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  • 1980-1984  (574)
  • 1980  (574)
  • Biochemistry and Biotechnology  (252)
  • Engineering  (233)
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  • 101
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1381-1393 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is used to analyse heat and mass transfer problems in porous media, in which the thermophysical properties are allowed to vary as functions of temperature and moisture. An example is given of the application of the method to the problem of timber drying.
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  • 102
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1570-1574 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for solving field problems using a finite element formulation, to be executed with the aid of a micro-computer. In order to reduce the requirements regarding memory space, the coefficients of the matrix defining the system of equations are not stored, but calculated when they are needed, in a modification of the usual finite element procedure. The method is applicable to all problems for which Gauss-Seidel iteration converges, and can handle problems involving more than 100 degrees-of-freedom on a computer with 8,000 bytes memory. Computing time may run up to several minutes per cycle of iteration, but on a small, personal computer, this is still acceptable.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1659-1680 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for the adhesive of a lap joint is presented. The element is based on the assumptions common to the theories of Goland and Reissner and Ojalvo and Eidinoff. Deficiencies of the lap joint theories of those workers and of a previous finite element formulation of the adhesive are pointed out and the covergence of the new formulation to their results is discussed. Experimentally determined extreme fibre strains in the adherends are compared with those determined numerically using the new finite element formulation.
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980) 
    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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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1730-1733 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1747-1769 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite elements with polynomial interpolation functions of a degree higher than 2 are used comparatively little on large FEM systems, except in shell elements. However, the author has had several years' experience in the use of the so-called ‘isoparametric, reduced Hermitian element’,4 Which has behaved excellently in an industrial as well as an educational environment. The reason for the interest in the Hermitian concept is that the overcompatibility of the element reduces the number of unknowns, the solution time and the discontinuities in stresses between elements.Explicit formulae for the family of interpolation polynomials of order q and degree p = 2q + 1 are given and hierarchical Hermite elements are introduced. The families of Hermite and serendipity elements are isomorphic and the latter may thus be extended to arbitrary high order.For some problems the equidistant node configuration in Lagrange elements of degree 3 and higher is not optimal with respect to smoothness, and a new type of element, the ‘Lobatto element’, is introduced.The methods consistently produce results of an accuracy which is above the requirements of usual engineering applications, but in graphics smoothness of curves is important for a convincing representation. The methods are of particular interest in industries working with structures composed of almost linear materials with well-known properties.
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  • 107
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1771-1812 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An assessment of flat triangular plate bending elements with displacement degrees-of-freedom at the three corner nodes only is presented, with the purpose of identifying the most effective for thin plate analysis. Based on a review of currently available elements, specific attention is given to the theoretical and numerical evaluation of three triangular 9 degrees-of-freedom elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid stress model (HSM) element and a selective reduced integration (SRI) element. New and efficient formulations of these elements are discussed in detail and the results of several example analyses are given. It is concluded that the most efficient and reliable three-node plate bending elements are the DKT and HSM elements.
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1613-1626 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of infinite elements is briefly reviewed. New more logical and general formulations of infinite elements are presented. The simplicity of the programming is emphasized. Results are given for elasticity and potential problems. Future extensions are discussed.
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  • 109
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1681-1689 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Convection-diffusion equations are difficult to solve when the convection term dominates because most solution methods give solutions which oscillate in space. Previous criteria based on the one-dimensional convection-diffusion equation have shown that finite difference and Galerkin (linear or quadratic basis functions) will not give oscillatory solutions provided the Peclet number times the mesh size (Pe Δx) is below a critical value. These criteria are based on the solution at the nodes, and ensure that the nodal values are monotone. Similar criteria are developed here for other methods: quadratic Galerkin with upwind weighting, cubic Galerkin, orthogonal collocation on finite elements with quadratic, cubic or quartic polynomials using Lagrangian interpolation, cubic or quartic polynominals using Hermite interpolation, and the method of moments. The nodal values do not oscillate for collocation or moments methods with Hermite cubic polynomials regardless of the value of Pe Δx.A new criterion is developed for all methods based on the monotonicity of the solutions throughout the domain. This criterion is more restrictive than one based only on the nodal values. All methods that are second order (Δx2) or better in truncation error give oscillatory solutions (based on the entire domain) unless Pe Δx is below a critical value. This value ranges from 2 for finite difference methods to 4·6 for Hermite, quartic, collocation methods.
