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  • 1980-1984  (241)
  • 1981  (241)
  • Engineering  (241)
  • Nuclear reactions
  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981) 
    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
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 1-1 
    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
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 3-16 
    ISSN: 0271-2091
    Keywords: Vector Upstream ; Differencing Scheme ; Significant Sources ; False Diffusion ; Spatial Oscillation ; Steady-state Linear Systems ; Convective Flow ; Rod Bundle Geometry ; Temperature Prediction ; 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 a finite difference scheme for modelling the convection/diffusion equation in strongly convective flow regimes including circumstances in which significant source terms are present.The main objective is to provide an alternative approach to central and/or upwind difference methods which for various reasons are unsatisfactory. To illustrate the main features of the scheme, an assessment of its accuracy is made by means of a Taylor expansion analysis and a study of its performance in two model problems. As a demonstration of its generality for use in large-scale practical problems, some numerical results are presented for the prediction of the temperature distribution in a flow through a partially blocked heated rod bundle.The main conclusions are that in almost all practical circumstances results obtained using the scheme are not susceptible to false diffusion or spatial oscillations, which are, respectively, the inherent weaknesses in many upwind and central difference scheme formulations, and in general its use results in improved overall accuracy.
    Additional Material: 6 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 63-79 
    ISSN: 0271-2091
    Keywords: Heat Transfer ; Convection Finite ; Element Method ; 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 simple method is proposed to generate high-order accurate convection operators for lumped-explicit schemes based on linear or multilinear finite elements. The basic idea is to reduce the truncation error on the first-order spatial derivatives by exploiting the consistent mass matrix of the finite element method in a purely explicit multistep procedure. The effectiveness of the method is demonstrated on pure convection problems in one and two dimensions.
    Additional Material: 11 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 17-43 
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Penalty Methods ; Pressure Filters ; 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 spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of both mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
    Additional Material: 8 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 45-61 
    ISSN: 0271-2091
    Keywords: Two Layer Flow ; Periodic Galerkin Method ; Mixed Interpolation ; Niigata Port ; 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 aim of this paper is to present the finite element method and its application to quasi-steady periodic two-layer tidal flow in estuaries and coastal seas. Formulating the weighted residual equations, using quadratic polynomials for velocity and linear polynomials for water elevation as interpolation functions and employing the periodic Galerkin method, the nonlinear simultaneous equations can be derived. The present method is used for the simulation analysis of the Niigata Port redevelopment planning.
    Additional Material: 11 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981) 
    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
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 81-97 
    ISSN: 0271-2091
    Keywords: Waves ; Mixed Finite Element ; Shallow Water ; 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 presents new finite element formulations of the shallow-water wave equations which use different basis functions for the velocity and height fields. These arrangements are analysed with the Fourier transform technique which was developed by Schoenstadt,1 and they are also compared with other finite difference and finite element schemes. The new schemes are integrated in time for two initial states and compared with analytic solutions and numerical solutions from other schemes. The behaviour of the new forms is excellent and they are also convenient to apply in two dimensions with triangular elements.
    Additional Material: 11 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 99-100 
    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
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 101-115 
    ISSN: 0271-2091
    Keywords: Subsidence ; Finite Elements ; Reservoirs ; Hydrocarbons ; Pore Pressure ; Consolidation ; Aquifer ; Waterdrive ; Permeability ; 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 fully coupled consolidation model has been developed for the simulation of the surface subsidence above gas reservoirs. The model is based on the Biot Theory and the material balance equation for hydrocarbon reservoirs. The model is extremely versatile and can handle such complex situations as vertical cross-sections where several gas reservoirs and aquifers are exploited at different levels. Computer runs were used to generate several reservoir formation profiles and the surface subsidence bowl for a variety of conditions. These results indicate the importance of various parameters which are disregarded in proelasticity models.
    Additional Material: 14 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 117-127 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Conservation Forms ; Inviscid Boussinesq 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 finite element discretization of the inviscid Boussinesq equations is studied with particular emphasis on the conservation properties of the discrete equations. Methods which conserve the total energy, total temperature and total temperature squared, or two of the above mentioned quantities, are presented. The effect of time discretization, and other numerical errors, on the conservation laws is considered. Finally, the theory is supported and illustrated by several numerical experiments.
    Additional Material: 5 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 129-144 
    ISSN: 0271-2091
    Keywords: Vorticity Conditions ; Integral Conditions Incompressible Navier-Stokes Equations ; Computation of 2D Viscous Flows ; Vorticity/Stream Function Splitting ; Noniterative Algorithms ; 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 establishing appropriate conditions for the vorticity transport equation is considered. It is shown that, in viscous incompressible flows, the boundary conditions on the velocity imply conditions of an integral type on the vorticity. These conditions determine a projection of the vorticity field on the linear manifold of the harmonic vector fields. Some computational consequences of the above result in two-dimensional calculations by means of the nonprimitive variables, stream function and vorticity, are examined. As an example of the application of the discrete analogue of the projection conditions, numerical solutions of the driven cavity problem are reported.
