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  • Engineering General
  • 1985-1989
  • 1980-1984  (260)
  • 1982  (260)
  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 2
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 1-23 
    ISSN: 0271-2091
    Keywords: Transition ; Boundary Layers ; Models of Turbulence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computational procedure for compressible axisymmetric boundary layers, on bodies of revolution, in transition from laminar to turbulent flow, is introduced. The procedure is an extension of a former method, due to Patankar and Spalding.The flow field is computed by solution of four simultaneous equations for the momentum, the thermal energy, the turbulence energy amplitude and the turbulent scale.The results show good agreement with existing theoretical and experimental data.
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  • 3
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 25-42 
    ISSN: 0271-2091
    Keywords: Penalty Method ; Incompressible Flow ; Reduced Quadrature ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The frequently used reduced integration method for solving incompressible flow problems ‘a la penalty’ is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.
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  • 4
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 43-60 
    ISSN: 0271-2091
    Keywords: Multigrid ; Iterative Improvement ; Geothermal Model ; Alternating-direction-implicit ; Tau-extrapolation ; Higher-order-accuracy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper considers the multigrid iterative method applied to the solution of finite difference approximations to a linear second-order self-adjoint elliptic equation. It represents an extension of work by Dinar and Brandt. We compare two methods to obtain fourth-order convergence. The first is local error extrapolation developed by Brandt, the second is iterative improvement developed by Lindberg. This work considers non-separable problems, but only on a rectangular domain with Dirichlet boundary conditions. We consider test cases with non-smooth (i.e. discontinuous second derivatives) as well as smooth solutions. We also apply the multigrid method to an elliptic equation with non-separable coefficients which occurs in a geothermal model. In this case an analysis of the error fails to show any advantage in a fourth-order difference scheme over a second-order scheme. However, we do demonstrate that the multigrid iteration performs well on this problem. Also, this example shows that the multigrid iteration can be combined with iterative improvement to create an efficient fourth-order method for a non-separable elliptic equation which is coupled with a marching equation. Other work has found an advantage in this fourth-order scheme for a similar geothermal model.
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  • 5
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 89-112 
    ISSN: 0271-2091
    Keywords: Two Step Scheme ; Selective Lumping Method ; Tidal Flow ; Osaka Bay ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element method for solving shallow water flow problems is presented. The standard Galerkin method is employed for spatial discretization. The numerical integration scheme for the time variation is the explicit two step scheme, which was originated by the authors and their co-workers. However, the original scheme has been improved to remove the erroneous artifical damping effect. Since the improved scheme employs a combination of lumped and unlumped coefficients, the scheme is referred to as a selective lumping scheme. Stability conditions and accuracy are investigated by considering several numerical examples. The method has been applied to the tidal flow in Osaka Bay and Yatsushiro Bay.
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  • 6
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 113-114 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 7
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 61-88 
    ISSN: 0271-2091
    Keywords: Vector ; Differencing ; Finite ; lEement ; Scheme ; Recirculating ; Laminar ; Flow ; False ; Diffusion ; Conservation of Energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite-difference and finite-element techniques have been used to calculate the steady laminar flow over a flat plate normal to an air stream, up to a Reynolds number, Re, based on the plate half-width, of 100. The boundary conditions simulate a central splitter plate downstream of the body, to prevent vortex shedding, so the flow is characterized by a closed recirculation region which grows with increasing Re but at Re = O(100) is very similar in size to the turbulent recirculating region that occurs in the corresponding high Reynolds-number flow. Motivation came, in part, from the increasing efforts of turbulence modellers to calculate complex turbulent flows (containing elliptic regions) and our belief that the numerical methods commonly employed for such work can be inaccurate. The predictions are compared with each other and with some expectations based on classic solutions of the Navier-Stokes equations, and the nature of the numerical errors is demonstrated. It is concluded that effort comparable with that expended in developing turbulence models should be directed to developing higher-order numerical methods, before the numerical accuracy of predictions of, for example, bluff-body flows can be made sufficiently high to sustain detailed discussion of the adequacy of turbulence models in such situations.
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  • 8
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 9
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 115-122 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Free Surface ; Porous Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An inexpensive, finite difference numerical method is developed for the approximate solution of general, free surface, porous flow problems. The method is so designed that the required numerical boundary conditions coincide exactly with the required physical boundary conditions. In the present paper, application is made to prototype, steady state, dam flow problems.
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  • 10
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 151-171 
    ISSN: 0271-2091
    Keywords: Penalty method ; Incompressible Flow ; Finite Elements ; Convergence ; Existence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier-Stokes equations. Conditions for the equivalence of two penalty-finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.