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  • 110
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    International Journal for Numerical Methods in Engineering 16 (1980), S. 149-170 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of the paper is two-fold: Firstly, we develop stream function--vorticity and primitive variable finite element models of two-dimensional barotropic equations that satisfy the conservation of mean vorticity, mean squared vorticity (or enstrophy) and mean kinetic energy, and scondly, we present a comparative study of a number of numerical schemes for their accuracy in phase speed as well as in amplitude calculations for a two-dimensional, time-dependent, stream function--vorticity equation for periodic fluid motion in a channel. A circular vortex is placed in a uniform channel flow of a constant velocity (U) as an initial condition. An analytic solution exists for the problem such that the vortex moves with a constant speed U conserving the shape of the vortex: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {\psi \left({x,y,0} \right) = - Uy + \psi _0 \exp \left[{ - a^2 \left({x^2 + y^2 } \right)} \right] \equiv F\left({x,y} \right)} \hfill \\ {\psi \left({x,y,t} \right) = F\left({x - Ut,y} \right)} \hfill \\ \end{array} $$\end{document} where U, ψ0 a are constants. This example makes it easier to identify the cause of phase speed error, either due to linear or non-linear processes, and furthermore, to find a satisfactory scheme for time integration. The numerical schemes compared include: Arakawa Jacobian,1 Arakawa-Matsuno scheme, Galerkin finite element, Lax-Wendroff, leap-frog, and Crank-Nicholson. The effect of a variational adjustment (see Sasaki16) is also studied. Computational time, RMS errors in stream function and vorticity, and the conservation of the mean kinetic energy and enstrophy are compared at the end of 120 (one period) and 240 (two periods) time steps. The study indicates that the numerical scheme that employs finite elements in space (same as Arakawa Jacobian) and Crank-Nicholson in time is the most accurate among the schemes studied.
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  • 111
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1281-1282 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 112
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1325-1334 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A two-dimensional finite element mesh generator capable of discretizing arbitrarily shaped flow regions is described. This economical, interactive computer code, written in FORTRAN IV and employing PLOT 10 software together with TEKTRONIX graphics terminals (4000 series or similar devices), generates a triangular network of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. The algorithm is an easy-to-use preprocessor and mesh generator delivering for a particular source program suitable input data which contribute to a higher degree of accuracy, efficiency and flexibility of the numerical scheme.The code was tested for the triangularization of the confluence region of the Ohio and Tennessee rivers with two islands forming subchannels of different sizes.
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  • 113
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1363-1380 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational algorithm, based on the combined use of mixed finite elements and classical Rayleigh-Ritz approximation, is presented for predicting the nonlinear static response of structures; The fundamental unknowns consist of nodal displacements and forces (or stresses) and the governing nonlinear finite element equations consist of both the constitutive relations and equilibrium equations of the discretized structure. The vector of nodal displacements and forces (or stresses) is expressed as a linear combination of a small number of global approximation functions (or basis vectors), and a Rayleigh-Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The global approximation functions (or basis vectors) are chosen to be those commonly used in static perturbation technique; namely a nonlinear solution and a number of its path derivatives. These global functions are generated by using the finite element equations of the discretized structure.The potential of the global-local mixed approach and its advantages over global-local displacement finite element methods are discussed. Also, the high accuracy and effectiveness of the proposed approach are demonstrated by means of numerical examples.
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  • 114
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1419-1420 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 115
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1422-1426 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 116
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1447-1455 
    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 displacements in beam finite elements used as eccentric stiffeners or as portions of composite cross-sections, leads to an error in the static deflection. A modified element reduces this error. The behaviour of these two elements under free vibration is examined. The linear element is shown to be in considerable error in the dynamic case also.
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  • 117
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1489-1506 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis is presented which indicates that special reduced integration of the displacement compatible Lagrange family of finite elements can give numerical models preserving characteristics of equilibrium formulations. A number of examples show that bounds on the discretization error can be obtained in both an energy norm and locally. The process is therefore recommended for error analysis and for the assessment of the reliability of displacement compatible finite element solutions.
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  • 118
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1557-1561 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 119
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1580-1583 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 120
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1585-1594 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is presented for measuring the effectiveness of a finite element approach when compared with a reference finite element approach with respect to accuracy and computation. The effectiveness measure is applied to the Hughes reduction method for structural eigenvalue problems and three proposed analogous methods for fluid or fluid-structure problems. Comparisons of the three methods with consistent interpolation solutions indicate that improved effectiveness can be obtained.
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  • 121
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1627-1642 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is devoted to a comparison of the relative accuracy of two-dimensional vs. three-dimensional finite element representations of contaminant dispersion in shallow lakes. Formulations of both types are developed, followed by numerical calculations of a hypothetical lake. The results indicate that for typical lakes a two-dimensional dispersion analysis can be employed in the absence of a significant advective contribution. With significant advection the two-dimensional approach is not sufficiently accurate. A two-dimensional dispersion analysis requires approximately the same computational resources as a three-dimensional circulation analysis.
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  • 122
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1691-1704 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods for solving the following data-fitting problems are discussed: given the data (xi, yi, fi),i = 1,…,N construct a smooth bivariate function S with the property that S(xi, yi) = fii = 1,…,N. Because the desire to fit this type of data is encountered frequently in many areas of scientific applications, an investigation of the available methods for solving this problem was undertaken. Several aspects, such as computational efficiency, fitting characteristics and ease of implementation, were analysed and compared. Within the context of a general-purpose method for large sets of data, two of these methods emerged as being generally superior to the others. It is the purpose of this paper to describe these two methods and present examples illustrating their use and application.
