finite element analog of the balance of mass for each species, along with the corresponding equations for the balance of mass, momentum and energy for the mixture. Numerical results are obtained for a steady-state, incompressible, isothermal, viscous mixture of two gases for several boundary conditions. Favourable agreement is obtained between the finite element results and analytical solutions.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620040304
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  • 114
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    A unidimensional convergence test for matrix iterative processes applied to Strapdown Navigation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 115-130 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The investigation of the convergence properties of matrix iterative processes usually involves test matrices of high order. This fact may prohibit an analytic approach to the problem. In this paper a method is presented which converts the multidimensional test procedure into a scalar one. The method is presented in conjunction with the problem of matrix orthogonalization which exists in Strapdown Inertial Navigation. Three examples are presented in which the convergence of matrix orthogonalization techniques is investigated. The examples demonstrate the use of the unidimensional convergence test in determining the order of the processes and in finding sufficient conditions for convergence. Numerical results are presented.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110112
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  • 115
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    A note on an element ordering schemeThis work was supported by S R C Grant B/RG/5549/4 made jointly to Brunel University and Imperial College of Sceience and Technology for research on Finite Element Techniques. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 194-198 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper contains an algorithm for the ordering of elements in the finite element method, which can be utilized in the Non-assembly Method of the author and in the Frontal Solution Method of B. M. Irons.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110120
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  • 116
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    Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 231-246 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees-of-freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110203
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  • 117
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    A Block-Stodola eigensolution technique for large algebraic systems with non-symmetrical matrices (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 247-267 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Block-Stodola eigensolution method is presented for large algebraic eigensystems of the form AU = λBU where A is real but non-symmetric. The steps in this method parallel those of a previous technique for the case when both A and B were real and symmetric. The essence of the technique is simultaneous iteration using a group of trial vectors instead of only one vector as is the case in the classical Stodola-Vianello iteration method. The problem is then transformed into a subspace where a direct solution of the reduced algebraic eigenvalue problem is sought. The main advantage is the significant reduction of computational effort in extracting a subset of eigenvalues and corresponding eigenvectors. Theorems from linear algebra serve to underlie the basis of the present technique. Complex eigendata that emerge during iteration can be handled without doubling the size of the problem. Higher order eigenvalue problems are reducible to first order form for which this technique is applicable. The treatment of the quadratic eigenvalue problem illustrates the details of this extension.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110204
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  • 118
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    A hybrid crack element for rectilinear anisotropic material (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 377-382 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110211
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  • 119
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    Application of the front solution to two and three-dimensional elastoplastic crack problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 393-395 
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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.1620110215
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  • 120
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    Comment on the paper ‘a finite element solution program for large structures’ (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 404-405 
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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.1620110219
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  • 121
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    A homework exercise in finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 411-417 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest an exercise which illustrates many of the fundamental ideas of finite elements, and is nevertheless easily programmed and quickly solved. It is governed by a partial differential equation on a circular region, but by maintaining symmetry the stiffness matrix becomes small and tridiagonal. The accuracy of linear elements can be studied in detail, and a straightforward extension leads to the eigenvalue problem, elements of higher degree, numerical integration, isoparametric elements, and a simple example in plasticity.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110302
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  • 122
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    Numerical Fourier analysis in the range of higher frequencies (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 469-480 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel method is proposed for the numerical computation of Fourier coefficients in the range of higher frequencies for which hitherto no practical method was available. The accuracy of the results obtained by application of this method is discussed, and bounds of a correction term are determined accordingly. An example from the field of Diesel engine research is given, and the computed spectrum is compared with the spectrum recorded by an electronic harmonic analyzer.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110307
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  • 123
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    Least square and Galerkin finite element solution of flow past a flat plate (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 185-190 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620110118
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  • 124
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    Announcements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 204-207 
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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.1620110123
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  • 125
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    Finite element solutions of the non-self-adjoint convective-dispersion equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 269-287 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element formulations based on the Galerkin and variational principles have been developed for the self-adjoint and non-self-adjoint problems represented respectively by the flow and convective-dispersion equations in the cylindrical polar system of co-ordinates. The formulation based on the variational principle is shown to be restricted to dispersion-dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.