    Additional Material: 3 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 145-169 
    ISSN: 0271-2091
    Keywords: Numerical Model ; Estuary ; Open Boundary Condition ; Three dimensional ; Hydrothermal Biscayne 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 three-dimensional time dependent free-surface model has been used to simulate the velocity and temperature distributions in Biscayne Bay, an estuarine basin in South Florida. Comparisons with tide gauge data and airborne infrared temperature data have been made. Analyses of three-dimensional velocity structure, phase relationships of velocity with depth and horizontal location have been conducted.One of the major concerns with three-dimensional models is the specification of conditions at open-boundaries, since it is rare that complete time dependent variations of variables at these boundaries are available. Two sets of approximate boundary conditions at the Biscayne Bay-Atlantic Ocean interface have been used for computations. It was found that specification of averaged surface height variation at open boundaries yield significantly better results than specification of estimated values of velocity.
    Additional Material: 22 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 205-206 
    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
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981) 
    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
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 171-204 
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Penalty Methods ; Pressure Filters ; 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 spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. The automatic pressure filter associated with the penalty method is also explained. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
    Additional Material: 19 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. i 
    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
    Type of Medium: Electronic Resource
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 207-223 
    ISSN: 0271-2091
    Keywords: Numerical Solution ; Integrated Compartment Method ; Fluid Dynamics ; Incompressible 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 most common numerical methods that are used by physical scientists to approximate partial differential equations employ finite differences and/or finite elements. In addition, compartment analyses have been adopted by ecological system analysts to simulate the evolution of processes governed by differential equations without spatial derivatives. An integrated compartment method (ICM) is proposed to combine the merits of these three numerical techniques. The basic procedures of the ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. These procedures are applied to the Navier-Stokes equations to yield the computational algorithm from which computer programs can be coded. The computer code is designed to solve one-, two-, or three-dimensional problems as desired. The program is applied to two simple cases: wake formation behind an obstacle in a channel and circulatory motion of a body of fluid in the square cavity. These preliminary applications have shown promising results.
    Additional Material: 9 Ill.
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 225-235 
    ISSN: 0271-2091
    Keywords: Turbulence ; Fluid Flow ; Mathematical Models ; Reynolds Stresses ; Channels Lateral Motion ; 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 solution for the stress transport turbulence model equations for the situation where the flow is unidirectional is now commonly applied to flows with weak secondary currents in closed ducts, open channels, and rod bundles in nuclear reactor channels. Here, perturbations to the unidirectional flow solutions are studied by solving the exact equations using an iterative procedure. Now the equations also contain the small lateral velocity gradients formerly neglected. The applicability as well as the limitation of the use of the unidirectional flow turbulence model for the description of channel flow with lateral motion are discussed. Modifications for weak lateral motion are suggested.
    Additional Material: 8 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 273-290 
    ISSN: 0271-2091
    Keywords: Large Eddy ; Simulation ; Isotropic ; Turbulence ; Filtering ; 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: HOMTY, a code for Large Eddy Simulation of homogeneous isotropic turbulence is proven by successful simulation of two experiments. The role of each term in the equations of motion and the concept of filtering is examined. It is shown that ‘prefiltering’ is unnecessary, and the resulting additional term in the equations, instead of transferring energy to the subgrid scales, backscatters energy from the resolved large wavenumerbers to the small ones. The kinetic energy decay exponent is shown to depend on the low wavenumber part of the velocity spectrum. Pressure statistics are computed and found to be in agreement with previous computations.
    Additional Material: 14 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 237-272 
    ISSN: 0271-2091
    Keywords: Diffraction ; Refraction ; Gravity Water Waves ; Wave Equation ; Homma's Island Tsunamis ; 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 linear wave equation correct to first order in bed slope is used to calculate the wave field in the sea around an idealized island. This is of circular cylindrical shape and is situated on a paraboloidal shoal in an ocean of constant depth (Figure 1). The sides of the island are assumed fully reflecting. The incident waves are plane and periodic. Wave periods up to 30 min are investigated, and the Coriolis force is neglected. The solution of the wave equation is represented by a finite Fourier series, and a large number of very accurate numerical computations are carried through. The results appear partly in figures showing amplitude and phase angle curves (in some cases extending to the water area of constant depth outside the shoal), partly in figures showing amplitude vs wave period in fixed points. Comparison with solutions to the linearized long-wave equation is made, and the validity range of the corresponding shallow water theory is given. The influence of the shoal is studied by investigating the wave field around an island in an ocean of constant depth. New criteria are given for the applicability of a geometrical optics approach (i. e. refraction). Complete numerical refraction solutions for points at the shoreline (corresponding to many wave orthogonals ending at the point) for shallows water waves, as for the general case, demonstrate the inadequacy of this approach for long-period waves (seismic seawaves: tsunamis). All non-linear effects, including dissipation, are excluded.
    Additional Material: 24 Ill.
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981) 
    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
    Type of Medium: Electronic Resource
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 291-294 
    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
    Type of Medium: Electronic Resource
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 291-291 
    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
    Type of Medium: Electronic Resource
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. i 
    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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  • 26
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 295-304 
    ISSN: 0271-2091
    Keywords: Numerical Methods ; Turbulence ; Separation ; 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: Flow over a downstream-facing step is predicted using the F.E.M. A two-equation model of turbulence is employed where the transport of turbulence kinetic energy and dissipation rate are depicted using transport-type equations, i.e. the two-equation model of turbulence. The results obtained are compared with other models and experimental results. Generally, the model was found to be under-predictive with regard to the reattachment length when previous empirical data was used in the transport equations.