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  • 11
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 123-149 
    ISSN: 0271-2091
    Keywords: Three-dimensional ; Flow ; Computation ; Scheme ; Time ; Marching ; Conventional ; Damping ; Old Time Level ; Current Time Level ; Fourier Perturbation ; Staggered Grid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical stability of a number of computation schemes currently used for three-dimensional, inviscid, compressible flow is analysed using one-dimensional Fourier analysis. Whereas Reference 1 analysed schemes which were modified to render them amenable to simple analysis, the present work analyses the stability of schemes as actually used by Highton,3 Ahrabian,1 Denton2 and Spalding.6 The use of current values of the variables as they become available is shown to bring a general improvement to stability margin. The manner of damping introduced by the time marching formulation is shown to be deleterious to modifications which reduce truncation error. Staggered grid schemes can be formulated to second order accuracy with better stability margin than the corresponding first order scheme. While unstaggered grid schemes can be formulated to second order error and remain stable, their stability margin becomes very small. Agreement of the theory with numerical experiments continues to be of a high order for both one and three-dimensional disturbances.
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  • 12
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 173-184 
    ISSN: 0271-2091
    Keywords: Advection-diffusion ; Characteristics ; Space-time ; Finite ; Elements ; Water Resources ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new finite element method is presented for the solution of two-dimensional transport problems. The method is based on a weighted residual formulation in which the method of characteristics is combined with the finite element method. This is achieved by orienting sides of the space-time elements joining the nodes at subsequent time levels along the characteristics of the pure advection equation associated with the transport problem. The method is capable of solving numerically the advection--diffusion equation without generating oscillations or numerical diffusion for the whole spectrum of dispersion from diffusion only through mixed dispersion to pure convection.The utility and accuracy of the method are demonstrated by a number of examples in two space dimensions and a comparison of the numerical results with the exact solution is presented in one case. A very favourable feature of the method is the capability of solving accurately advection dominated transport problems with very large time steps for which the Courant number is well over one.
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  • 13
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 185-207 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional, finite-amplitude wave propagation in an inviscid, subsonic, perfect gas medium is analysed by explicit finite-difference methods. A two-step, Lax-Wendroff method and the single-step, Lax-Friedrichs method are used. A prescribed propagating velocity or pressure disturbance is applied along a single row of grid points normal to the stream direction and results in a 'forced' outflow boundary. The inflow boundary is placed far from outflow by utilizing a streamwise expanding grid and uniform inflow is imposed. Side boundaries are spatially periodic. The numerical solutions are compared with analytical small-perturbation solutions; higher-order effects arising from non-linearities are revealed by Fourier analysis. Solutions which closely approached a periodic state were obtained. The Lax-Wendroff method combined with the expanding grid is shown to be accurate and stable, the Lax-Friedrichs scheme produced highly damped solutions.
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  • 14
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 221-221 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 15
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 209-219 
    ISSN: 0271-2091
    Keywords: First Order Equation ; Hyperbolic Conservation Equation ; Discontinuous Solutions ; Least Squares ; Finite Differences ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Least square methods have been frequently used to solve fluid mechanics problems. Their specific usefulness is emphasized for the solution of a first-order conservation equation. On the one hand, the least square formulation embeds the first-order problem into equivalent second-order problem, better adapted to discretization techniques due to symmetry and positive-definiteness of the associated matrix. On the other hand, the introduction of a least square functional is convenient for finite element applications.This approach is applied to the model problem of the conservation of mass (the unknown is the density ρ) in a nozzle with a specified velocity field (u, v), possibly including jumps along lines simulating shock waves. This represent a preliminary study towards the solution of the steady Euler equations.A finite difference and a finite element method are presented. The choice of the finite difference scheme and of a continuous finite element representation for the groups of variables (ρu, ρv) is discussed in terms of conservation of mass flux. Results obtained with both methods are compared in two numerical tests with the same mesh system.
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  • 16
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 17
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 222-223 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 18
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 225-238 
    ISSN: 0271-2091
    Keywords: Normal Direction ; Boundary Conditions ; Incompressible ; Mass Conservation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Various techniques for implementing normal and/or tangential boundary conditions in finite element codes are reviewed. The principle of global conservation of mass is used to define a unique direction for the outward pointing normal vector at any node on an irregular boundary of a domain containing an incompressible fluid. This information permits the consistent and unambiguous application of essential or natural boundary conditions (or any combination thereof) on the domain boundary regardless of boundary shape or orientation with respect to the co-ordinate directions in both two and three dimensions. Several numerical examples are presented which demonstrate the effectiveness of the recommended technique.
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  • 19
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 263-276 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Waves ; Coastline ; Dampers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem of truncating nearshore finite element wave models is addressed. Incorrect treatment of the artificial boundaries of the model will cause spurious wave reflections. Three methods for dealing with these boundaries: application of constraints, use of the Smith condition and longshore dampers, are proposed. Numerical results show the dampers to be the best method.