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    URL: http://dx.doi.org/10.1002/nme.1620110205
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  • 126
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    The indirect design of fluid channels using a global variational method with trial functions not satisfying the prescribed boundary conditions (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 579-591 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The indirect design problem for compressible fluid flow in a channel determines the physical shape of the channel from the prescribed flow on the channel boundary. In this paper, a global variational method for the solution of this problem is described.The non-linear equations are solved by iteration; at each step of this iteration the solution to the equations (which are now linear) is found by a global variational method. The variational method differs from conventional methods in that the trial function does not satisfy the prescribed boundary conditions, but the method reproduces the conditions on the boundary.Results are presented for various physical quantities associated with the channel.Some comments are made on the extensions of these methods to supersonic flow and to the realistic cascade design problem.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110314
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    Matrices for scientists and engineers, W. W. Bell (University of Aberdeen), Van Nostrand Reinhold, 1974. £3·95 paperback £7·75 cloth (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 605-605 
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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.1620110318
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  • 128
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    On computer-aided analytic element analysis and the similarities of tetrahedron elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 611-622 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complete analytical analysis of three-dimensional, quadratic displacement tetrahedron elements is presented. The results show that the element stiffness can readily be obtained from the much simpler stiffness matrix of the linear displacement element. Thus, the task of obtaining the matrix of the quadratic displacement element is, in effect, reduced to finding that of the linear displacement element.The analysis has been made possible only by using a symbolic manipulation language (PL/I-FORMAC) on a computer. A rather general program for computer-aided basic element analysis is presented. It seems that the extremely effective tool of symbolic manipulation has hardly been used until now in mechanics.
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    URL: http://dx.doi.org/10.1002/nme.1620110402
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    Errata (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), 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
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    Optimization methods for engineering design, R. L. Fox, Addison-Wesley, Massachusetts, 1971. Price: £6·05 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 452-452 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620040315
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    Fuller Obituary on Professor B. Fraeijs de Veubeke (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 407-407 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110221
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    A numerical method for the solution of certain classes of nonlinear Volterra integro-differential and integral equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 431-438 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A direct numerical method is presented for the solution of classes of non-linear, singular Volterra integral and integro-differential equations of the types where y is the unknown and the Fs and Gs are given but to a large extent arbitrary functions of their arguments. The adaptation of the method to other equations, in particular with different kernels, is immediate.
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    On the elastic plastic initial-boundary value problem and its numerical integration (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 817-832 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An interative approach is proposed for the numerical analysis of elastic-plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic-perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.
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    Elasto-plastic finite element analysis (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 875-881 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An elasto-plastic finite element small displacement procedure to predict the behaviour of structures under cyclic loads is presented. The solution combines incremental procedure with correction for equilibrium and iterative scheme. Applications are made for a rectangular strip and a notched bar under cyclic axial loads. Flow theory of plasticity with either isotropic hardening or kinematic linear hardening is used.
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    A classification and survey of numerical methods for boundary value problems in ordinary differential equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 771-796 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The objective of the paper is a survey and classification of available numerical methods for boundary value problems with an emphasis on two point boundary value problems. In the paper a general two point boundary value problem is stated first and later available numerical methods are classified into five main groups according to their approach in numerical solution. In the next sections of the paper, each of these main groups are described and appropriate subgroups are defined and discussed.