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  • 123
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 124
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1813-1822 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a method for the automatic triangulation of arbitrary multilateral plane domains. In addition, the method can be used in connection with that suggested by Zienkiewicz and Phillips4 for the subdivision of curved-boundary domains. The method can be described as general fully automatic and computer oriented. A Fortran computer program has been prepared by the author. Output can be of interactive, graphical or alphanumerical form. The program has been applied to a number of cases. The resulting triangulations are always satisfactory, even when vigorous changes of mesh sizes are encountered.
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  • 125
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1873-1876 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 126
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 16 (1980) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 127
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    International Journal for Numerical Methods in Engineering 16 (1980), S. 35-49 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently, theoretical error analysis for alternating-direction methods using isoparametric elements has been done by the author. Here the implementation of these methods is described for nonlinear parabolic boundary-value problems, and numerical results using these methods are presented. With an alternating-direction method, multidimensional problems can be solved as a series of one-dimensional problems. This results in great savings of both computation time and storage compared to standard finite element techniques.
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  • 128
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    International Journal for Numerical Methods in Engineering 16 (1980), S. 121-136 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the use of a penalty method to enforce the constraint of incompressibility in nonlinear elasticity. As an example, a problem involving the use of the Newton-Raphson method in conjunction with incremental loading and a successive mesh refinement scheme is presented. It is shown that during the incremental loading phase and the Newton-Raphson refinement on a fixed mesh, all tangent stiffness matrices are positive definite for the chosen energy density and load increment. But when the mesh is refined and the solution is interpolated as a starting value on the new mesh, the tangent stiffness matrix is indefinite. A theoretical analysis of the associated mixed method and a new equivalence theorem are seen to lead to a way to retain positive definiteness. The key is the use of an equivalent tangent stiffness matrix which is the reduced Hessian matrix. The numerical example shows that both positive definiteness and the quadratic convergence rate of the Newton-Raphson method are obtained.
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  • 129
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    International Journal for Numerical Methods in Engineering 16 (1980), S. 51-64 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discretization procedure applied to the evolution equations of non-linear heat transfer is usually twofold; first, a semi-discretization in space is realized (by finite elements in the present case), leaving a set of first order non-linear differential equations and, second, the time integration of these equations is accomplished by a step-by-step procedure (e.g. by one-step implicit schemes), thus yielding a set of non-linear algebraic equations for each time-step considered.This paper discusses the two classes of methods one can resort to for solving these final non-linear algebraic systems: (1)Tangent methods derived from the Newton-Raphson (NR) or modified NR techniques, in which successive linearized systems based on the tangent Jacobian matrix are solved until coveragence is reached; owing to the second order accuracy of this method the required number of iterations per step is small, especially if the capacity heat flows are mildly non-linear; tangent methods applied to diffusion problems suffer, however, an important shortcoming; the Jacobian matrices are unsymmetrical and thus require extended core storage and special care in the organization of the solution procedure. Some economy may be realized by either the modified tangent method (the tangent matrix is kept constant for several iterates) or the restricted tangent method (a single iterate per time-step).(2)Secant methods obtained by direct linearization of the time-step equations, in which out-of-balance heat flows are computed at each iteration and serve to correct the solution until heat flow equilibrium is restored; in comparison with tangent methods, a greater number of iterations per step is expected for reasonable accuracy, but the system matrix is always built and inverted only once per time-step and, above all, is symmetrical. it is shown how the pseudo-force formulation with a few corrective loads updating enjoys nearly the same convergence properties as the modified tangent method without involving unsymmetrical system matrices. This constitutes the best suited method for mildly non-linear problems of heat transfer.Some simple numerical experiments are presented that show the relative advantages of the two methods on bench-mark problems.
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  • 130
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    International Journal for Numerical Methods in Engineering 16 (1980), S. 171-184 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element method is presented for the numerical solution of the Burgers' equation. The method is based on a weighted residual formulation in which the method of characteristics is incorporated by employing isoparametric space-time elements with the sides joining the nodes at subsequent time levels oriented along the characteristic lines of the hyperbolic partial differential equation associated with the Burgers' equation.This method is capable of solving the Burgers' equation accurately for values of viscosity ranging from very small to large. The utility and accuracy of the method are demonstrated by a number of examples and a comparison of the numerical results with the exact solution is presented in one case.