    Additional Material: 8 Ill.
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  • 27
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 305-322 
    ISSN: 0271-2091
    Keywords: Diffusion ; Convection ; Heat Transfer ; 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 Scope of this paper is to develop the basic equations for a variational formulation which can be used to solve problems related to convection and/or diffusion dominated flows. The formulation is based on the introduction of a generalized quantity defined as the hear displacement. The governing equation is expressed in terms of this quantity and a variational formulation is developed which leads to a system of equations similar in form to Lagrange's equations of mechanics. These equations can be used for obtaining approximate solutions, though they are of particular interest for application of the finite element method.As an example of the formulation two finite element models are derived for solving convectiondiffusion boundary value problems. The performance of the two models is investigated and numerical results are given for different cases of convection and diffusion with two types of boundary conditions. The applications of the developed formulations are not limited to convection-diffusion problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation.
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  • 28
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 323-346 
    ISSN: 0271-2091
    Keywords: Finite Element ; Incompressible Material ; Divergence-free Bases ; 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: Explicit basis functions are constructed for 9-node biquadratic velocity fields which guarantee that a weak form of the continuity equation is satisfied. The corresponding pressure approximations are either piecewise constant, piecewise linear or piecewise bilinear. These results are extended to give bases for bilinear velocity/piecewise constant pressure elements and also to some three-dimensional brick elements.
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  • 29
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 347-364 
    ISSN: 0271-2091
    Keywords: Incompressible Flows ; Pressure Modes ; Vortices ; Finite Element ; 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 presents some seemingly new elements for the computation of two and three-dimensional incompressible flow. We want to obtain elements satisfying the Babǔska-Brezzi condition for mixed methods and thus introducing no spurious pressure modes (cf. Sani et al.1). In order to present clearly the advantages and disadvantages of our new elements we compare them on a qualitative basis with more standard ones. Of particular importance for incompressible flow is the size and shape of vortices that can be produced by the elements. We shall try to describe this as precisely as possible. The conclusion is that the elements introduced here should be quite competitive on a cost/precision scale.
    Additional Material: 18 Ill.
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  • 30
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 389-392 
    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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  • 31
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 365-387 
    ISSN: 0271-2091
    Keywords: Lagrangian Advective Schemes ; Numerical Diffusion ; Navier-Stokes ; 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 one-dimensional transport test applied to some conventional advective Eulerian schemes shows that linear stability analyses do not guarantee the actual performances of these schemes. When adopting the Lagrangian approach, the main problem raised in the numerical treatment of advective terms is a problem of interpolation or restitution of the transported function shape from discrete data. Several interpolation methods are tested. Some of them give excellent results and these methods are then extended to multi-dimensional cases.The Lagrangian formulation of the advection term permits an easy solution to the Navier-Stokes equations in primitive variables V, p, by a finite difference scheme, explicit in advection and implicit in diffusion.As an illustration steady state laminar flow behind a sudden enlargement is analysed using an upwind differencing scheme and a Lagrangian scheme. The importance of the choice of the advective scheme in computer programs for industrial application is clearly apparent in this example.
    Additional Material: 24 Ill.
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  • 32
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 33
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 34
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 1-14 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Finite element solutions of consolidation problems often exhibit oscillating pore pressures, which tend to increase when the time steps are reduced. This phenomenon is investigated and a lower limit for the time steps is derived, in terms of the mesh size and the coefficient of consolidation near the draining boundary.
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  • 35
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 33-56 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A numerical approach is presented for the ‘identification’ (or back calculation) of the earth pressure acting on embedded or retaining structures. The procedure is applicable to structures of any shape and requires a set of in situ measurements that may include displacements of points on the structure, values of concentrated forces, values of distributed loads at some locations, etc. Possible limiting values of the unknown loads, non-linear structural behaviour, varying accuracies of the input data are accounted for in the problem formulation. Depending upon the type of problem, the solution is reached by means of the unconstrained or constrained minimization of a suitably defined error function. As an example, the proposed approach is applied to the identification of the earth pressure acting on some typical geotechnical engineering structures.
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  • 36
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 97-113 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Elastic wave radiation from an equivalent cylindrical cavity due to an underground explosion is considered in detail. Both static and steady state dynamic finite element models are used to investigate the surface displacements due to the interaction of such wave radiation with both the free surface topography and stope formation. For a blast 430 m below the surface the models predict a negligible displacement effect due to the irregular topography but a significant effect due to the stope. A comparison between the models and a site experiment verified the cylindrical wave nature of the problem. Due to experimental uncertainties however it was difficult to clearly detect the surface displacement effect due to the large underground open stope.
    Additional Material: 11 Ill.
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  • 37
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 139-163 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately.The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically.
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  • 38
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 115-138 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The quasi-static development of the force, pore pressure and displacement is obtained in the system of a circular elastic pile partially embedded in a saturated porous elastic soil, and loaded axially on the top. The porous elastic soil is governed by Biot's theory. The problem is decomposed into two systems, namely, an extended porous elastic half-space in the absence of the pile characterized by the material constants of the medium, and a fictitious pile represented by a Young's modulus equal to the difference between the Young's moduli of the real pile and the medium. The problem is found to be governed by a Fredholm integral equation of the second kind. Laplace transforms are applied to time functions involved, and Hankel transforms to the radial coordinate of which the origin is at the centre of the pile. Numerical solutions are obtained for final and initial solutions for various practical values of the parameters involved.