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    An isoparametric Hermitian element for the solution of field problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 945-962 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A two-dimensional isoparametric Hermitian element is investigated for use in potential field problems with irregular geometry. Nodal degrees-of-freedom are the potential, the gradients in the directions normal and tangential to the element sides, and the twist. In applying the isoparametric principle a simple approximation is used which in general guarantees C1 continuity only at the element corners. The present version is restricted to 90-degree interior angles.The element is applied in the Galerkin solution of the steady-state continuity equation and several examples are presented. It is found that in cases where the potential field is simple but the element is strongly distorted, gradients obtained from the Hermite are not as accurate as those from the Lagrange-type cubic element having the same number of degrees-of-freedom. When the potential field is complex and the distortion is small, the Hermitian gradients are comparable to those of the Lagrange cubic; with increasing distortion they are comparable at the boundaries but less so in the interior. The errors in the potentials themselves are very similar, both elements giving a high degree of accuracy.Since all of its degrees-of-freedom are shared by four elements in the interior of a grid, the Hermite element is approximately 20 per cent more efficient than the Lagrange cubic for all but the smallest grids. Also, since the Hermite uses fewer nodes, data handling is greatly reduced. The element appears to be attractive at least in the area of groundwater flow.
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    Optimization methods applied to hydrodynamic bearing design (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1005-1027 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimization techniques are applied to the design of both hydrodynamic journal and tilting pad thrust bearings. Fletcher's adaptation of Davidon's gradient search method is further modified to deal with non-linear constraints in journal bearing design. A form of the Sequential Simplex is used for tilting pad thrust bearings. Penalty functions and variable transformations are used in both cases. Composite objective functions are included and the effect of weighting on each component of the composite function is investigated.
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    Optimum design of laminated fibre composite plates (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 623-640 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method is presented for the minimum weight optimum design of laminated fibre composite plates, subject to multiple inplane loading conditions, which includes stiffness, strength and elastic stability constraints. The buckling analysis is based on an equivalent orthotropic plate approach leading to two uncoupled eigenproblems per load condition. Overall computational efficiency is achieved by using constraint deletion techniques in conjunction with Taylor series approximations for the constraints retained. The optimization algorithm used, namely the method of inscribed hyperspheres, is a sequence of linear programs technique which exhibits rapid convergence in this application. Several example problems are given to demonstrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.
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    Error analysis of penalty function techniques for constraint definition in linear algebraic systems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 709-728 
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    Notes: The penalty function approach has been recently formalized as a general technique for adjoining constraint conditions to algebraic equation systems resulting from variational discretization of boundary value problems by finite difference or finite element techniques. This paper studies the numerical behaviour of the penalty function method for the special case of individual equation constraints imposed on a symmetric system of linear algebraic equations. Constraint representation and computational roundoff error components are distinguished and asymptotically characterized in terms of the penalty function weight coefficients. On the basis of this study, practical rules for the automatic assignment of values to those coefficients within the linear equation solver are proposed. Numerical problems encountered in the case of more general constraints are briefly discussed, and procedures for circumventing such difficulties are suggested.
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    Application of optimization and finite element methods to a cracking problem in timber (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 756-758 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 2 Ill.
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    Announcements (1977)
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 766-767 
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    Keywords: Engineering ; Engineering General
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    Erratum (1977)
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 770-770 
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    Superposition method of finite element and analytical solutions for transient creep analysis (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1107-1115 
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    Keywords: Engineering ; Engineering General
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    Notes: Based on the Lagrange multiplier's concept, a superposition method of analytical and finite element solutions has been developed to solve efficiently various non-linear and/or time-dependent problems in structural mechanics. According to the theory, the transient creep behaviour of a cantilever beam is analysed as an expository example.
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    An introduction to the mathematical theory of finite elements, J. T. Oden and J. N. Reddy, Wiley, New York, 1976. No. of pages 429. Price $32·00, £17·50 (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1198-1198 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Creep analysis of reinforced and prestressed concrete structures under non-uniform temperature distributions, using elastic solutions (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 883-895 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The analysis of stresses and deformations in concrete structures subjected to temperature gradients is described. As a result of the spatial variation of temperature, the creep compliance is a function of position. Previous work has shown that the constitutive equations for concrete creep can be expressed in a form which is invariable although ageing is included in the analysis. Thus viscoelastic methods can be used and correspondence principles can be developed; emphasis is placed in the present work on those which are based on the Laplace transform. A particular form is described, in which replacement of the elastic modulus by a function of the transformed creep compliance gives transformed values of stress; these values are easily obtained numerically by the finite element method using elastic analyses. The transformed values of stress are then expressed as approximate functions of the transformed creep compliance; inversion of the ensuing functions gives the stress as an approximate function of time. Two applications are given; the first considers a simple axially loaded column with reinforcement and the second deals with a thick cylinder subjected to a temperature gradient.