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  • 131
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    International Journal for Numerical Methods in Engineering 15 (1980) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 132
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 13-30 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is sometimes convenient to express a numerical algorithm in terms of a network model. The physical picture given can often help the engineer to visualize the properties of the method. In field problems, a lumped network model corresponds to a space discrete field while a transmission-line model corresponds to a field which is discrete in space and time. In this paper, the relationship is given between the lumped network models and transmission-line network models used in the steady-state solution of Maxwell's equations in two and three space dimensions. The use of dual networks is also discussed. An analysis is given for the velocity of waves travelling in any direction across the networks and this is used to compare the accuracy of the models. The use of diakoptics or substructures for the solution of large networks is outlined and this is illustrated by a compound two-dimensional example.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 87-96 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general procedure for calculating the buckling of stiffened skew plates by the Rayleigh-Ritz method with B-spline functions as co-ordinate functions.Convergence of the solutions is investigated in a few typical cases and is found satisfactory. The results are compared with existing values based on other numerical methods and found to be in good agreement. Buckling characteristics of stiffened skew plates are also studies with varying stiffness parameters of stiffeners, skew angles and aspect ratios.
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  • 134
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    Notes: This paper describes the essential features of the program package MAGGY2. With MAGGY2, magnetostatic problems in two dimensions can be analysed. The co-ordinate system may be Cartesian, cylindrical or polar. A finite element method with bilinear isoparametric quadrilaterals is used. Input must be given in the problem-oriented language MAGLAN. This language is based on the idea that a user of MAGGY2 wants to describe his problem rather than give commands for its solution. The algorithm and the problem-oriented language are described. Some examples showing the use of the package are given.
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  • 135
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 129-144 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Upwind and central difference schemes for laminar and turbulent flows over a step in a two-dimensional channel are compared with each other and with experiment. Vorticity ω and stream function ψ are used as dependent variables and it is shown that an upwind difference method can give predictions which agree with experiment for high Reynolds number flows. The numerical implementation of the boundary conditions is found critically to determine the solutions obtained. Explicit prescription of ψ and ω at the inlet leads to incorrect values of the inlet velocity component perpendicular to the flow and a solution that does not agree with experiment. Experimental evidence is not available at low Reynolds numbers, but it is found that upwind differences give recirculation zones 8 per cent shorter and 8 per cent less intense than the more conventional conditionally stable central difference method.The distribution of the false diffusion effect in the upwind scheme is considered, and it is shown by use of a simple example that previous statements as to possible minimization of this effect are not generally true.The difficulty of determining the pressure distribution from the vorticity and stream function model is analysed and illustrated.Further, turbulent separated flows are seen to contain regions where two-dimensional time-dependent flow does not exist, and conventional theories do not give good results.
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  • 136
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 161-161 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 137
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 162-166 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 138
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 189-208 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified approach is presented for the static and transient dynamic linear and geometrically nonlinear analysis of Mindlin plates including initial imperfections. The effects of transverse shear deformation and rotatory inertia are automatically taken into account. A finite element idealization is adopted and the quadratic Lagrangian Mindlin plate element is used together with selective integration. Several numerical examples are presented and compared with results from other sources.
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  • 139
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 225-235 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several computer codes have incorporated the ‘overlay’ material models: the volume element, which is characteristic of the material, is composed of sub-elements with different kinematic hardening, perfectly plastic or even viscoplastic flow rules and different elastic properties, these sub-elements exhibiting all, however, the same total strain.1,2In this paper it is demonstrated how the simple mathematical framework we first proposed for elastic-plastic structures with kinematic hardening material,3 and we extended to some elastic viscoplastic ones,4 can easily be applied to these particular ‘overlay’ materials.One of the interesting advantages of this approach is a straightforward analysis of structural response under cyclic loadings by applying the linear elastic analysis.
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  • 140
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 296-301 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method able to evaluate the response of harbours of constant depth to periodic plane waves in the presence headlands of breakwaters near the harbour mouth is described and tested on a particular case.The method, based on Green's function theory, is rather general, and can also treat the response of an off-shore harbour, as well as the diffraction field due to only breakwaters or headlands, when the interaction with the coastline must be taken into account.
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  • 141
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 319-319 
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  • 142
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    International Journal for Numerical Methods in Engineering 15 (1980) 
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  • 143
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 333-341 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for calculating natural frequencies and mode shapes of large structural systems with substructures and the subspace iteration is developed. The method uses only substructural stiffness matrices and the mass matrix for each finite element of the system. The mass matrix for the entire structure or any of its substructures need not be computed. However, efficiency of the method is improved when mass matrix for the entire structure is computed and saved in the computer core. No approximating assumptions are made. Thus, natural frequencies and mode shapes for the finite element model employed are the same with or without the substructuring algorithm. This is demonstrated by computing first ten natural frequencies and the corresponding mode shapes for an open truss helicopter tail-boom structure.