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  • 39
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 195-215 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A mathematical model has been developed to represent the physical phenomena that occur during the desiccation and one-dimensional consolidation of successive layers of hydraulically transported sediments as they are periodically deposited in a containment area. The governing boundary value problem, defined in terms of pore water pressures, consists of two field equations (one for the saturated domain and one for the unsaturated domain), a drainage boundary condition, an evapotranspiration boundary condition and a series of continuity conditions at the interfaces between different layers. A number of simplifying assumptions were made to render the field equations tractable, and a step-by-step numerical procedure was used to solve the linearized boundary value problem; at the end of each step, the errors introduced by the simplifying assumptions were corrected. Based on a thorough study of the convergence and stability conditions associated with the numerical approximation employed, a system of automatic corrections was incorporated into the computer program to reduce the time increment if stability problems originate during the solution. Based on the results of a parameter study, it was found that, although drainage conditions at the bottom of the, layer do exert some influence on the consolidation rate during deposition of the dredgings, the evapotranspiration potential renders this effect almost negligible when desiccation takes place at the surface. In contrast, transpiration plays an important, role on the consolidation rate during the early stages of desiccation, but its effect is reduced considerably as the water table approaches an equilibrium position.
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  • 40
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 41
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 229-245 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: In this paper models are given for analysis and description of non-linear properties of joints, weak intercalations and interfaces in rock masses.Models for analysis consist of four parts, i.e. shear displacement model, normal deformation model, shear strength model and a relationship between unit shear stiffness and normal stress.The method of non-linear analysis given in this paper is based on an incremental procedure.The proposed method is available for different types of shear-displacement curves, and also adapted to the complicated process of loading-unloading-reloading.The results of computer simulation of an in-situ shear test obtained by this method gave a good fit to the measured data.The method of non-linear analysis of joint elements has been used in some practical rock engineering problems, and some interesting results and conclusions have been obtained.
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  • 42
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 285-294 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A general form of the yield criterion derived from a special rate-type constitutive equation for a granular material provides an appropriate yield surface over a narrow range of material parameters. The complete yield surface is described using a single equation.
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  • 43
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 345-368 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A method allowing for the presence of infinitely distant boundaries in prismatic bodies is developed. The method is closely related to the consistent boundary concept used in dynamic applications but the development presented is algebraic and context free and is thus applicable to a wide variety of geotechnical problems both static and dynamic.
    Additional Material: 14 Ill.
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  • 44
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 369-378 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: This paper examines the problem of the interaction between a loaded rigid circular foundation located at the surface of an isotropic elastic halfspace and an inclined concentrated anchor load which is located at a finite depth along the axis of symmetry. Such inclined loads can be induced by, for example, anchor regions supporting earth retaining structures. The loaded rigid circular foundation resting in smooth contact with the elastic soil mass experiences a displacement and a tilt due to the action of the inclined anchor load. The magnitude of the rotational settlement is evaluated in exact closed form.
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  • 45
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 379-403 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Solutions for the magnitude and rate of settlement of rigid foundations supported by soil reinforced with granular piles are presented. An analytic solution using the theory of elasticity is developed for the settlement of the foundation and expressions for evaluating the moment and shear distributions across the foundation are given. A solution for the increase of the rate of settlement due to the presence of the granular piles has been found by a numerical solution of Biot's equations of consolidation.
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  • 46
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 165-176 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The theoretical aspects of mining in rock subject to tectonic stressing are still insufficiently clear. While rock mechanics uses Heim's rule and assumes the virgin stress to be generally lithostatic, earth science resorts to the folding theory and to different approaches in explaining geological phenomena.In this paper, a procedure is proposed for determining tectonic stresses in mining ground below a surface fold, the latter being assumed to originate through local buckling of the surface layer under tectonic action. For the purpose of this hypothesis, the concept of displacement along the interface of the layer and the surrounding incompetent rock is defined. In the case of elastic or viscous incompetent rock, the induced stress is obtainable by an integral equation approach.A numerical technique was developed accordingly for the zone of contact strain, and special attention is paid to interpretation of the singular integrals representing the boundary stress. Numerical results are presented as an illustration.
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  • 47
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 177-193 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Heated salt mine room and pillar simulations have been performed to provide information regarding parameters affecting room closure rates to designers of radioactive waste isolation facilities. A coupled secondary creep and heat transfer formulation with large strain capabilities was used to assess the effects of variations in creep law parameters, thermal properties, imposed boundary conditions, temporal integration and meshing resolution on room closure rates. Results indicate that the greatest effect results from variations in parameters appearing in the creep constitutive equation.