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  • 20
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 239-251 
    ISSN: 0271-2091
    Keywords: Regular ; Discontinuous Boundary Elements ; Fluid Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.1 In this paper is presented a 'Regular Boundary Element Method' as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular integral equations obtained by moving the singularity outside the domain of the given problem. It is also shown that non-conforming elements may be used whereby freedoms are not defined at the geometric nodes under the boundary element discretization. A linear element is developed here; higher order variants could easily be defined. Satisfactory numerical results have been obtained using the proposed regular method with both conventional (continuous across the boundary) and non-conforming boundary elements for two-dimensional inviscid laminar fluid flow problems having regular and singular solutions.
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  • 21
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 253-261 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Sloping Shelf ; Moving Shoreline ; Finite-difference Integration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite-difference method is described for the numerical integration of the one-dimensional shallow water equations over a sloping shelf that allows for a continuously moving shoreline. An application of the technique is made to the propagation of non-breaking waves towards the shoreline. The results of the computation are compared with an evaluation based upon an exact analytical treatment of the non-linear equations. Excellent agreement is found for both tsunami and tidal scale oscillations.
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  • 22
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    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 23
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 313-315 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 24
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 277-297 
    ISSN: 0271-2091
    Keywords: Advection ; Convection ; Estuary ; Finite ; Element ; Hermite ; Polynomials ; Diffusion ; Dispersion ; Transport ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Space-time finite element solutions of the convection-dispersion equation using higher-order nodal continuity and Hermitian polynomial shape functions are described. Five separate elements ranging from a complete linear element with C0,0 nodal continuity to a complete first-order Hermitian element with C1,1 nodal continuity are subjected to detailed analysis. Wave deformation analyses identify the source of leading or trailing edge oscillations, trailing edge oscillations being the major source of difficulty. These observations are confirmed by numerical experiments which further demonstrate the potential of higher-order nodal continuity. The performance of the complete first-order Hermitian element is quite satisfactory and measurably superior to the linear element.
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  • 25
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 299-311 
    ISSN: 0271-2091
    Keywords: Turbines ; Compressors ; Optimal Design ; Blade Design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Hamilton's variational principle is applied to derive a system of conditions which expresses the balance of momentum and energy of an ideal gas across the selvadgesThe reviewer of this paper confesses to be unfamiliar with the term 'selvadge(s)' which appears frequently herein. Clearly, however, it (variously) means 'boundary', 'edge', 'projection of edge line' (meridional or axial), 'locus of leading edges', etc. of bladed zones within the flow tracts of turbines. This system provides the background for a correct formulation of optimal design problems for turbines and compressors. The exposition follows the model of a large number of blades when the basic equations can be averaged over the azimuthal co-ordinate.An analysis is given of the obtained conditions and a computational algorithm described.
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  • 26
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 317-330 
    ISSN: 0271-2091
    Keywords: Transonic flow ; Turbomachines ; Finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this work a study of the application of the finite element method to transonic flows in axial turbomachines is undertaken.Solution techniques capable of accurately predicting flows from the incompressible regime up to the establishment of shocks in the transonic regime are presented. In the subsonic and shockless transonic regimes a local linearization method capable of very rapid convergence is used. In the full transonic regime the artificial compressibility method is employed to exclude downstream influences in the supersonic regions. The two approaches can be combined in a unified package and appropriate switches introduced to select the relevant method in any flow regime.
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  • 27
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 331-347 
    ISSN: 0271-2091
    Keywords: Fluid Flow ; Turbulent ; Non-circular Passages ; Secondary Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference method has been developed to predict the overall features of the local mean flow in fully developed turbulent non-circular passage flows. The main transport effects of secondary flow have been identified and simulated with diffusion transport in a simple way which eliminates solution of the cross-plane momentum and continuity equations and produces a compact calculation method. Predictions are presented for four different passage shapes and are discussed in relation to experimental measurements and predictions from other more complex methods. Although some minor details were not predicted, the main effects of secondary flow on the mean flow were found to have been quite well simulated, yielding predictions that are in reasonable overall agreement with experiment.
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  • 28
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 349-366 
    ISSN: 0271-2091
    Keywords: Viscous Flow Modelling ; Convection Modelling ; Flow Boundary Treatment ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Stream function-vorticity finite element solution of two-dimensional incompressible viscous flow and natural convection is considered. Steady state solutions of the natural convection problem have been obtained for a wide range of the two independent parameters. Use of boundary vorticity formulae or iterative satisfaction of the no-slip boundary condition is avoided by application of the finite element discretization and a displacement of the appropriate discrete equations. Solution is obtained by Newton-Raphson iteration of all equations simultaneously. The method then appears to give a steady solution whenever the flow is physically steady, but it does not give a steady solution when the flow is physically unsteady. In particular, no form of asymmetric differencing is required. The method offers a degree of economy over primitive variable formulations. Physical results are given for the square cavity convection problem. The paper also reports on earlier work in which the most commonly used boundary vorticity formula was found not to satisfy the no-slip condition, and in which segregated solution procedures were attempted with very minimal success.