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  • 144
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 361-379 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, efficient finite element method has been presented for the solution of a variety of scalar field problems in two dimensions. It is based on the mapping of the physical problem domain into an ‘image’ domain in the w-plane. The governing equation(s) and the boundary conditions in the physical plane are also appropriately transformed into the w-plane. The processes of standard finite element analysis are then implemented to obtain a solution in the w-plane.The method has been explained in detail, with illustrative examples where appropriate; it has several important advantages over the standard finite element method, particularly for the solution of infinite or semi-infinite domain problems. The method has been demonstrated to be simple, efficient, economical and potentially capable of dealing with a large repartoire of two-dimensional problems, including non-homogeneity, nonlinearity, etc.
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  • 145
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 451-456 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Closed form finite element solutions are obtained for the uniformly loaded membrane in Rn, n = 2,3 discretized with first-order elements. It is verified on this model that the pointwise error in the displacement is 0(h2 log 1/h). Slopes converge pointwise at the optimal rate 0(h).
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  • 146
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 557-573 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Both the central and upwind difference schemes are commonaly employed to solve the Navier-Stokes equations governing the two-dimensional laminar flow of an incompressible laminar flow of an incompressible viscous fluid. By a judicious choice of a damping parameter and using direct methods for solving the systems of linear equations appearing in an iterative procedure, the central difference scheme could be made to give convergent results even for large Reynolds numbers. Using a model problem of flow through a driven square cavity it is shown that the converged results so obtained become progressively oscillatory and inaccurate as the Reynolds number increases. It is known that the central difference scheme gives more accurate results than the upwind difference scheme, at least for small values of Reynolds number. However, for a reasonably small mesh size the numerical solutions obtained by using either the central or the upwind difference scheme do not differ appreciably at low Reynolds numbers. There is a small range of Reynolds numbers for which the central difference scheme may yield more accurate results than the upwind difference scheme; however, this range is not known a priori.
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  • 147
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 599-610 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Numerical solutions for two-dimensional or axisymmetric viscous fluid flow problems are usually based on the stream function/vorticity formulation. Frequently, however, the pressure distribution is of prime interest. Difficulties have been reported in the literature with the use of obvious pressure marching schemes. Consequently, several investigators have preferred to use an iterative method which involves solving a Poisson equation with Neumann boundary conditions. In this paper, the fundamental cause of failure of the marching schemes is investigated. The authors introduce the concept of compatible pressure and vorticity schemes and show that lack of compatibility has been the principal reason for the poor results obtained using marching schemes. Compatible pressure marching methods are developed and shown to give good results. Comparisons are made between the Poisson equation method and the compatible marching method. To make the comparisons meaningful, special test cases with analytical solutions have been used.
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  • 148
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 629-634 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 149
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 583-597 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The procedures for utilizing substructuring and static condensation in structural analysis are well known. However, until recently there have been no general-purpose structural mechanics computer systems that offer multi-level substructuring combined with a convenient method for defining the structural model. Now that such systems are available, engineers must decide when substructuring techniques are useful. Substructuring, with and without condensation, has proved to be highly efficient in the analysis of certain classes of structure. It can reduce computer costs by a factor of from 2 to 100. Yet, indiscriminate use of condensation may result in unnecessary and expensive computations. This paper examines the advantages and disadvantages of substructuring relative to data entry and computational efficiency. Guidelines are proposed for engineers to follow when using substructuring in the analysis of linear and nonlinear structures. The FINITE system is used to illustrate actual implementation of substructuring features in a general purpose finite element system.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 626-628 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Grading rules for consistent and lumped elements are opposite. Optimal mass matrices on finite difference considerations are very sensitive to mesh grading. Sensitivity of the solution accuracy to the mesh ratio increases with element order.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 635-638 
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  • 152
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 677-683 
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  • 153
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 661-675 
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    Notes: A modification (Irons;6 Concus et al. 1) to the conjugate gradient (CG) method by Hestenes and Stiefel5 has recently renewed the interest in this elegant technique which appears to be extraordinarily promising for large sparse systems Ax = b, where A is a symmetric positive definite matrix. A good approximation K-1 for the inverse of A is needed in the modified algorithm. For finite difference sets of equations, Meijerink and van der Vorst9 and Kershaw7 have experienced a very fast convergence with a matrix K-1 determined by the incomplete Cholesky decomposition of A.A further acceleration of the iteration may be achieved by preliminarily processing the initial guessed solution by the Newton iterative scheme before using the modified conjugate gradient (MCG) method. The initial Newton iterations (NI) have the useful property of significantly reducing the components of the residual r0 along the eigenvectors of AK-1 associated with the eigenvalues lying in the vicinity of 1. The latter are expected to include the vast majority of the eigenvalues of AK-1. As a result the MCG method is left with a smaller number of r0 components to set to zero in a reduced dimensional eigenvector space and hence the solution is arrived at in fewer iterations. Depending on the desired final accuracy, up to 50 per cent of the MCG iterations may be equivalently replaced by an equal number of NI which are computationally faster.This approach has been applied to the solution of finite element sets of linear equations arising from the arbitrarily irregular triangle discretization of groundwater flow domains in both steady and unsteady conditions. For diagonally dominant matrices the results emphasize the excellent performance of the MCG method which proved much faster than the first-degree Chebyshev iteration (CHI) and required a number of iterations an order of magnitude smaller than the successive over-relaxation technique (SOR) with optimum over-relaxation factor.