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  • 48
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 225-228 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 49
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 217-224 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: For non-linear dynamic problems, it has been recognized that an explicit time-integration method of approach is a very efficient way of solving the dynamic equations of motion. The numerical formulation and computation for such problems fall into the two general categories of finite elements and finite differences. Over the years, there have been many arguments between schools which adopt the finite element approach and those which adopt the finite difference approach. At one extreme, arguments areconcerned with the superiority of each approach and at the other end of the spectrum the arguments are about which approach is a subset of the other. The most common of these arguments are concerned with efficiency and accuracy. This publication addresses the accuracy issue with specific reference to explicit calculations in which the analysis domain is discretized into triangular or quadrilateral plane-strain elements. It concludes that if the same basic assumptions are made in the two approaches, they, will give identical answers for problems in this category.
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  • 50
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 455-457 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Additional Material: 3 Ill.
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  • 51
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 460-461 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 52
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 459-459 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 53
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 263-283 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Ground freezing technology is favoured in civil engineering, mainly in tunnelling. The time-dependent material characteristics in the form of creep control the bearing capacity of any frozen earth support system. The finite element method in connection with an initial strain algorithm is able to include these effects. The information about stress redistribution and deformation rate is important for an economic design. Case histories of different tunnel linings in frozen soil and two other examples of realized projects show the usefulness of such a procedure.
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  • 54
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 247-261 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Evidence for threshold gradients is reviewed. The consolidation problem, with threshold gradient, is properly formulated and solved numerically. An approximate analytical solution is also developed. The influence of a threshold gradient on the time rate of settlement is examined, and it is shown that by modifying the definition of the degree of consolidation a good approximation to the threshold gradient problem can be obtained directly from the Terzaghi solution. It is also shown that threshold gradients will have no influence on odometer testing and their effect is, therefore, to reduce the primary compression below that predicted from standard tests.
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  • 55
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 327-344 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Perhaps the most widely used non-linear elastic soil behaviour law uses the hyperbolic functions to define tangent modulus and Poisson's ratio versus strain.1,2 This paper presents the results of analytical studies with the hyperbolic elastic finite element technique for the prediction of static earth pressures against a 10-story basement wall. Carefully performed laboratory tests of the backfill material and measurements of earth pressures during backfilling provided the basis fora, refinement of the current hyperbolic elastic method. The refined analysis resulted in closer agreement of calculated earth pressures with measured values.
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  • 56
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 449-454 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Estimating subsurface pore water pressures in natural slopes along the periphery of rivers and reservoirs for future conditions, created by the operational requiremets to meet increases in energy demand from the observed data of the past and present, operations, is possible with the use of a mathematical model. An effective algorithm for calculating pore water pressure at any location in a slope stability section is to use a complete polynomial and to assure geometric invariance of the calculated results.
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  • 57
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 405-428 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A layer of fill deposited in a soft wet condition will consolidate under its own weight and will commonly undergo comparatively large strains in the process. Neither of these aspects of behaviour can be modelled by traditional consolidation theories. In this paper, a consolidation model is developed from the theory proposed by Gibson et al.5 and is applied here to soil consolidation during and after soil deposition. No restriction is made on the magnitude of strain, so that the boundaries are not taken as being fixed in space, but are allowed to move as required by the process of consolidation. However, perhaps the more important aspect is the consideration of self-weight, since in many instances, the surface loading applied to soft, soils is small, and the majority of the compression of the layer occurs while the effective stresses reach equilibrium with the weight of the soil. Although some idealizations have to be made in assuming relationships between soil parameters, it is shown that the self weight effects in consolidation can be significant, and fundamental to an understanding of soft soil behaviour.
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  • 58
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 429-447 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A simple algorithm (PILLR) for obtaining by two-dimensional analysis thee essential results that would be obtained in an actual three-dimensional finite element analysis of stress about mine pillars in flat-laying stratified rock is presented. A series of comparisons between the distributions of the local factor of safety calculated from the results of three-dimensional analysis and that obtained in the PILLR two-dimensional analyses for pillars of length/width ratio ranging from 0.33 to 8.0 shows the algorithm to be quite effective. The average vertical stress over the horizontal mid-plane of the pillar in the PILLR two-dimensional analyses is always within 0.5 per cent of the exact average; the local safety factor distribution is always within 10 per cent of the three-dimensional result. The ratio of the computer core x time product for the 2D' to 3D analyses is approimately 1/150. Additional improvements ard possible, although with the current PILLR algorithm 3D analyses require less than 1 minute for execution. This fact makes technically sound 3D mine pillar design analyses economically feasible on a routine basis.
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  • 59
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 60
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 15-41 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equations for large strain analysis of elastic-plastic problems are reconsidered. An improved form of these equations is derived, which is valid for small increments of strain and large increments of rotation. Special attention is paid to the integration procedures for these equations in the deformation history. It is shown that the tangent modulus procedure for integration of the constitutive equations is conditionally stable, and that implicit methods, such as the ‘mean normal’ method, are to be preferred. A novel procedure is introduced for the treatment of nonlinear geometric effects. The performance of various element types is examined, with specific attention to effects of ‘locking’ and distortion. Several applications are discussed to illustrate the various aspects of the formulation developed ein this paper.