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  • 29
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 407-409 
    ISSN: 0271-2091
    Keywords: Incompressible Fluid Flows ; Cavity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 30
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 367-386 
    ISSN: 0271-2091
    Keywords: Free Surface ; Thermocapillary ; Convective Flows ; Curvilinear Co-ordinates ; Interface Equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The importance of convective flows generated by surface tension gradients, in comparison with the ones generated by other driving forces, has been investigated in connection with space technological applications involving fluid processes. A theoretical model of the boundary conditions at the interface, considered free and diffusive, has been derived in general tensor form to allow for the use of non orthogonal curvilinear co-ordinates. For the study of flow fields contained in enclosures, these co-ordinates are more suitable to fit all teh boundaries, in particular near the contact angle between the interface and the solid walls, thus giving more accurate numerical solutions.A computational procedure to solve the complete set of bulk and surface equations is proposed and applied to a simplified two dimensional flow in a rectangular enclosure with a temperature gradient between the lateral walls. The numerical results show the importance of considering the interface to be deformable and diffusive for an accurate evaluation of the convective flow in the fluid bulk.
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-410 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 32
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 387-405 
    ISSN: 0271-2091
    Keywords: Hyperbolic ; Non-standard Finite Elements ; High Order ; Domain of Dependence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The method of non-standard finite elements was used to develop multilevel difference schemes for linear and quasilinear hyperbolic equations with Dirichlet boundary conditions. A closed form equation of kth-order accuracy in space and time (O(Δtk, Δxk)) was developed for one-dimensional systems of linear hyperbolic equations with Dirichlet boundary conditions. This same equation is also applied to quasilinear systems. For the quasilinear systems a simple iteration technique was used to maintain the kth-order accuracy.Numerical results are presented for the linear and non-linear inviscid Burger's equation and a system of shallow water equations with Dirichlet boundary conditions.
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-412 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 21-46 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: An analysis is presented of the non-linear creep effects around a deep circular tunnel driven in ‘squeezing’ ground. The time-dependent behaviour of the geotechnical medium is described by means of a simple viscoplastic rheological model capable of approximating primary, secondary and tertiary creep behaviours. It is shown that tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the ‘evolutive’ procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 47-76 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: In this paper, the ability of a displacement-type finite element analysis to predict collapse loads accurately is investigated. For the usual assumptions of ideal plasticity and infinitesimal deformations, attention is focused on undrained geotechnical problems. The theoretical criterion originally developed by Nagtegaal et al.1 is applied to each member of the serendipidity quadrilateral and triangular family of elements, up to and including those with a quartic displacement expansion. This method of assessing the suitability of a particular type of element is shown to be valid for any constitutive law which attempts to enforce the constant volume condition at failure, such as critical state type soil models. The method is also generalized to permit an assessment, a priori, of the suitability of any given mesh which is composed of a finite number of elements of the same type. It is postulated that the 15-noded, cubic strain triangle is theoretically capable of accurate computations in the fully plastic range for undrained geotechnical situations which involve axial symmetry or plane strain. This prediction is verified by a series of numerical experiments on footing problems. Extending the work of Nagtegaal et al., 1 it is established theretically that if lower order finite elements are employed rigorously for non-trivial undrained problems with axial symmetry, then it is impossible to predict the exact limit load accurately, regardless of how refined the mesh may be.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 77-94 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: It is commonly accepted that the mechanical behaviour of granular masses is strongly affected by their microstructure, namely the relative arrangement of voids and particles, i.e. the granular fabric. Therefore, parameters which characterize the granular fabric are of paramount importance in a fundamental description of the overall macroscopic stresses and deformation measures. In this paper several measures of granular fabric are introduced for a random assembly of spherical granules, using a statistical approach. In particular, a second-order symmetric tensor, Fij, emerges from this consideration, which seems to be of fundamental importance for the description of fabric, and which is closely related to the distribution of the contact normals in the assembly. The relation between fabric measures presented here and those discussed by other investigators is also discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 141-145 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: A mapping finite element method is proposed for the solution of elastic problems in two-dimensions. This method, based on the logarithmic condensation of physical space, is found to give significantly greater accuracy than when the problem is solved in the physical plane using the standard FEM. Logarithmic condensation of space also permits the solution of large aspect-ratio problems of this type, accurately and economically.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 129-139 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: Collapse loads are overestimated by finite-element or finite-difference procedures when the material discretization does not allow locally incompressible plastic flow: for example, constant-strain triangles or tetrahedra give unacceptable results. The use of different discretizations for the isotropic and deviatoric parts of the strain tensor is advocated for preventing this problem. The technique can be easily implemented in existing two- and three-dimensional computer programs. Its effectiveness is demonstrated by several examples.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-148 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-149 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. ii 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 173-194 
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    Keywords: Engineering ; Engineering General