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  • 154
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    International Journal for Numerical Methods in Engineering 15 (1980) 
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 809-832 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents isoparametric finite element formulation for special classes of elements referred to as ‘transition elements’ for axisymmetric stress analysis. The transition elements are necessary for applications requiring the use of both axisymmetric solids and axisymmetric shells. These elements permit transition from the axisymmetric solid portion of the structure to the axisymmetric shell portion. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the accuracy and applications of such elements.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 855-866 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Hybrid elements for the representation of elastic media are based upon extended variational principle. In the discretization process the hybrid deformation model requires an expansion of the displacement field as well as of the Lagrange multipliers at the boundary. Using an extension of the common shape function concept, these hybrid elements can be reduced to the basis of the simple minimum principle of potential energy with only one expansion of the displacements. An application to plate elements is given and a discussion about some consequences of the approach.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 925-929 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The structural design problem is acknowledge to be commonly multi-criteria in nature. The various bases for multi-criteria optimization methodologies are outlined and a computationally viable method for generating Pareto optimal solutions is adopted for the structural design problem where the criteria may be non-commensurable. A numerical example on optimal truss design illustrating non-commensurable criteria is given.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 930-934 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Some comparisons between the finite element method and two early methods in the calculus of variations are presented.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 949-949 
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  • 160
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 943-948 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 15 (1980) 
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  • 162
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1021-1039 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new approach to the generation of near-optimum finite element meshes is presented. Like other current methods, the procedure presented uses the results of a previous analysis to improve the idealization, but unlike other procedures a new element mesh is generated in each cycle with the aid of interactive computer graphics. The procedure generates near-optimum two-dimensional meshes on one cycle employing a grid optimization criterion based on variations in the strain energy density and using a software system which operates like an interactive finite element preprocessor. The example problems presented demonstrate the efficiency and flexibility of the approach.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1075-1081 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A detailed study is made of the error growth associated with explicit difference schemes for a conduction-convection problem. It is shown that the error can become arbitrarily large after a finite number of time steps even though it ultimately decays to zero. Certain ambiguities reported in the literature can thereby be resolved.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1053-1074 
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    Notes: An analysis procedure for the plane strain contained plastic deformation problem is proposed. It is shown that, when piecewise-linear elastic-plastic laws are adopted, the plane strain problem can be formulated in terms of exactly the same variables appearing in a plane stress problem, even if the transverse stress and plastic strain components do not vanish in general. The two problems are governed by the same equilibrium and compatibility equations and the only difference is in the elastic-plastic material constitutive laws, in complete analogy with the linear elastic case.The problem is discretized by using a compatible finite element model on which basic elastic-plastic constitutive laws for an element in plane strain conditions can be obtained. When the assemblage is performed, the resulting set of governing relations presents a mathematical structure which enable, for solution, techniques efficiently used for truss and frame problems. Some solutions for axisymmetric tubes subjected to pressure and temperature gradients are illustrated.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1106-1106 
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1108-1111 
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1177-1186 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An efficient implicit finite difference method, called the Keller's box scheme, is applied to solve an eighth-order nonlinear two-point boundary value problem. The example considered here is the compressible boundary layer equations at a general three-dimensional stagnation point. The solutions obtained are compared with results from other methods and the potential advantages of the method are demonstrated.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1221-1238 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A numerical scheme is developed to simulate the non-isothermal steady-state behaviour of a MOS field effect transistor. In a desire to develop a fast, stable numerical scheme, physical instabilities were eliminated by using a simplified device model. The numerical technique developed permits a computer solution of the majority carrier transport equation, the nonlinear heat conduction equation, in which the heat generation term is obtained from the solution of the transport equation, and a number of auxiliary differential equations.The simplified model of the MOS transistor adopted will not, of course, produce any information on the actual operation of the short channel MOS transistor of practical interest today, but the numerical scheme can be extended to simulate short channel models that are of great practical interest.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1279-1280 
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1207-1220 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A nonlinear analysis is carried out for the motion of the inviscid, incompressible fluid in a two-dimensional, rigid, open container which is subjected to forced sinusoidal pitching oscillation. Firstly, the problem is defined as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions. Next, the problem is formulated in the form of a pseudo-variational principle, which provides a basis for our discretization. The finite element method and finite difference method are used spacewise and timewise, respectively. Due to the strong nonlinearity of the problem, an incremental method is used for the numerical analysis. Numerical results obtained by the present method are compared with solutions of the linear theory and experimental data. The difference between linear and nonlinear analysis has been clearly indicated.