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    Discussion of ‘Finite element residual schemes for unconfined flow’ by Chandrakant S. DesaiInt. J. num. Meth. Engng, 10, 1415-1418 (1976). (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 908-910 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 3 Ill.
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    A finite element free boundary formulation for the problem of multiphase heat conduction (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 933-943 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The problem of heat conduction in a multiphase medium is a free boundary problem in which the free boundary is the phase transition line. The solution to this problem is highly irregular in that the temperature gradient is discontinuous at the free boundary. Two-dimensional, discontinuous, space-time finite elements are introduced to obtain a finite element, free boundary formulation for this problem. The jump in heat flux and position of the phase transition line become dependent variables in the finite element model. The resulting models give accurate results while allowing the calculation of free boundary problems with a fixed finite element mesh.
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    Numerical analysis of flow with or without wake past a symmetric two-dimensional profile without incidence (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 975-993 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Formulated in the hodograph plane, the bi-dimensional flow of a perfect fluid past a symmetric body leads to an elliptic variational inequality. By this way we show the existence of a one-parameter family of solutions. Furthermore the study gives us a simple and effective method for calculating the solutions. The results obtained with some typical profiles are given and compared with previous works.
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    Static stability of plates using fully conforming element (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 995-1003 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper the geometric stiffness matrices of a 12 degree-of-freedom rectangular element based on a fully compatible displacement field are developed for the first time and used to solve the elastic stability problem of rectangular plates under combined in-plane forces.The rapid convergence of buckling solutions based on the derived geometric stiffness matrices is demonstrated for plates with various boundary and loading conditions. Comparison of results shows that the present conforming element gives in all cases better results than the well known 12 degree-of-freedom non-conforming rectangular element.
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    An alternate finite difference operator for plates of variable stiffness (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1044-1048 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite difference approximation for the equilibrium equation of a thin, laterally loaded, elastic plate of variable stiffness is developed; it uses plate stiffnesses at node points and at points midway between the nodes of the rectangular grids. Displacement and moment results using this operator and an alternate one are compared.
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    Call for papers (1977)
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1056-1056 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Compact computation of natural frequencies and buckling loads for plane frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1067-1081 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Existing theory is assembled to give a method which needs only the core of a mini-computer to calculate the eigenvalues of large rigidly jointed plane frames with certainty, the eigenvalues being natural frequencies and critical load factors in free vibration and buckling problems, respectively. The method is illustrated by annotated listings of vibration and buckling programs, each involving under two hundred Fortran statements and with low number storage requirements (see Table I). The use of the programs as ‘black boxes’ is fully explained, with illustrative examples.The member theory used is the ‘exact’ classical Bernoulli-Euler uniform member theory. Possible applications include: evaluation of answers from approximate methods; calculation of critical loads for substitution in the modified Merchant-Rankine formula to estimate collapse loads of frames; and calculation of shifts in natural frequencies caused by structural damage, in connection with structural integrity monitoring of inaccessible structures.
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    A finite element convergence study for accelerating flow problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1155-1174 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence properties of several non-linear solution procedures were examined with respect to the accelerated flow of a fluid in a converging channel (the Hamel problem), using two different finite element computer programs with different elemental construction. The Reynolds number varied from that for creeping flow to 1088 without exceeding the radius of convergence. Special attention was given to the successive substitution and Newton-Raphson solution algorithms, with a significant advantage in rate of convergence noted for the latter.