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    Notes: The theory developed in Part I of this paper is extended to apply to the consolidation of horizontally layered soils under both axially symmetric and general surface loading. The method again leads to a considerable reduction in the amount of core storage necessary for computer solution and can be implimented on a mini-computer.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 151-171 
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    Keywords: Engineering ; Engineering General
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    Notes: A method for the analysis of the consolidation of a horizontally layered soil under plane conditions is developed. The method depends upon the transformation of the governing equations by a Fourier trasform. This transformation has the effect of reducing the partial differential equations of consolidation to ordinary differential equations. The ordinary differential equations are then solved using a finite layer or finite difference approach. Once the solution in the transformed plane has been found, the actual solution is synthesized by Fourier inversion. The method leads to a considerable reduction in the amount of core storage necessary for solution and enables the solution of quite significant problems to be obtained on a mini-computer.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 392-392 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 441-459 
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    Notes: The present study is a continuation of the numerical modelling of geologic structures by the authors (see J. N. Reddy et al., Finite-element modelling of folding and faulting, this journal). The present paper is concerned with the computation of the stress and fracture density distributions in single layer folds by the finite-element method. It was found that variations in fracture patterns are related to several variables: (i) the viscosity of the competent layer, (ii) the ratio of the viscosity of the competent layer to the viscosity of the matrix, (iii) the cohesive strength of the material, and (iv) the boundary velocities during deformation. The fracture prediction is based on the Mohr-Coulomb criterion, which is a function of the stresses only. Prediction of fracture density is based on a function of the strain energy. It is found that there is a good correlation between the computer predicted fractures and the fracture pattern produced by the expermental buckiing of rock-beams. Itis, concluded that the viscosity ratio controls the location of fractures in single layer folds.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 483-490 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 491-491 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 491-492 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 211-218 
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    Notes: The bearing capacity of deep foundations has been analysed using finite elements in conjunction with elasto-viscoplasticity. The influence of elastic parameters, mesh size and strain conditions on computed collapse loads was observed. Axisymmetric problems in particular were of interst, because it was found that good numerical solutions could be obtained through to collapse provided reduced integration was used.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 219-241 
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    Notes: Closed-form solution to the problem of free vibrations of vertically inhomogeneous earth dams, modelled as truncated-wedge-shaped shear beams, has been obtained by implementing an inverse procedure in which the determination of the function descrbing the inhomogeneity constitutes part of the problem. The resulting cube-root variation of the shear-wave velocity with distance from the crest compares very favourably with measurements in two Japanese dams. The results of the method are presented in theform of natural periods, modal shapes and average seismic coefficients for a number of truncation ratios. Compared with an ‘equivalent’ homogeneous dam, the inhomogeneous experiences sharper amplification of modal displacements and greater averge seismic, coefficients near the crest and has natural periods which are closer to each other. This behaviour is in better agreement with the observed response of a 37m-high dam during five earthquake motions.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 287-290 
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    Notes: The effectiveness of the heat balance integral approach in determining the extent of frost penetration of the ground is illustrated.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 293-306 
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    Notes: The problem of a massless, rigid disc vibrating harmonically on a ‘constrained’ transversely isotropic elastic half space is considered. The material is called constrained because it is assumed that the elastic constants satisfy a certain equation. The problem for each mode of vibration is reduced to the solution of a Fredholm integral equation of the second kind. Results are presented to show the general effect of the material anisotropy.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 353-382 
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    Keywords: Engineering ; Engineering General
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    Notes: Talbingo Dam is a well instrumented, 162m high rockfill structure with an upstream sloping silty clay core, located in the southern New South Wales, Australia. A non-linear finite element analysis of its behaviour was carried out under plane strain conditions, simulating its construction, reservoir filling and steady seepage loading stages. Material parameters are determined from triaxial tests on the rockfill, core, filter and transition materials, compacted to field dry density and moisture content. All materials show non-linear stress-strain behaviour, with rockfill exhibiting work softening at large strain. Mohr envelopes for rockfill are slightly curved but linear approximations are acceptable. When compared with stresses and deformations at maximum cross section, the analytical results show good agreement in most areas. A non-linear model for pore pressure response is used successfully to predict the high pore pressures in the lower region of the core. A stability analysis performed for the end of construction stage, based on finite element stresses, shows that the design safety factors are slightly conservative.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 383-390 
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    Notes: For many soils experimental evidence suggests that deviation from normality between the plastic strain increments and the yield function is exhibited mainly in the volumetric behaviour, whereas the deviatoric behaviour exhibits normality. An analysis of the consequence of this observation is presented, and it leads to an expression for the plastic potential function as composed of two functions, a yield function and another dependent only on the hydrostatic pressure; the latter is considered to constitute the concept of correction functions presented recently by Desai and Siriwardane13.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 391-392 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 109-128 