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  • 172
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1595-1602 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Geometric programming is a powerful technique and its application to mechanism synthesis has not been fully explored. In this paper, slider-crank mechanism is chosen since the objective function consists of a large number of terms while there are only two design variables. Thus the degree of difficulty is more and does not lend itself to easy application of the geometric programming. Here, modification of the objective function is suggested so that the degree of difficulty reduces to zero even when the working space constraint is imposed. This results in a near optimum solution. Application of signomial geometric programming is illustrated through a numerical example.
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  • 173
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1713-1723 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general analytical and numerical procedure, based on the linear theory, is outlined for the elastic stress and deflection analysis of complex shells of revolution with arbitrary stiffness and density distributions, under arbitrary static and dynamic loads. The equations of motion admit shear deformation and rotary inertia. A numerical solution is obtained by recourse to Fourier expansion for the circumferential direction, to finite differences for the meridonial direction, and to Houbolt's method for the time domain. Numerical results are presented.
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  • 174
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 31-40 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Transformation of dependent variables as, for example, the Kirchhoff transformation, is a classical tool for solving nonlinear partial differential equations. This approach is used here in connection with the finite element method and explained first in case of nonlinear heat conduction problems without phase change. The main applications of the method given in the paper concern a nonlinear degenerate parabolic equation for fluid flow through a porous medium and Stefan (moving boundary) problems.
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  • 175
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 41-54 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is proposed for the study of growth, under normal internal pressure, of pre-existing hydraulically induced planar cracks. The continuous growth process is approximated by a stepwise one, and during each growth step the volume of fluid within the crack cavity is assumed constant. The normal distance through which each point on the crack edge moves outwards is controlled by the level of stress intensity factor KI at each point, and the crack-resistance characteristics of the material, which can be expressed by some critical level of KI, denoted by KIC. For the present study, that distance was assumed proportional to (KI - KIC)4 for KI 〉 KIC. The evaluation of KI at the crack edge is achieved by utilizing the method discussed by Mastrojannis et al.1 The proposed method was applied to the study of the initial stage of growth of a circular crack under linearly varying normal pressure, and of an elliptical crack under uniform normal pressure.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 63-85 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis of axisymmetric free jet impingement on to finite disks was performed using the finite element method. The method employed the velocity potential as the dependent variable and six-node triangle elements to represent the region of flow. The analysis was divided into three parts corresponding to three distinct regions of the flow: (1) In the disk region, the free jet impinged on to a finite disk which was oriented normal to the flow. The jet was subjected to zero or normal gravity and to surface tension effects of varying degrees. (2) Upon leaving the disk region, the jet entered the plume region where it was acted upon internally by surface tension and externally by zero or normal gravity. (3) In the collision region, the flow from the plume region collided symmetrically at some downstream area about the axis of symmetry. The major result achieved from this investigation was the development of techniques to locate the free surface in all three regions for a range of conditions. The velocity profiles along selected lines of constant values of the potential were determined, and a successful comparison was made between the numerical results and existing experimental data.
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  • 177
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 145-156 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element program capable of analysing finite plane strain deformations of incompressible rubberlike (Mooney-Rivlin) materials has been developed. Two problems, namely a long wall loaded uniformly in two directions and a thick-wall cylindrical pressure vessel loaded internally, have been solved. The computed values of displacements, strains, stresses and hydrostatic pressure agree very closely with their values obtained analytically.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 343-349 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complementary energy method for the stability analysis of plates is presented. Buckling loads of rectangular plates with different boundary conditions are obtained, and the convergence of the solution is studied.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 405-419 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 180
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 421-436 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The side and corner flow rules for viscoplastic materials with singular yield surfaces are discussed and applied in numerical solution of several boundary-value problems. The differences in predictions of displacement and stress fields for different flow rules are demonstrated.