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    An unconditionally stable explicit algorithm for structural dynamics (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1579-1592 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents an unconditionally stable explicit algorithm for the direct integration of the structural dynamic equations of motion. The algorithm is restricted to a diagonal mass matrix and positive definite symmetric stiffness and damping matrices. The algorithm is based on splitting the stiffness and damping matrices into strictly lower and upper trangular form. Unconditional stability is proven, but only for the undamped case and a completely symmetric splitting of the stiffness matrix. An alternate splitting method is also presented and numerical examples indicate superior performance over the symmetric splitting, but only a conditional stability. A spring-mass-dashpot model is used to illustrate the algorithm.
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    Differentiation and integration using Bernstein's polynomials (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1627-1630 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 1 Ill.
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    Newtonian die swell evaluation for axisymmetric tube exits using a finite element method (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1621-1626 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Using a finite element method, a value of 13.2 per cent is obtained for the die swell of a highly-viscous Newtonian fluid flowing at very low Reynolds number from a circular tube of constant radius. The same method is then used to obtain die swell values for a variety of axisymmetric tube exits. It is found that, in general, conical constrictions at or near the tube exit result in a decrease in die swell, while conical expansions increase the die swell.
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    The steady state response of geometrically non-linear shallow arches (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1261-1269 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The non-linear steady state response of structures with curvature is investigated through the expository example of a shallow circular arch. A consistent mass finite element formulation is employed to derive the governing non-linear differential equations.These equations are solved by assuming a single mode expansion reducing the governing equations to the single degree-of-freedom Duffing's equation with a quadratic term. The non-symmetric amplitude-frequency curve is derived and compared with results previously obtained by direct integration of the equations of motion.
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    Temperature load on thick curved shell elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1329-1333 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Temperature load on a shell is usually represented as initial strains in the tangent plane directions of the shell, since strains in shell surface normal directions are neglected. It is shown, however, that this simplification may give rise to significant errors for thick curved shell elements. A procedure to overcome this problem is presented. In particular the eight-node subparametric thick shell element is considered.
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    Futher limitations on general hexahedron finite elements with derivative degrees of freedom (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972), S. 137-139 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: It is shown that isoparametric finite elements with derivative degrees of freedom of second order or higher in the local curvilinear space demand an excessive number of degrees of freedom in the global space. To illustrate this limitation as it pertains to the continued development of higher order elements, discussion is centered around the general hexahedron element.
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    More on reduced integration and isoparametric elements (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972), S. 141-142 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 1 Ill.
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    Elasto-plastic stress analysis. A generalization for various contitutive relations including strain softening (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972), S. 113-135 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Several iterative processes for solving elasto-plastic problems are discussed in the context of a general formulation which includes: 1Associated and non-associated plasticity relations.2Strain hardening as well as strain softening behaviour.Advantages of the ‘initial stress’ process are emphasized for a wide category of problems and the isoparametric formulation is used throughout.
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    Vibration problems using isoparametric shell elements (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972), S. 142-145 
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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.1620050114
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    Direct finite element analysis of elastic contact problems (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972), S. 145-147 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 6 Ill.
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    Masthead (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Finite elements of non-linear continua, J. T. Oden, McGraw-Hill, New York, 1972. Price: $8.40 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972), S. 148-148 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620050117
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    A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1879-1892 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the non-linear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C0-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.
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    Closed form elastic-plastic stiffness matrix for axisymmetric finite elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 59-65 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note presents the closed form equations for the stiffness terms in the elastic-plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl-Reuss flow rule and von-Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
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    Certain properties of numerical schemes used to solve the blade-to-blade flow problem (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 85-92 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The compressible potential flow on a blade-to-blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non-linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade-to-blade configurations.
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    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 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    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.
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    Discussion of a paper by E. O. FrindInt. J. num. Meth. Engng, 945-962 (1977). (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 183-185 
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    Notes: In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.