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    Notes: This paper deals with a numerical formulation of the kinematic limit analysis method. This formulation, based on a finite element discretization, is available for axisymmetric cases. The linearization of the yield Tresca and Von Mises criteria leads to linear programming problems. The velocity fields described here are plastically admissible only on an average. The influence of this approximation is quantified for the triaxial test problem and the stability of circular excavations.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 95-108 
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    Notes: The notion of overall macroscopic stress in granular masses is examined from a fundamental point of view by a statistical consideration of the contact forces that are transmitted by the contacting granules at the microscale. This examination leads in a natural way to relations between the macroscopic stress and the resulting granular fabric. The overall stresses are expressed in terms of the contact forces in two different but complementary ways: (1) by a statistical averaging over the sample volume of contact forces and “branches” which are vectors connecting the centroids of two contacting granules; and (2) by defining the overall tractions transmitted across an interior imagined plane as the sum of the contact forces which represent the mechanical effect of granules on one side of a unit area of this plane, upon those on the other side. Conditions under which the two representations of overall stresses are equivalent, are examined in detail. In addition, explicit results are given, which, define stresses in terms of the fabric and other microstructural characteristics of the granular mass.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 243-275 
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    Notes: An incremental formulation of constitutive laws is first presented and the fundamental notion of incremental non-linearity, necessary for the description of cyclic behaviour of soils, is emphasized.The incremental constitutive law for soils and its principal assumptions, which make it more general than the classical elastic-plastic models are detailed.The constitutive parameters of Hostun sand and Grundite clay are then given, as well as a comparison of theoretical results with experimental axisymmetrical and true triaxial measurements (Hostun sand tests at Grenoble and Grundite clay tests at Berkeley). Different cyclic behaviour simulations are presented, as well as an example of cyclic liquefaction of Monterey loose sand. Finally, a simple shear test is simulated.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 277-286 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A continuum finite element formulation that models the failure of a rock mass, the collapse of this rubble into a void space and the associated bulking of the rubble is presented. This formulation is incorporated into a finite element computer program that treats the large deformation non-linear motion of axisymmetric and two-dimensional continua. A dynamic relaxation procedure is used for the solution algorithm. Example calculations are given that demonstrate the formulation.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 291-292 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 461-481 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: This paper draws attention to the great influence certain types of discontinuities in foundation rock masses can have on dam design. By means of two practical examples, the role of numerical procedures in the solution of stability and deformation problems posed by foundation heterogeneities is discussed and emphasized. Some basic theoretical considerations regarding the limit-states and the concept of safety to be used in dam design are also presented as a complement to the analyses description.The case of the Ãgua Vermelha dam, recently built in southern Brazil, is the subject of the first example. Here, a major joint in the basaltic foundation was the decisive geological feature for the stability analyses which were performed by means of the finite element method. The second example refers to the Itaipu dam, a record-breaking Brazilian-Paraguayan hydroelectric development. Marked sub-horizontal discontinuities between lava flows, greatly reducing the strength and stiffness of the basaltic rock masses, were of main concern in this case. The results of the foundation studies, with due help of numerical procedures, called for the construction of concrete shear keys, in order to achieve a satisfactory margin of structural safety.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1297-1311 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two new finite elements are developed for the Mindlin theory plate bending problem. The formulation is based on the modified Hellinger-Reissner principle with independent transverse shear strains. Numerical examples indicate that, with properly assumed transverse shear strains, these new elements designated as PLAT8 and PLAT8H do not exhibit locking effect even for very thin plates.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1313-1319 
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    Keywords: Engineering ; Engineering General
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    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 three function evaluations for each sub-interval and is of order O(h7), where h is the space chop. Results of computational experiments comparing this method with other known methods are given.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1321-1336 
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    Keywords: Engineering ; Engineering General
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    Topics: Mathematics , Technology
    Notes: A time-dependent transport equation is solved numerically by using a Petrov-Galerkin technique on a time-dependent grid. A piecewise linear trial solution and piecewise Hermite cubic test functions are used. The same method is also applied to a time-independent problem, in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid-generation techniques. Several numerical examples are given.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1337-1347 
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    Keywords: Engineering ; Engineering General
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    Topics: Mathematics , Technology
