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  • Chemical Engineering  (1,250)
  • Engineering General  (708)
  • 1985-1989  (1,174)
  • 1980-1984  (784)
  • 1975-1979
  • 1925-1929
  • 1987  (1,174)
  • 1982  (784)
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  • 1985-1989  (1,174)
  • 1980-1984  (784)
  • 1975-1979
  • 1925-1929
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  • 1
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1021-1034 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Equations are derived that relate the orientation of “pseudo-affine” reoriented structural units after a biaxial deformation to the degrees and the directions of the effective drawings. The connection between these drawing parameters and those externally applied is analyzed in detail. It is shown how a comparison of these two sets of drawing parameters allows conclusions regarding the distribution throughout the material of the stresses that cause the deformation, the inhomogeneity of the deformation, and the role of non-orienting flow during deformation. In particular, the orientation of biaxially drawn poly(ethylene terephthalate) films is investigated, and it is shown what general information can be obtained on the deformation behavior of this material on the basis of these considerations.
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  • 2
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1059-1068 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Scale-up from small laboratory size extruders to large production size extruders is a procedure of great practical importance. Many scale-up rules and theories have been proposed in the past, however it is not always clear how the different scale-up methods will affect extruder performance. A basic analysis of scale-up in plasticating single screw extruders is developed from which the effect of a certain scale-up strategy on extrusion performance can be evaluated in terms of solids conveying, melting, melt conveying, mixing, residence time, heat transfer, power consumption, and specific energy consumption. Various existing scale-up theories are evaluated and compared using the basic analysis. A number of existing scale-up theories have some significant drawbacks, in particular with non-constant specific energy consumption and imbalance between melting rate and pumping rate. Conditions that are desirable to achieve in scale-up are enumerated and ranked in terms of importance. This leads to two new scale-up methods that result in constant mechanical specific energy consumption and high throughput rates. The first scale-up method keeps the specific surface area constant. This scale-up should work well for high values of the Brinkman number. However, at low values of the Brinkman number, the melting rate may be insufficient. The second scale-up method keeps the melting rate at low Brinkman number equal to the pumping rate and, thus, should be useful in cases where the first scale-up method cannot be used.
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  • 3
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987) 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1128-1136 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The plane strain fracture toughness and fracture mechanisms of several tough engineering plastics have been studied and compared with poly(methyl methacrylate) (PMMA), a relatively brittle polymer. The tough polymers all are observed to form a multiple craze zone at the crack tip, which is shown to be the primary source of plane strain fracture toughness in these materials. The multiple craze zone is retained during slow crack growth but is metastable, and at a critical stress intensity and associated crack velocity, the system passes through a transition to a greatly accelerated single craze mode of unstable propagation.
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  • 5
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1148-1155 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The optical properties of bisphenol-A polycarbonate resin as described by the complex index of refraction, N = n - ik, are derived by Kramers-Kronig analysis of experimental absorption and reflectance data obtained in the range 40μm ≥ λ ≥ 105 nm. Electronic absorption processes in polycarbonate are characterized by two broad absorption peaks centered at ∼200 and ∼100 nm.
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  • 6
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1182-1186 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Three-layer coextruded blown (either blend or composite) films, made of low-density polyethylene and linear lowdensity polyethylene (1:1 ratio) of identical density, were compared. The tensile properties of both systems are nearly as high as those of the linear polyethylene while high strain rate properties including impact strength and tear resistance of the composite film are superior. Some structural insight was obtained by thermal analysis and thermoelastic measurements. Structure property relationships are discussed in light of the unique behavior, structure, and morphology of linear low-density polyethylene. The two polyethylenes are only compatible to a rather limited extent mainly affecting their blend behavior. However, a strong mutual reinforcement effect was observed.