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  • 61
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 923-930 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presented an efficient computational algorithm for the eigensolution for real symmetric positive definite matrices. The algorithm is based on the Cholesky decomposition and will be referred to as the Cholesky algorithm. The efficiency of the algorithm is due to the combination of several iteration cycles into one, as well as to a judicious choice of shifts. The latter is accomplished by combining an approach based on Sturm's theorem for the initial stages of the process with another approach based on Gersch-gorin's theorem for the subsequent and final stages of the process. The efficiency of the proposed algorithm was tested against that of the QL method and was found to be superior. Moreover, its superiority increases with an increase in the order of the eigenvalue problem. For an eigenvalue problem of order 100, the proposed algorithm produced a solution in about one-half the time required by the QL method.
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  • 62
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 931-938 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of the finite element concept in the time domain has resulted in a reinterpretation of many previously recorded recurrence formulae and the discovery of new ones. An important new feature common to all such schemes is the fact that a weighted forcing term is used. This precludes the application of unrealistic forcing terms resulting in a direct finite difference derivation and ‘smooths’ oscillation due to sudden changes of boundary condition. This problem is discussed in the context of various two- and three-level time schemes.
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  • 63
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 951-956 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 64
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 939-950 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods are formulated and investigated for the effectiveness factor problem for heat and mass transfer with chemical reactions in catalyst pellet models. A Galerkin finite element method is compared with a previous C1 collocation method7. A scheme that is conceptually intermediate between these two methods and accordingly has been termed collocation-Galerkin is formulated and numerical experiments considered. Of particular interest here are superconvergence results at the Gauss and Jacobi points, respectively. Numerical studies of superconvergence in the presence of a nonlinear reaction-rate term are presented. An integral formula is devised and used to compute the flux at the pellet surface to optimal accuracy. Numerical experiments are conducted to demonstrate the improvement in computed fluxes.
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  • 65
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    International Journal for Numerical Methods in Engineering 17 (1981) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 66
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    International Journal for Numerical Methods in Engineering 17 (1981), S. i 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1430-1435 
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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 17 (1981), S. 1436-1440 
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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 17 (1981), S. 557-572 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Singular finite element displacement functions for linear elastic fracture mechanics applications are investigated. The displacement fields are expressed in terms of polynomials. These polynomials are expanded in varying degrees of r and θ in order to examine the effect of the number and type of terms on the solution to various problems with known solutions. Methods of estimating the stress intensity factors for mode 1 and mode 2 are presented. Numerical results evaluating the effect of various r and θ terms on the solutions are presented.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1455-1467 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A solution strategy for the analysis of nonlinear structures is described. The strategy is a simple extension of existing Newton-type procedures, and can easily be incorporated into existing computer programs.Earlier work which contributed to the development of the strategy is reviewed and the theory of the procedure is presented. Six examples, covering several different types of structural behaviour are described. These examples suggest that the strategy is remarkably stable and efficient.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 645-647 
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    Keywords: Engineering ; Engineering General
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  • 72
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    International Journal for Numerical Methods in Engineering 17 (1981) 
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  • 73
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 649-662 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The nature of adaptive processes is reviewed using as an example a specific finite element problem. Several possible formulations for the objective of mesh refinement processes are given. For the most natural of these objectives the A*-algorithms of artificial intelligence turn out to provide a solution process which is known to be optimal in a certain sense. But practically, there is insufficient information and these processes tend to be inefficient. On the other hand, if the objective is replaced by a strictly local objective based on Pareto-optimality, the error estimates of the resulting mesh sequence are shown to exhibit the order of convergence which is known to be best possible for the type of elements used.
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  • 74
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 663-678 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper deals with constructing finite difference formulaes for approximating ordinary derivatives in a uniform or non-uniform mesh. The corresponding order of truncation error is also established. The accuracy and versatility of the proposed formulae are illustrated through numerical solution to two-point boundary value problems.
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  • 75
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1576-1588 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time-dependent inelastic torsion of prismatic shafts. Several cross-sections and two types of twisting history are considered in the numerical examples. The shaft material is assumed to obey an elastic-time hardening creep constitutive model.
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  • 76
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 707-718 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The use of quasi-Newton methods is studied for the solution of the nonlinear finite element equations that arise in the analysis of incompressible fluid flow. An effective procedure for the use of Broyden's method in finite element analysis is presented. The quasi-Newton method is compared with the commonly employed successive substitution and Newton-Raphson procedures, and it is concluded that the use of Broyden's method can constitute an effective solution strategy.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 719-733 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Cracked plates of power hardening material under plane strain and incompressibility conditions are investigated in this work by using a penalty function and superposition method. The present numerical method is found to be quite efficient for the relevant problems if the hardening exponent of material is not so large.
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  • 78
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 735-745 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Recent finite element analysis of adaptive refinement has focused attention on high-order approximation within elements. High-order approximation may be attained over curved elements with either rational basis functions expressed directly in the global co-ordinates or with a particular class of isoparametric basis functions. Theory for construction of high-order rational bases yields modifications to the blending method for a special class of elements in order to achieve higher order approximation within these elements.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1605-1611 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method is presented for the approximate solution of the axisymmetric problem of an annular crack Embedded in an infinite elastic solid and subjected to a normal internal pressure. The numerical results Obtained for the stress intensity factors are in good agreement with those obtained by Smetanin2.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1631-1646 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper deals with an application of the boundary element method to the analysis of nonlinear sloshing problems, namely nonlinear oscillations of a liquid in a container subjected to forced oscillations. First, the problem is formulated mathematically as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions, assuming the fluid to be inviscid and incompressible and the flow to be irrotational. Next, the governing equation (Laplace equation) and boundary conditions, except the dynamic boundary condition on the free surface, are transformed into an integral equation by employing the Galerkin method. Two dynamic boundary condition is reduced to a weighted residual equation by employing the Galerkin method. Two equations thus obtained are discretized by the use of the finite element method spacewise and the finite difference method timewise. Collocation method is employed for the discretization of the integral equation. Due to the nonlinearity of the problem, the incremental method is used for the numerical analysis.Numerical results obtained by the present boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory. Good agreements are obtained, and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems.