    Notes: A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko-Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by-product of the algorithms is that they provide a systematic and economical means for computing the stepsize at each iteration stage when a Newton-like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1349-1360 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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    Notes: In designing a structure for a given purpose, the designer should aim at the most economical design from many points of view. Minimum weight designs may not be the most economical ones. Nevertheless, such designs provide insights into other types of design and may pave ways for improvements in design procedures. Minimum weight designs of continuum structures may be formulated as numerical optimization problems using either the finite difference method or the finite element method, and the resulting minimization problem may be solved using techniques of numerical optimization. This paper, on the other hand, considers the formulation of the minimum weight design of a spherical cap as a dynamic programming problem and its solution. The paper also discusses the advantages and limitations of the approach.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1385-1399 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational method of flux analysis is applied to the study of the swirling flow of different regimes through a diffuser pipe. The flux analysis method is an iterative procedure to construct a system of orthogonal curvilinear co-ordinates consisting of stream-surface and normals following the flow. Examples of the inviscid swirling flow of an incompressible fluid are calculated, and deformations of vortices in a diffuser pipe are studied. For a simple vortex with rigid rotation the deceleration of flow is remarkable on the axis, where the total energy has the lowest level. For a Burgers type vortex, provided the circulation number exceeds a critical value, the rate of deceleration of flow along the axis become more pronounced for only a slight increase of swirl strength, and ultimately a stagnation point appears on the axis. The present method, however, may not be applied to the flow with stagnation point.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1401-1411 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An exact expression is derived for the potential due to a uniform source distribution over a triangular domain. This expression, which is valid for arbitrary field points, is important for the numerical solution of electromagnetic field problems. Numerical values of the potential are calculated by using the expression obtained, and are compared with the results derived by numerical integration.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1412-1415 
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    Topics: Mathematics , Technology
    Notes: Expressions involving products of exponential functions and polynomials are encountered in the finite element formulation of the diffusion-convection equation. Integrals of such expressions over finite elements are necessary to derive the element matrices. The derivation of the formula for such integrations is presented.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1420-1423 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1423-1423 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1429-1454 
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    Topics: Mathematics , Technology
    Notes: Simple mixed models are developed for the geometrically nonlinear analysis of shells. A total Lagrangian description of the shell deformation is used, and the analytical formulation is based on a form of the nonlinear shallow shell theory with the effects of transverse shear deformation and bending-extensional coupling included. The fundamental unknowns consist of eight stress resultants and five generalized displacements of the shell, and the element characteristic arrays are obtained by using the Hellinger-Reissner mixed variational principle. The polynomial interpolation (or shape) functions used in approximating the stress resultants are, in general, of different degree than those used for approximating the generalized displacements. The stress resultants are discontinuous at the element boundaries and are eliminated on the element level.The equivalence and ‘near-equivalence’ between the mixed models developed herein and displacement models based on reduced/selective integration of both transverse shear and extensional energy terms is discussed. The use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated. Analytic expressions are derived for the rigid-body and spurious (or zero energy) models for the various mixed models and their equivalent displacement models. Also, the advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and to compare their performance with other mixed models reported in the literature.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1455-1468 
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    Keywords: Engineering ; Engineering General
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    Notes: Hybrid stress elements are known to provide accurate results for analyses of plate bending; in particular, for the prediction of moment distribution. The construction of hybrid stiffness matrix requires numerical inversion of a moment matrix, evaluation of some relatively complicated boundary integrals and several matrix transformations. Each of these operations can be time-consuming, and the matrix inversion can result in a loss of numerical accuracy.This paper devises methods to explicitly invert the moment matrices. We find that for triangular elements the inverse is independent of the element shape and is only inversely proportional to its size. We also use a novel set of displacement variables, which greatly simplifies the boundary integration. The displacement variables are chosen in a hierarchical form so that lower order elements can be determined by straightforward reduction of excess terms in a higher order element. Except for the nodal displacements at the vertices, the present approach involves only variables at the midpoints of the sides of an element.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1497-1504 
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    Notes: A hybrid integral equation method is formulated to study the diffraction of oblique waves by an infinite cylinder. The water depth and the geometry of the floating cylinder are assumed to be uniform in the y-direction (one of the horizontal axes). Numerical discretization and integrations are performed in the vertical plane. Analytical solutions are used in far fields such that radiation boundary conditions are satisfied. Numerical results are obtained for the case of wave scattering by a floating rectangular cylinder in a constant water depth. The accuracy and efficiency of present method are compared with those obtained by other numerical techniques.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1529-1546 
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    Keywords: Engineering ; Engineering General
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    Notes: The finite element solution of various partial differential equations leads to large linear equation systems, which may have a DBBF (double bounded band form) coefficient matrix, if periodicity conditions are taken into account. An efficient Fortran program solving such equation systems, developed for Control Data computers from the Cyber 70/170 series, utilizes the original block-indexed approach to reduce input-output time in communication with disc memory. Program performance is presented in some detail and quantitative comparison with other possible algorithms is carried out. An appendix lists the complete program.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1547-1563 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of steady, two-dimensional seepage from a nonsymmetric channel through a homogeneous porous medium underlain at a finite depth by a drain, is solved using the Baiocchi transformation and method. Because of the nonsymmetry in the problem, both free surfaces must be included in the solution domain of the problem. Thus, several interesting complexities are introduced into the solution of the problem. First, there are the two solution domain extensions (one across each free surface) and then the formulation of the new dependent variable throughout the extended solution domain. Secondly, the projection operator has two bounds in the numerical scheme. Finally, there are two compatibility conditions - one for the flowrate and one for the value of the new dependent variable at the left-hand side free surface-channel intersection. A secant method for the solution of two simultaneous nonlinear equations was used to obtain the values of these parameters. Results from the proposed method compared favourably with what few results were available in the literature.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1565-1568 