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  • 7
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1203-1208 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A Viton copolymer containing vinylidene fluoride (VF2) and hexafluoropropylene (HFP), and a terpolymer containing VF2, HFP, and tetrafluoroethylene (TFE) were cross linked using varying amounts of Bisphenol AF to yield two series of fluoroelastomer networks, Stress-strain isotherms in elongation were determined for these samples at several temperatures and at two degrees of swelling with phenyl acetate. Strain-induced crystallization was observed, as evidenced by upturns in the isotherms at high elongations. It appears to be more pronounced in the terpolymer samples, presumably because the TFE units not only can crystallize themselves, but can co-crystallize with the VF2 units. The crystallization was found to persist upon moderate increase in temperature, but was suppressed when the networks were swollen, Thermoelastic (force-temperature) measurements were used to obtain values of the fraction fe/f of the elastic force that is due to energetic effects. Negative values were obtained for both types of samples and, in the case of two samples studied in detail, their magnitudes increased with increase in elongation. The magnitudes were larger and the increases more pronounced in the case of the terpolymer networks, as would be expected from a greater tendency for straininduced crystallization.
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  • 8
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1221-1228 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The transesterification reaction of molten ethylene and vinyl alcohol copolymers (EVA), in presence of paraffinic alcohols and basic catalysts, leads to high conversion of the ester groups to secondary alcohol in both discontinuous and continuous processing equipment. Various kinds of alcohols and two different catalysts were used. Sodium methoxide is a powerful catalyst for the equilibrated transesterification reaction, but we also observed side reactions, such as cross-linking with low-molecular-weight alcohols and hydrolysis of the catalyst followed by partial saponification of the EVA. Kinetic studies were performed in the presence of dibutyltin dilaurate, an efficient catalyst without any side reactions. The solubility of the main alcohol reagents was verified by diffusion measurements. The general reaction scheme and the related kinetics, corresponding to a homogeneous system, lead to a fair evaluation of the rate constants.
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  • 9
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 27 (1987), S. 1252-1257 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The mechanical properties of polyurethane-unsaturated polyester interpenetrating polymer networks (IPNs) that were prepared by reaction injection molding (RIM) process were measured with variations In composition, cross-link density, and relative reaction rate. From dynamic mechanical analysis (DMA), it was found that the two component polymers had a good compatibility over the whole composition range. The tensile strengths of the blends were greater than those of the pure components and had a maximum value at 50/50 composition. The modulus of elasticity and surface hardness decreased and the impact strength increased as the polyurethane content was increased, but the changes were not high at low polyurethane content, below 50%. For higher cross-link density, the compatibility was enhanced and the mechanical properties were improved. When the reaction rates of the components were different, some extent of phase separation was found in DMA and the properties were affected adversely.
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  • 10
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 11
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 41-66 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A system for describing three-dimensional surfaces in a form suitable for finite element analysis is described. The system makes extensive use of real-time interactive computer graphics techniques for both input and display. Discrete transfinite mappings are used as the mathematical basis for the surface representation. The mathematical basis and the reasons for choosing this form of representation are discussed. Explicit forms of the mappings based on Lagrange polynomial interpolation functions are presented. Finally, the interactive graphics procedures for defining finite element meshes are described.
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  • 12
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 99-109 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two highly accurate implicit Padé approximations to the transient heat conduction equation are investigated using the conjugate gradient method to solve, for the temperatures. The accuracy and stability of the approximations are discussed and numerical examples are presented showing the relative performance. Comparisons with the Crank-Nicolson method are also presented.
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  • 13
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    International Journal for Numerical Methods in Engineering 18 (1982), S. i 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 14
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 195-210 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A clearer insight into the ‘shear locking’ phenomenon, which appears in the development of C0 continuous element using shear-flexible or penalty type formulations, is obtained by a careful study of the Timoshenko beam element. When a penalty type argument is used to degenerate thick elements to thin elements, the various approximations of the shear related energy terms act as different types of constraints and, depending on the formulation, two types of constraints which are classified as true or spurious may emerge. The spurious constraints, where they exist, are responsible for the ‘shear locking’ phenomenon, and its manifestation and elimination is demonstrated in a very simple example. The source of difficulty is shown to be the mathematical operations involved in the various shape function definitions and subsequent integration of functionals. It is seen that formulations that ensure only true constraints in the extreme penalty limit cases display far superior performance in the thick element situation as well, and thus guidelines for the development of efficient elements are drawn. A similar type of behaviour is observed in a shallow curved beam element and here ‘inplane locking’ can be eliminated by selective integration to obtain an improved curved beam element. However, ‘inplane locking’ does not cause a spurious constraint as the error quickly vanishes with the reduction of element size for a reasonable radius of curvature conforming with shallow shell theory.