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    Masthead (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    A least squares finite element approach to unsteady gas dynamics (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1-10 
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    Keywords: Engineering ; Engineering General
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    Notes: A numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
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    Finite element analysis of steady-state elasto-visco-plastic flow by the initial stress-rate method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 47-57 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady-state visco-plastic flows.
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    A finite element formulation for large elastic-plastic deformation analysis of polycrystals and some numerical considerations on polycrystalline plasticity (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 101-114 
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    Keywords: Engineering ; Engineering General
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    Notes: A finite element formulation for large elasto-plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress-strain curves for several proportional loadings, effect of change of loading path on stress-strain curve, subsequent yield loci for uniaxial and equi-biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.
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    Addendum to the paper ‘finite element analysis of steady-state elasto-visco-plastic flow by the initial stress-rate method’ (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 382-383 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    A 2nd order numerical method for laminar flow at moderate to high Reynolds numbers: Entrance flow in a duct (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 405-414 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 4 Ill.
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    On least squares approximations to indefinite problems of the mixed type (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 453-469 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    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.
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    Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1851-1863 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The boundary control problem of optimal heating of an infinitely long slab with tempertue-dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods.In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co-ordinate is discretized by use of the finite element method, while the Runge-Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization.
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    Call for papers (1979)
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1879-1879 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Derivation of first-passage time distribution of a single lift for arbitrary traffic (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1-11 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The distribution of the first-passage time is of decisive importance in lift (elevator) design. It yields the easure of performance of the system, the expected number of stops, the interval (i. e. time elapsed between two successive departures from a given floor) and many other parameters and factors determining the required number of lifts in a building. The derivation is based on the transition probability matrix of the operation policy, and consists in solving a system of linear equations.
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    On the analysis of accuracy for two-equation transient problems (1980)
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 55-62 
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    Notes: Fourier analysis of numerical accuracy has traditionally concentrated on the propagation behaviour of various methods. When systems of equations in more than one unknown are involved, analysis of propagation accuracy alone is shown to be incomplete. A distribution factor is introduced to complement the Fourier analysis in these cases, and application of the concept to two problems commonly encountered in the water resources field is demonstrated. The distribution factor is shown to provide important information which cannot be obtained from the customary analysis of propagation accuracy.
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    Finite element methods for an optimal steady-state control problem (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1375-1382 
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    Keywords: Engineering ; Engineering General
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    Notes: An optimal steady-state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.
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    Sensitivity Of matrix eigenvaluesThis work was done while both authors were summer visitors to Argonne National Laboratory in connection with the LINPACK project. (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1367-1373 
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    Notes: A recent paper by Donald Gignac describes some difficulties with a certain matrix eigenvalue problem. This paper shows that the difficulties result from the naturue of the matrix itself. Quantities called condition numbers, which measure the sensitivity of the eigenvalues, are computed, and numerical results given.
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    Efficient implementation of anisotropic three dimensional boundary-integral equation stress analysis (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1383-1397 
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    Keywords: Engineering ; Engineering General
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    Notes: The boundary-integral equation medthod is particularly well suited for solution of stress concentration and elastic fracture mechanics problems. The method was not previously applicable to anisotropic three dimensional problems because no efficient technique existed for calculation of the required point load solution for an infinite body. A technique has been developed to evaluate numerically the anisotropic point load soultions, and used to generate data bases for various materials. An intrpolation technique is used to evaluate the point load solutions efficiently within a higher order boundary-intgral equation code. The effectiveness of the technique is verified by solution of problems involving both uniaxial stress states and stress concentrations.
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    The limitations of the patch test (1980)
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 177-188 
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    Keywords: Engineering ; Engineering General
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    Notes: A simple approximation by nonconforming finite elements is presented that passes the patch test of Irons and Strang but does not yield approximate solutions converging to the solution of the given boundary value problem. It is constructed from continuous piecewise linear functions perturbed by step functions. Further, strange convergence properties of such approximations are explained in all details because they may be typical for the behaviour of nonconforming finite elements violating the basic precondition for convergence.