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    Keywords: Engineering ; Engineering General
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    Topics: Mathematics , Technology
    Notes: The use of warping displacement functions for the torsional stiffness representation of beams with rectangular cross-sections is studied. These functions can directly be employed in the displacement-based formulation of Hermitian and isoparametric three-dimensional beam elements for linear, elastic-plastic or large displacement/large rotation analysis. the results of some studies are given to demonstrate the applicability and use of the proposed functions.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1576-1580 
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    Notes: The nine-node quadrilateral is much more accurate than its eight-node relative if elements are non-rectangular. However, the nine-node element may display spurious low-energy modes under 2 × 2 Gauss quadrature. These modes can be controlled by using the 3 × 3 quadrature rule, but at added cost. This paper investigates two inexpensive control devices that can be used with 2 × 2 Gauss quadrature.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1569-1575 
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    Notes: We report on a very effective program for uniform approximation of functions (or discrete data) by generalized rational functions of any number of variables over point sets so large that conventional methods are inapplicable. The points need not be arranged in a regular pattern, but if they are, the number of points is normally limited only by the computer time available. The program extends the differential correction algorithm discussed in an earlier article in this journal by combining it with a first Remes-type exchange procedure, while retaining the flexibility and robustness of differential correction. Furthermore, this algorithm is guaranteed to converge in theory. Testing has shown that, even when the point set is small enough for differential correction to be applied directly, this algorithm is usually faster. We discuss the algorithm and program along with several numerical examples, one of which involves more than three million data points. A FORTRAN listing with illustrative output can be obtained from the first author.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1581-1581 
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    International Journal for Numerical Methods in Engineering 18 (1982) 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1582-1582 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1583-1585 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1601-1611 
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    Notes: A closed solution for dynamic problems with the transform technique is possible for linear behaviour only. Therefore, a strategy for the solution involving nonlinear material behaviour has been developed. Herewith, an iterative equalization is made possible by the repeated transform of the differential equations given through the initial strain method.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1623-1654 
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    Notes: A frontal solution program is presented, based on the original work of Irons, published in 1970. The main drawback of the original frontal solution program that the complete front matrix has to reside in core has been overcome by ‘partitioning’ the front matrix. The programming strategy has been optimized to (a) minimize the number of I/O operations on the partitioned front-matrix (b) optimize the speed of I/O transfer between high speed memory and slow peripheral (or secondary) storage media, and (c) make the program transportable and easily implementable on different types of computers, including mini- and micro-computers.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1613-1621 
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    Notes: Third- and fourth-order accurate Nørsett rational approximations to the exponential and associated semi-implicit Runge-Kutta methods are used for the construction of efficient, accurate and unconditionally stable schemes for the direct numerical integration of the linear, nonhomogeneous, second-order equations of structural dynamics.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1587-1600 
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    Notes: A new finite element procedure for calculating stress intensity factors in elastic crack problems is developed. In common with a number of other approaches in the literature, the procedure combines the analytical singular fields present in a problem with a finite element treatment of the residual regular problem. What distinguishes the procedure is the use of path-independent integrals to balance the analytical and numerical contributions. A set of test problems with exact solutions is analysed and demonstrates that the procedure is readily implemented and can accurately evaluate stress intensity factors with a modest amount of computational effort. The application of two competing methods to the test problems further demonstrates that the new procedure is markedly superior in both its initial accuracy and its rate of convergence. The paper concludes with two additional illustrations of the procedure as applied to the single-edge crack and the centre crack; these also yield accurate results for little computational effort.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1655-1677 
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    Notes: A review of 4-node, 12 degrees-of-freedom quadrilateral elements for thin plates is presented. A new element called DKQ is discussed. The formulation is based on a generalization of the efficient and reliable triangular element DKT presented in References 1 and 2 and on the rectangular element QC presented in Reference 3. These elements are derived using the so-called discrete Krichhoff technique. A detailed numerical evaluation of the behaviour of the DKQ element for the computation of displacements and stresses for thin plate bending problems is presented and discussed. The DKQ element appears to be a simple and reliable 12 degrees-of-freedom thin plate bending element.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1685-1697 
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    Keywords: Engineering ; Engineering General
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