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  • 15
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 321-322 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 323-341 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The rate of convergence of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased. Alternative stragegies are examined in the light of recent theoretical results and computational experience.
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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 381-396 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Upwind finite element schemes remove spurious oscillations that occur in the solution of diffusion convection equations. Up to now these schemes lose part of their accuracy when the Peclet is large. As an improvement, it is proposed to move the integration nodes along the ‘streamlines’ before evaluating the elementary convection matrices. The displacements of the nodes along the streamlines, which are one-dimensional manifolds, are calculated analogously to well-known one-dimensional formulae. The last section of this paper illustrates this new method with the help of four examples which show its validity.
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  • 18
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 314-320 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Quarter-point elements are used very frequently for fracture mechanics computations, because the quarter-point technique yields the required singular interpolation without any modification to existing software. This advantage is particularly significant for three-dimensional stress intensity factor computations because of the difficulty of implementing other techniques. However, in practical 3-D applications, the crack front is usually curved, and this note proves that a crack front distortion leads to a negative Jacobian in the region surrounding the crack front. The numerical difficulties to be expected depend on the aspect ratio of the elements.
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  • 19
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 343-350 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a smoothing technique to the oscillated contact pressure obtained by penalty methods for a class of unilateral contact problems in linear elasticity. The main result is to show that the smoothed contact pressure satisfies the so-called Babuska-Brezzi condition which dominates the convergence of the penalty method. One numerical example is described.
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  • 20
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 435-444 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for the exploitation of screw translation symmetry for the vibration analysis of structures is presented. The method is capable of providing significant computational economies over the use of the lower axial translational symmetry of such structures.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 629-630 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 22
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 632-634 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 23
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 661-673 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimal structural desingn generally deals with frame or shell structures where the optimization is limited to resizing of structural members to obtain optimum cross-sections or thicknesses. Shape optimization solves another class of problems involving continuous structural components where the optimum shape (the shape of the boundaries and the surfaces of the components) is determined. This report describes shape optimization of three-dimensional structural components. The finite element method of analysis is used employing the 20-noded isoparametric element. The objective function, mass, is minimized by the direct use of nonlinear mathematical programming, specifically the feasible direction method. Numerical shape representation and the selection of design variables are the most important aspects of the problem. The problem is addressed from a practical standpoint and techniques are presented to minimize the number of desingn variables. Isoparametric representation of the surfaces and the numerical superposition of shapes are discussed. These techniques are compared and demonstrated on simple cantilever beams and their minimum mass designs are obtained. In one example, the optimum shape of a non-uniform cross-sectinal beam is obtained under stress constraint. The final design has a crosssectional shape varying over the length of the beam which could not be predicted using the bending theory of beams. One major difficulty encountered in some problems was that the shape changes during the optimization process may require a change in the finite element mesh because the initial configuration of the finite element mesh may result in very distorted elements for the new shape. The analyis with a mesh containing distorted elements may not be possible at all or the results of the analysis may be inaccurate.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 727-735 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Vector functions having a constant or zero divergence over a quadrilateral domain are derived using a parametric co-ordinate formulation. Expansion functions with a constant curl, defined over parallelograms and triangles, which can be used in moments-based investigations of electromagnetic wave interactions with surfaces and apertures, are then obtained. Finally, two basis functions, which have appeared in the literature and have been used to solve field problems associated with rectangular apertures and arbitrary surfaces, are identified as special cases of these expansion functions.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 927-944 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element formulation for stress analysis of a twisting beam is developed. The formulation is effective for a prismatic beam with solid section as well as a thin-walled beam, and can be applied both to a pure-torsion problem and a warping-torsion problem. The formulation is of a great advantage to an elastic-plastic torsion problem. The formulation does not stand on the assumption of a thin-walled structure, and therefore torsional rigidity of the section can be evaluated exactly without using the so-called Saint-Venant's torsional constant. Torsional rigidity is, in this paper, evaluated directly by a warping function of the section. Warping function is evaluated numerically due to shape of the section, due to progress of plastic region and due to effect of finite displacement (finite rotation, small strain). Pure-torsion and warping-torsion of a rectangular beam and an H-beam, which have an elastic-plastic material property, are analysed, and the extension to the finite displacement problem is discussed. Many numerical examples are provided in order to check the accuracy of the formulation.