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    Primitive variable finite element formulations for steady viscous flows (1980)
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 209-223 
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    Keywords: Engineering ; Engineering General
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    Notes: The solution of incompressible, viscous flow problems using the primitive variable finite element approach is formulated in a coherent and physically reasoned exposition. In particular, it is shown that terms associated with changes in momentum caused by lack of mass conservation should logically be included in the governing equations. Previous formulations have not considered this possibility. Numerical results are presented to show the effect of inclusion of these extra terms; however, it is concluded from the numerical results for the specific case which was tested that there is no obvious benefit obtained by including these terms.
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    A method for space truss analysis in the post-buckling range (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 237-247 
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    Keywords: Engineering ; Engineering General
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    Notes: A dual load method of truss analysis is presented that allows highly nonlinear member behaviour to be followed. In particular, a brittle type of strut behaviour is considered. The method assumes that the inelastic strut response is known and that piecewise linearization of the behaviour is acceptable. An example is given to illustrate the type of problem that can be handled. The example involves negative stiffness of the members and consequently attention must be given to the equation solving procedure for the structure. A comparison is made with some observed test results.
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    An approximate laplace transform inversion using exponential series representation (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 291-295 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A numerical Laplace transform inversion technique is described, which is a modification of the inversion method using an exponential series representation. By adding an auxiliary function and using Erdélyi's inversion formula, the proposed technique provides the inverse approximation with improved accuracy near t = 0. Numerical illustrations shows that this procedure also works in cases when the original method of schapery fails to give satisfactory results.
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    A first-order blending method for triangles based upon cubic interpolation (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 308-318 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for interpolating in triangles is described. Bivariate cubic polynomials are utilized to define an interpolant which assumes arbitrary position and slope on the entire boundary of a triangular domain. Some examples and applications are discussed.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150214
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    Numerical fourier transformation: Singularity expansions and product integration (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1473-1477 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120914
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    ‘Potential energy with iterative correction’… or deterioration, that is the question (Reply by Authors to M. Crisfield's Discussion1 of ‘A Critical Assessment of the simplified Hybrid Displacement Method’2) (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1461-1472 
    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.1620120913
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    An investigation of first- and second-order mixed plate-bending elements (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 351-360 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical convergence of first- and second-order plate-bending elements is investigated. Using iso-parametric formulation, general bilinear and biquadratic quadrilaterals, with the three moment components and the transverse deflection as dependent variables, are obtained. The same elements are also used as degenerate triangles by collapsing one side. A constant bending moment patch test, applied numerically to the elements, indicated poor performance for linear triangles, while the bilinear, quadratic and biquadratic elements behaved well, with exact results in uniform meshes. Further numerical examples showed the same general trend as the patch test. Although bilinear, quadratic and biquadratic elements were always able to yield the correct solutions with mesh refinements, the linear triangles were in general unable to do so.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150305
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    Finite difference analysis for developing laminar flow in circular tubes applied to forced and combined convection (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 381-404 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The complete two-dimensional partial differential equations for developing laminar flow in a circular tube have been treated by a finite difference analysis. Property variation with temperature, especially that of viscosity, is allowed for in a flexible manner. The continuity and momentum equations, and then the energy equations, are solved by direct elimination at each axial step, and marching procedure used in the axial direction. A new technique is that the stepwise energy balance is rigidly satisfied throughout by using it as a constituent equation in place of the ‘explicit’ wall thermal boundary condition normally used.The analysis predicts the complete developing hydrodynamic and thermal fields, together with friction factors and heat transfer coefficients. It has been tested for a range of fluid velocity and thermal boundary conditions and for various fluids, including high viscosity oils, water and air.Data for constant wall heat flux have already been published. 1,2 Predictions for constant wall temperature presented here are for forced and combined convection and are compared with experimental data of Test3 and Zeldin and Schmidt4.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150307