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  • 181
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 457-463 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, rapidly convergent procedure is described for solving a third-order symmetric eigenvalue problem Au = λ Bu typically arising in vibration analysis. The eigenvalue problem is represented in terms of its variational dual, the Rayleigh quotient, and the eigenosolution is obtained through a topographical search for points of quotient stationarity. The associated computer routine is compact and can easily be incorporated within the calling program. Degenerate eigensolutions cause no difficulty. An example FORTRAN routine is given.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 477-477 
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  • 183
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    International Journal for Numerical Methods in Engineering 15 (1980) 
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  • 184
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 519-536 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the hitherto unpublicized flexibilities inherent in the longevity-based Frontal concept of Irons. Diverse applications such as Guyan-reduced superelement generation, substructuring, matrix storage in Frontal form, Frontal matrix multiplication and Frontal Subspace Iteration method are discussed. It is observed that most of these extensions require only minor modifications to Irons'original program. The first part of the paper reviews the development in the Frontal method so far. Part II describes the experiences related to the largest multi-algorithm Frontal package reported to date. Suggestions for a simplified Frontal algorithm are also given and would be useful to those who wish to write their own solver, or improve an existing one. An algorithm and a computer program for Frontal multiplication are also provided.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 753-766 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper evaluates the relative merits of the band-schemes over the frontal-routines in the solution of the linearized algebraic equations resulting from a nonlinear structural analysis. Through examples it is shown that the use of the former in the nonlinear analysis programs results in considerable savings in computer time. This is especially so when the structure under consideration is subject to dynamic loads due to earthquakes or simulated ground motions.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 733-751 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A concise and efficient algorithm is presented for deriving finite element shape functions from an arbitrary set of independent functions. Based on special one-dimensional interpolatory schemes derived via the algorithm, a variety of two- and three-dimensional interpolatory schemes are developed which are useful for modelling singular behaviour. The methodology presented is general and may be fruitfully applied to the development of ‘special’ finite element shape functions for a variety of other situations.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 779-789 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An accurate and economical eight-node quadrilateral membrane element based on stress assumptions is presented. It is shown that this element offers distinct advantages over other available membranes.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 790-790 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 790-790 
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    Keywords: Engineering ; Engineering General
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  • 190
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 843-854 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed initial-boundary value problem associated with a hyperbolic integro-differential system is solved by means of the ‘summed progressing wave’ formalism. Once the numerical problem has been set, the pertaining solution methods are described. A simple approximate solution is also proposed. Attenuation functions are calculated through a novel method using the semi-group property exhibited by the exponential of an integro-differential operator. The long-time solution of the problem at hand can be brought out owing to this procedure.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 833-842 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new computational scheme, named the ‘Integrated Load Increment’ method (ILI), has been developed to handle elasto-plastic analysis of solids by the finite element variational technique. This scheme allows considerably larger loading steps to be applied to the structure without deviating from its nonlinear, load-deformation relationship. It has been shown that these relationships can be evaluated by integrating the nonlinear constitutive equations within each load increment under certain conditions. A numerical example on a pressurized thick-walled cylinder indicates that a 240 per cent improvement in computational efficiency and substantial reduction of loading steps over the conventional load incremental method can be achieved by the ILI technique.
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  • 192
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 867-888 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Univariate minimization is considered for constrained optimization with the Kavlie-Moe extended interior penalty. An algorithm is derived using a linear-plus-hyperbolic fit suggested by R. L. Fox for interior penalties. A linear extension to the linear-plus-hyperbolic permits rapid convergence with extended interior alties. However, constraint deletion and approximation of remaining constraints before each minimization also characterize the environment. These and other complexities impede accurate fitting of larger intervals. Thus, following Murray, a mixed strategy is adopted with function comparison reductions of interval size to supplement curve fitting.Analysis shows how quadratic and cubic fit searches break down under certain limiting conditions of interior, extended and exterior penalties. A quadratic-extended linear curve derived for exterior penalties and the linear-plus-hyperbolic similarly fail on extended interior penalties. Examples of constrained optimization with extended interior penalties were run on the Stanford IBM 370/168 computer. A stiffened two-panel box provides eight optimization variables with many constraints on demensions and against failure. The extended linear-plus-hyperbolic surpasses cubic and linear-plus hyperbolic fitting, especially when the Fiacco-McCormick multiplier for the penalty becomes small. The value of feedback from curve fitting to decide function comparison use is also illustrated.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1149-1159 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for improving the convergence rate of iterative processes is presented. This method monitors the sequence of approximations produced by an iterative process, and generates a new iterative process, or sequence of processes, each with more rapid convergence characteristics than the previous one. This method of process modification can be applied to many iterative techniques currently in use. Examples of application of the method are given, using both nonlinear and linear systems. In one of these examples it is shown that the method can be applied to a divergent iterative process, producing a convergent one. It is also shown how the technique can be applied to equations of one variable, yielding a method with convergence characteristics similar to those of Newton's method, but without the explicit calculation of derivatives.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 949-953 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1095-1105 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a procedure for obtaining a fully stresses shape of elastic continuum under arbitrary design conditions is proposed, by using the optimum distribution of the material properties such as the Young's modulus or the plate thickness. By using this technique, the optimum multiple-connected shape can be created from the original shape of simply body. The optimum shape of a road-pole subjected to an uniformly distributed load is determined by using the technique, and from the results the effectiveness of the technique is examined numerically.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1282-1286 
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1303-1313 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The integral equations arising from the Green's formula, applied to the two-dimensional Helmholtz equation defined in a limited domain, are considered and the presence of instabilities in their numerical solution, when a real Green's function is adopted, is pointed out.A complete study has been carried out for a circular domain and the conditions under which such instabilities can occur in a domain of arbitrary geometry have been investigated. In particular, it has been shown that in every case the use of a complex Green's function is able to avoid their presence.
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1355-1361 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 15 (1980), S. 1403-1407 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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