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 955-957 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 967-979 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, efficient and economical numerical technique for the analysis of shallow shells-of arbitrary shape is presented. The technique is based upon the method of constant-deflection contours combined with the well-known finite element method. In the proposed method the elemental stiffness matrix is derived from a system of two consistent partial differential equations for two scalar functions using Galerkin's method. Several representative examples are included to indicate the effectiveness of the method.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 997-1017 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An equation solver for the large unsymmetric systems of linear equations arising in the application of the boundary integral equation method to problems of linear elasticity in homogeneous or piecewise homogeneous solids is presented. The solver uses Gaussian elimination. The advantages of the solver over many existing eliminational or iterational methods are that it ignores many of the large groups of zeros that occur in piecewise homogeneous work, and also restrains growth of the number of non-zero matrix entries. Memory requirements and computation times therefore are reduced for many piecewise homogeneous problems.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1055-1061 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods are described for forming element matrices for a wide variety of operators on tetrahedral finite elements, in a manner similar to that previously employed for line segments and triangles. This technique models the differentiation and product-embedding operators as rectangular matrices, and produces finite element matrices by replacing all required analytic operations by their finite matrix analogues. The method is illustrated by deriving the conventional matrix representation for Laplace's equation. Computer programs are available, which generate universal finite element matrices for use in various applications.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1101-1103 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Ingraffea and Manu1 and Lynn and Ingraffea2 have shown that the size of the quarter-point elements can affect the computed elastic stress intensity factor. The nature of the effect is such that, all other details remaining constant, there is a particular crack tip element size which minimizes the error in the computed stress intensity factor. Here, size of element means the radial edge length. The reasons for this size dependence are discussed below. It will be seen that the discussion is in terms of the need to simultaneously represent the singular and finite stress terms in a given problem. The discussion has relevance to other formulations of crack tip elements.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1115-1130 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a previous paper it has been proved by the author that the integral equations arising from the application of Green's formula to the Helmholtz equation in a limited domain can show a certain type of numerical instability, if a real Green's function is used. It has been also proved that such instabilities cannot arise if a complex Green's function is employed.However, it has been found in this latter case also that numerical instabilities can occur. This has been proved and thoroughly analysed for a circular domain, and a technique of avoiding these instabilities has been devised.Furthermore, when this technique is followed, very accurate results can be obtained, regardless of wavenumber used. Thus, only three or four segments are sufficient to describe a wavelength, contrary to what until now has been obtained, i.e. that at least six segments are always necessary. This last result has been shown to be valid also for geometries other than the circular one.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1145-1151 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1699-1717 
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    Notes: Dependence of dynamic response of nonlinear mechanical systems on design variables is analysed. An adjoint variable method is used to derive first- and second-order derivatives of measures of dynamic response with respect to design variables. A computational algorithm is presented for numerical calculation of first and second design derivatives. A simple oscillator example is solved analytically and by the adjoint variable method, with identical results. A burst fire automatic weapon mechanism with linear and nonlinear damping is treated numerically. It is shown that quadratic appriximations of dynamic response, using results of second-order design sensitivity analysis, can be substantially better than conventional linear approximations.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1739-1739 
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    International Journal for Numerical Methods in Engineering 18 (1982) 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1745-1764 