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    A numerical method for solving two-point boundary value problems for nonlinear ordinary differential equations (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 464-469 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for solving two-point boundary value problems associated with systems of first-order nonlinear ordinary differential equations is described. It needs four function evaluations at each point and is of order h6, where h is the space chop. Results of computational experiments, which include perturbation of the initial conditions, comparing this method with other known methods are given.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150313
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    A method for the automatic generation of triangular elements on a surface (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 470-476 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is given to discretize a polygon or curved surface into triangular arrays. The method first involves the manual division of the array into quadrilaterals with specified numbers on rows and columns. The individual points are then filled in automatically and elements are automatically generated. A point of particular importance is that the number of columns or rows may be made to change. A subroutine is given to perform this task.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150314
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    Design oriented analysis of imperfect truss structures - part II - approximate analysis (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 483-494 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approximate analysis method for calculating local and system geometric imperfection influences on the displacements, stresses and buckling load of imperfect truss structures, is developed. The structural response, as a function of the design variables, is expressed in this approximate analysis which is much faster and cheaper than the ‘accurate’ analysis. The accurate analysis for a particular design is used as a base for each approximate analysis which then gives the response information needed for other designs in the neighbourhood about the base point design. Comparison of the approximate behaviour predictions with accurate results based on the more refined analysis methods shows that the quality of the proposed approximate analysis procedure is adequate for guiding a structural design procedure. It is evident that the approximate analysis is capable of describing the nonlinear behaviour of the structure, but when nonlinearity increases, the quality of the approximate analysis tends to deteriorate.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150402
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    Reduction of the error in eccentric beam modelling (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 575-582 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The usual linear shape function for approximating axial displacement in beam finite elements used as eccentric stiffeners leads to an inconsistency which can result in large errors in the deflection of plates or composite beams. The introduction of an additional degree-of-freedom for these elements circumvents this problem.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150408
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    A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 639-648 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary-location method is developed for finite element simulation of steady, two-dimensional flows of Newtonian liquid with free boundaries. In the method, boundary shape and position and the velocity and pressure fields are determined simultaneously. Inertial, viscous, gravitational, and surface tension effects are included in the development. The complete set of nonlinear finite element equations is solved by a modified frontal method combined with Newton-Raphson iteration to speed convergence. The finite element used to illustrate the method approximates the pressure as a piecewise constant function and the velocity and free boundaries as piecewise linear functions. Example calculations for flow from a slit show that the method can be effective.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150502
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    A one-step method for direct integration of structural dynamic equationsThis work has been made in the framework of ELFI program supported by ENEL. (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 685-699 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The choice on an efficient direct integration procedure for linear structural dynamic equations of motion is discussed. It is suggested that as accuracy parameter the truncation error on the exponential terms contained in the modal contributions of the exact solution be assumed. This error does not always coincide with the local truncation error. These considerations were used to design an unconditionally stable one-step method whose accuracy is 0(h4). Numerical comparisons with some well-known integration schemes showed the efficiency of the proposed method.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150506
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    A generalized automatic mesh generation scheme for finite element method (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 713-731 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a generalized method which generates linear, triangular, quadrilateral and pentahedral elements for the finite element method. Depending on geometrical and material variations, the region to be discretized is manually divided into blocks such as lines, triangles, quadrilaterals, pentahedrons and hexahedrons in several appropriate co-ordinate systems. However, no connectivity information of the adjacent blocks is required by the user as input. The continuity of the generated nodal co-ordinates and element configurations at the block interface are automatically maintained to describe the geometry of structures, no matter how these five types of blocks are connected. Furthermore, a mesh grading algorithm which generates reliable mesh grade distributions in the interior of the triangular and quadrilateral blocks is established corresponding to the arbitrarily defined subdivision numbers for each edge line of blocks. This algorithm is extended to the mesh grading in the interior of the hexahedral and pentahedral blocks. Element numbers are also renumbered in this scheme, in addition to node numbers, in order to increase the computational efficiency of the global matrix assembly. Additional facilities, i.e. loading data generation, boundary condition data generation and so on, are also discussed. An illustrative and a practical example are given to demonstrate the capabilities of this scheme.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150508
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