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  • 81
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1647-1657 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for solving boundary value problems for thin plate flexure as described by Kirchhoff's theory is proposed. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. A discretization leading to a matrix formulation is proposed. To solve problems with inner conditions in the plate domain, an elimination of boundary unknowns proves successful. The degenerate case where the boundary is free (which leads to a non-invertible matrix) is investigated. Three examples illustrate the efficiency of the method.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1689-1695 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An easy to use stability test is presented for finite elements which are under- or selectively-integrated. This test is reminiscent of the patch test in that it must be applied only to one prototype element, and it is a sufficient test for the nonsingularity of the global coefficient matrix. The minimum number of integration points which can be used with each of several common one-, two- and three-dimensional elements for a variety of steady-state and time-dependent, scalar boundary value problems are given.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1659-1688 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper shows that mixed interpolation is required because of the nature of the pressure terms in the equations. These lead to finite element equations which in many circumstances do not uniquely determine the pressure, if the same interpolations are used for pressure and velocities.Several new combinations of pressure and velocity interpolation are analysed with the aid of a novel diagrammatic technique. In particular we consider some very interesting combinations in which, over nearly all the flow, the pressure and velocity are approximated on elements by biquadratic polynomials which are continuous across element boundaries.The theory of this paper is shown to be in complete agreement with numerical experiment.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1697-1716 
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    Notes: A finite element method with transmitting boundary is developed for time-harmonic elastodynamics on infinite domains. Only a finite inner domain needs to be discretized into conventional finite elements, while the effect of the exterior domain is simulated by introducing the transmitting boundary stiffness matrix on the degrees-of-freedom of the transmitting boundary nodes. In order to incorporate the Sommerfeld radiation condition, the reciprocity relation, on the transmitting boundary for the radiating elastodynamic state under consideration and the one which is induced by a finite number of point source is used to calculate the transmitting boundary stiffness matrix. The effectiveness of the transmitting boundary technique has been demonstrated by solving the stress concentration problems of a homogeneous isotropic full space with a circular cylindrical cavity and of the one with a spherical cavity, which are subjected to plane incident waves, and the results are compared with the ones of the conventional FEM and the exact data.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1735-1739 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A numerical approximation for the two-dimensional Laplacian operator at a point is derived for the general case in which the point is surrounded by an arbitrary number of arbitrarily located coplanar nodes. The expression obtained is shown to generalize the usual Cartesian finite difference expression.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 829-852 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper is concerned with the large-deflection (bending and free vibration)analysis of thin elastic curved beams by conventional and mixed finite element methods. The conventional finite element method is based on the total potential energy expression, whereas the mixed method is based on a Reissner-type variational statement and involves the bending moments and deflections as primary dependent variables. Incremental and direct formulations are presented for both methods. The nonlinearity is included in the numerical method via an iterative procedure (i.e. the in-plane force due to the large deflection is not treated as constant but included under the integral in the energy expression). In the case of vibrations, the transverse shear and rotary inertia effects are also included. A number of numerical examples of beams with various edge conditions are analysed for deflections and natural frequencies, and the results are compared with those reported in the literature.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 871-877 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper considers some consequences of the common implementation of the finite element method in which element integrals are evaluated numerically by Gaussian quadrature. It shows that if the order of the Gauss scheme is less than the number of basis functions on an element, then the numerically evaluated capacity matrix for that element is singular. The capacity matrix of an assembly of such elements is also considered and is shown to be singular under certain conditions.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 879-907 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A curved triangular element for plate bending is developed, using the displacement method of formulation. The element has one outwardly curved side and conforms on an arbitrary quadratic boundary.To the user, the element appears as a single curved triangle. Internally, however, the element is subdivided into a straight-sided triangle and a ‘curved segment’. The straight-sided triangle is extensively documented in the literature2-5 and is referred to in the paper as the Cowper triangle. The curved segment is a two-noded element with 12 degrees-of-freedom. It has one straight side and one curved side.Independent expansions are assumed in each domain and explicit shape functions derived. The theoretical solution to a few practical problems is contained in each of the two expansions. In such cases, the curved triangle produces perfect results. Otherwise, the accuracy is of the same order as that obtained in similar problems with straight boundaries.The method is easily extended to elements of higher order.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 909-921 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for the solution of time-dependent inelastic deformation problems for metallic structures, in the presence of transient thermal stresses, is presented in this paper. A rate formulation of the equations is used and any of a number of recently proposed combined creep-plasticity constitutive models with state variables can be adopted to describe material behaviour. The computer program developed can solve planar (plane strain and stress) and axisymmetric problems. Using one of the above-mentioned constitutive models, numerical results are presented for several illustrative problems, and comparisons of results, using either the quasi-steady or the unsteady diffusion equation for the determination of the temperature field, are carried out.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1791-1810 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Two alternative hybrid-stress-based functionals are examined for the incremental elastic-plastic static analysis of single layer plates. Material nonlinear effects are incorporated via the initial-stress approach so that an equivalent nodal force vector is defined and the stiffness remains constant throughout the incremental loading. The alternative functionals differ in the incremental stress which is assumed to satisfy equilibrium; in the first, it is the actual stress increment, and in the second it is the elastic stress increment. Results are presented for two example problems, and comparisons of the alternative functionals and plausible iteration schemes are given. The effects of variation of pertinent solution parameters are also shown. A 4-node hybrid-stress plate element based on a Mindlin-type displacement field is used for most cases; however, limited results are also presented using an 8-node plate element, thus permitting comparisons of the relative efficiencies of the two elements.