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    Notes: Problems involving the diffusion and transport (angular dependence considered) of neutron radiation are frequently encountered in radiation physics and nuclear engineering. Neutron diffusion problems require substantial computer storage arising from the energy and spatial dependence, while in the case of transport problems the angular dependence of the neutron flux and of the neutron scattering process gives rise to a further considerable increase in storage. In the present work, a method has been developed which greatly eases the bandwidth problem in the solution of large systems of linear equations and algorithms have been developed to assemble and solve such systems of equations in one and two dimensions. The formalism used is the variational method and, for simplicity, linear interpolating functions have been used to derive a symmetric banded system of equations. Finite element algorithms have been implemented in the codes FEED1 and FEED2, which treat one and two space dimensions, respectively. Three benchmark problems are analysed in this paper and results are compared with finite difference discrete ordinate method solutions. It is shown that the finite element method provides fast and accurate solutions to neutron diffusion and transport problems.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1829-1854 
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    Notes: A general and systematic discussion on the use of the operational method of Laplace transform for numerically solving complex time-dependent linear problems is presented. Application of Laplace transform with respect to time on the governing differential equations as well as the boundary and initial conditions of the problem reduces it to one independent of time, which is solved in the transform domain by any convenient numerical technique, such as the finite element method, the finite difference method or the boundary integral equation method. Finally, the time domain solution is obtained by a numerical inversion of the transformed solution. Eight existing methods of numerical inversion of the Laplace transform are systematically discussed with respect to their use, range of applicability, accuracy and computational efficiency on the basis of some framework vibration problems. Other applications of the Laplace transform method in conjunction with the finite element method or the boundary integral equation method in the areas of earthquake dynamic response of frameworks, thermaliy induced beam vibrations, forced vibrations of cylindrical shells, dynamic stress concentrations around holes in plates and viscoelastic stress analysis are also briefly described to demonstrate the generality and advantages of the method against other known methods.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 11-29 
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    Notes: The dispersive properties of finite element semidiscretizations of the two-dimensional wave equation are examined. Both bilinear quadrilateral elements and linear triangular elements are considered with diagonal and nondiagonal mass matrices in uniform meshes. It is shown that mass diagonalization and underintegration of the stiffness matrix of the quadrilateral element markedly increases dispersive errors. The dispersive properties of triangular meshes depends on the mesh layout; certain layouts introduce optical modes which amplify numerically induced oscillations and dispersive errors. Compared to the five-point Laplacian finite difference operator, rectangular finite element semidiscretizations with consistent mass matrices provide superior fidelity regardless of the wave direction.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 89-98 
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    Notes: Masters are defined as the degrees-of-freedom that are retained in the reduced eigenvalue problem. Various qualitative guidelines to select masters are published in the literature, but it is difficult to apply them to complex structures. In this paper a computational algorithm to select masters for complex structures is presented. This algorithm is based on a guideline14 which assures that the associated Guyan reduction process is valid. This algorithm eliminates one degree-of-freedom at a time satisfying the guideline, and preserves lower frequencies in the reduced eigenvalue problem. The algorithm presented in this paper is used to select masters for four different structural models. The natural frequencies of the associated reduced eigenvalue problems are calculated and compared with those calculated from the full eigenvalue problems.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 135-149 
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    Notes: A finite element model for symmetrically loaded shells of revolution is described. The nonlinear geometric effects are accounted for by incrementing loads and iterating for equilibrium. The iteration process also allows for nonlinear materials. The shell model accounts for large strains, large rotations and shear deformation. Three example problems demonstrate the ability of this model to solve linear problems. Also, three example problems demonstrate the versatility and accuracy of this model for nonlinear problems. These nonlinear example problems are an axially loaded cylinder and an internally pressurized spherical shell that have large membrane strains, and a cylinder that deforms into a spherical shape, having large rotations.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 166-166 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 167-180 
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    Notes: The paper outlines a numerical procedure for the finite element solution of convective diffusion problems with significant convective terms using conventional (not upwinded) Galerkin methods in connection with ‘boundary-layer type’ elements. The underlying argument in the sequel is that the poor stability properties of conventional Galerkin methods are caused by the insufficient approximation of eigensolutions. These are located at some sections of the boundary and are only present within a generally very thin layer. Consequently, the identification of these layers and the satisfactory approximation of the eigensolutions are necessary and totally sufficient for a satisfactory solution. In the following we intend to present this procedure, its theoretical background and selected numerical results.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 245-257 
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    Notes: The solution of elastostatic bodies in frictionless contact is obtained by an automated direct method which exploits the theory of linear elasticity and circumvents the need for the inclusion of artificial interface elements, mathematical programming techniques or computation of contact pressure. The method is simple and economical to use and can be easily appended to existing numerical schemes such as the finite element method. The formulation and numerical algorithm are presented for body combinations which are independent of relative tangential displacements along the contact surface. The method is illustrated through an elementary example amenable to hand calculation. Numerical results for more realistic problems are given and compared to known solutions. It is concluded that the method provides a powerful means for both the analysis and design of contacting bodies when used in conjunction with a finite element computer program.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 291-309 
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    Notes: A finite element stress analysis capability for plane elasticity problems, employing the principle of stationary complementary energy, is developed. Two models are investigated. The first is a 24 d.o.f. rectangular finite element. The second model consists of an 18 d.o.f. triangular element. In order to allow for self-equilibrating stresses which are continuous within the element, the well-known Airy stress function ø is used. The function ø is represented by means of quintic Hermitian polynomials within the finite element. The values of the ø function and its derivatives up to order two are used as nodal parameters. For matching the stress function with the prescribed boundary tractions, additional equations are developed considering the force and moment equilibrium equations on the boundary consistent with the assumed stress function. These additional boundary equations are incorporated into the system equations using the Lagrangian multiplier technique. Excellent results are obtained for linear elastic problems even with coarse finite element discretization. Some examples of plane elasticity problems are solved and results compared.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 363-380 
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    Notes: The problem related to the derivation of conforming deep shell finite elements is examined in the light of the thin shell theory and using the classical Loves strain energy formulation. A family of quadrangular finite elements allowing for variable curvature is developed. It is shown how an exact conformity of the displacements can be ensured in a large number of cases.Various static and dynamic applications are used to illustrate the advantages of these elements.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 397-419 
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    Notes: The development of a geodesic beam finite element for use with a specific circular cylindrical shell finite element in the analysis of reinforced circular cylinders is described.The basic strain and curvature change equations are given and, from these, three versions of the geodesic beam element are developed. Two of the beams have nodal degress-of-freedom identical with the shell element. They differ in the treatment of the terms relating to rotation about the principal normal. The first version ignores this parameter but, under certain circumstances, the stiffness matrix contains terms which can contribute to the strain energy under arbitrary rigid body movement of the beam. This deficiency is removed by applying an aspect of Koiter's theory which is used to transform the curvature change equations.The introduction of additional rotational degress-of-freedom, at the end nodes of the beam element, produces a variation which is capable of accurately representing and transmitting in-surface bending effects to an adjoining beam element.Numerical evaluation successfully compares finite element solutions to basic problems for straight, circular and helical beams with theoretical strain energy solutions. Finally the beam is used in conjunction with a shell element to analyse an infinitely long circular cylinder, reinforced with equispaced rings, subjected to internal pressure.
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    International Journal for Numerical Methods in Engineering 18 (1982) 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 521-533 
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    Notes: Finite element analysis of engineering structures commonly requires the use of inter-nodal displacement constraints. Current algorithms for this facility - elimination, Lagrange multipliers and penalty function methods - are briefly reviewed. An alternative approach is proposed which avoids some of the problems of these methods. This technique uses solution of the unconstrained stiffness equation with an extended number of right-hand sides. The resulting solutions are then combined to satisfy the constraints. This method has application in the synthesis of sub-structures with incompatible boundary variables. It is particularly efficient when the constraint affects many variables but the kinematics of the constraint can be expressed in terms of few independent variables, e.g. rigid body motion of part of the structure. In common with the Lagrange method, it produces data for use in a nonlinear analysis with constraints. The formulation of ‘rigid body’ constraints in geometric nonlinearity is detailed and demonstrated.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 569-582 
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    Notes: All physical process change with time and although physicists and engineers often freeze them to simplify their model studies, this is not always possible. Add to this the existence of several subregions within the modelling domain with different physical properties, the size and number of which change with time, and one has produced what might appear to be an intractable problem. Previous studies have shown that adaptive grids are an inconvenient way of modelling such moving interface problems and suggested that the use of a fixed grid with special discontinuous elements affords an efficient solution technique.This work presents and develops the characteristic matrices for two such elements, namely a quadratic triangle with an internal interface modelled by two straight lines and a quadratic isoparametric element. Both these elements are tested against an analytical solution to a simple Poisson equation. Such tests reveal the performance of the proposed elements to be satisfactory except for the definition of gradients near the interface.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 591-607 