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  • 91
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1779-1789 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The following work proposes the use of a special description-language for producing input data of finite element programs. The programs now used require a detailed description of the structure to be analysed, and they require it in a form which is unfavourable to the user and which promotes errors. Therefore, a language was designed which allows a short and compact description of the structure. This description is then automatically transformed into the input data. In this paper, the design process and the characteristics of the language are presented. Some comments on its implementation, that is on the development of a special preprocessor, are made. As target system, the finite element program SAP IV has been chosen. Finally, we want to present an example of the improvements achieved by the use of this language and the SAP IV preprocessor, respectively.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1811-1821 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The transient thermal analysis of large aerospace vehicles such as the space shuttle requires models with thousands of degrees-of-freedom. The design of thermal protection systems for such vehicles requires the repetitive thermal analysis of the vehicle and the calculation of sensitivities - derivatives of the transient response with respect to design parameters. When the number of design parameters is large, the cost of the sensitivity calculations may become prohibitive. The present work is concerned with reducing the computational cost and errors in sensitivity calculations with one of the simplest available methods - the finite difference approach. A technique for calculating simultaneously the nominal and perturbed solutions required for the finite difference derivative is proposed. An expression for the optimum value of the perturbation parameter is obtained which permits reducing the computational error. An insulated cylinder is used as an example which demonstrates that significant improvements in accuracy and efficiency may be obtained.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 145-153 
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    Keywords: Engineering ; Engineering General
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    Notes: Numerical evaluations of elliptic integral solutions of some large deflection beam and frame problems are presented. The values are given in tabular form with up to six significant figures. The numerical technique used for evaluating the elliptic integrals is described.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 154-155 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1888-1889 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1882-1887 
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    Notes: A method for improving the computational accuracy of numerical derivatives based on cubic splines and computed from a given set of function values with possible errors is described. The method incorporates smoothing, a derivative profile and/or numerical derivatives in the computational process by solving a pentadiagonal system of linear equations. Results comparing the derivatives computed by the present method, cubic spline and finite differences are given.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 957-974 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The calculation of the response of rotationally periodic structures to transient forces and prescribed motions is considered. The work extends the work previously described by Thomas1 in which only the free and harmonic forced vibration problems were considered. It is assumed that the finite element method is to be used, so that the equation of motion of the structure contains a finite number of degrees-of-freedom whose responses are governed by mass, stiffness and damping matrices. It is shown that an exact solution to the equation of motion of the idealized full structure can be obtained by solving the equation of motion of a single substructure for a number of different spatial Fourier harmonics of force (and hence response). A modal method of solving this equation is described. a brief description of the implementation of the method in a suite of computer programs, and the application of the programs to a practical problems, is also given.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 975-989 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Families of difference schemes are developed for both the linear and nonlinear inviscid Burger's equation and a system of shallow water equations. Single-step and two-step (Lax-Wendroff type) families are described and comparisons are made with other difference schemes.The schemes are developed using a very limited portion of a space-time continua, coupled with Galerkin's method applied over a few triangular elements. The elements are geometrically flexible as a function of a geometry factor α, creating the idea of difference families.Stability is commented on, including the continuous relationship between stability and the families of schemes as a function of α. Numerical results are presented and commented on for the system of shallow water equations and the inviscid Burger's equation. Several areas for future research are described.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1093-1101 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The upwinded finite element method was introduced for the solution of conduction-convection problems by considering the model problem, u″-Ku′=0, K〉0, subject to the boundary conditions u(0)=1, u(1)=0. In this paper we consider the solution of this problem by the collocation method using piecewise cubic Hermite polynomials and a uniform grid. We consider the collocation points to be arbitrary parameters which enable us to express the collocation points in terms of the upwinding parameter of the upwinded finite element method. Various choices of the collocation points, including values which lead to complete accuracy in the nodal function values as well as the nodal values of the derivatives are discussed. Finally, we discuss the application of these points to slightly more general problems. Numerical results illustrating the behaviour of these points are given.
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1103-1117 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm and corresponding FORTRAN program for the solution of unsymmetric banded linear equation systems. The algorithm is based on the Crout method. A special technique, called double windowing, enables the solution of very large equation systems with a total equation number reaching 30,000 and a full bandwidth in excess of 1,000. Special attention was devoted to minimization of peripheral processor time (communication with backing disc memory). An appendix lists the complete program for Cyber series computers (CDC).
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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