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    Notes: To account for plastic deformation in plate and shell structures an elasto-viscoplastic solution algorithm is considered based on Perzyna's model for material behaviour. This algorithm can be employed to solve for time-dependent elasto-viscoplastic situations and by allowing steady-state conditions to be reached, elasto-plastic problems can also be considered.For the large displacement elasto-viscoplastic analysis of thin shells, an incremental stiffness procedure is employed together with a Lagrangian description of the stress and strain vectors. The Semiloof plate and shell elements are used for finite element space discretization.The procedures developed are applied to the solution of several numerical examples and the solutions compared with results from other sources where available.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 675-685 
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    Notes: The position, size and surface temperature of circular holes inside a two-dimensional heat conductor are optimized to produce a minimum variation in surface temperature over a portion of the outer boundary. This problem, whic arises in thermal desing of moulds and dies, resembles those encountered in structural shape optimization because the internal geometry of the heat conductor depends on the design variables. In this paper, some of the traditional difficulties associated with shape optimization are overcome by analysing steady heat conduction with a special boundary integral method developed for two-dimensional regions with circular hole. This approach eliminates the need to regenerate a finite element mesh over the interior of the region each time the geometry is changed during the design process. It also increases the efficiency of the analysis by reducing the number of unknowns in the numerical discretization of the region. Since the objective function depends only on the boundary temperatures, there is no need to determine temperatures in the interior.The analysis method is applied to two problems arising in optimal thermal design of compression moulds. These examples show that the number of holes choson for the design strongly affects their resulting optimal arrangement as well as the ultimate uniformity of the cavity surface temperature.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 755-764 
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    Notes: A triangular plate bending hybrid element is constructed according to Reissner's principle. It has 9 degrees-of-freedom and the shear effect is included. The C0 formulation of thick plate is directly developed to solve the thin plate by imposing the discrete Kirchhoff constraints. The matching problem for bending and shear in the hybrid model of thick plate is effectively treated by use of the principle of the energy regulation such that the unified analysis of thick and thin plates is realized. Finally, numerical examples are presented.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 798-798 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 798-798 
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    Notes: In this paper a triangular thin shell element is presented where C1 continuity is introduced by means of the penalty function technique. The displacement field has complete cubic polynomials for each component. The introduced constraint condition is the continuity of normal slopes of the transverse displacements along interelement boundaries. Classical thin shell theory for small deformations is applied. Several analyses of thin plates and shells are performed, including a large problem of practical interest, to study the effect of an increasing penalty factor. The accuracy of the results is estimated and compared to the actually occurred error. In the conclusions a recommended value for the penalty factor is given.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 909-926 
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    Notes: An interactive computer graphic system has been developed for generating and editing three-dimensional finite element meshes. The various difficulties inherent to the generation of solid three-dimensional geometries through an effective use of computer graphic techniques are examined to explain the advantages of this system. The method is a combination of discrete transfinite mapping and cubic spline blending algorithms, used, respectively, to create plane cross-sectional meshes, and to generate the three-dimensional geometry by interpolaring between the cross-sections. The communication between analyst and machine is based on a digitizing tablet and a refresh vector scope. The dynamic viewing capabilities and depth cueing of the vector display greatly enhance the perception of the mesh three-dimensionality. Multi-view dynamic display is also employed to facilitate node or element selection. The flexibility and usefulness of the system are illustrated with the help of three examples of practical interest.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 954-955 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 959-966 
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    Notes: Presented herein are methods to generate special interpolation formulae of the following type: (i) C0 continuous interpolation over triangular elements which induces a given type of singularity for the first derivatives at one of the vertices, and yet preserves ‘rigid and constant strain’ motions, (ii) C1 continuous interpolation over triangular elements which induces a given type of singularity for second derivatives at one of the vertices.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1019-1029 
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    Notes: An explicit algorithm which gives stable finite-difference schemes, of order of accuracy greater than two, for solving a quasi-linear hyperbolic system of partial differential equations in several space dimensions is presented. Third and fourth order accuracy schemes are derived using this algorithm. The fourth order scheme needs fewer flux evaluations than the scheme given by Abarbanel and Gottlieb.1 Numerical results obtained show that these schemes have the expected accuracy and stability.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1063-1076 
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    Notes: Displacement formulated singular elements are compared to isoparametric quarter-node elements. The total stress and displacement solution for each element is decomposed into singular and regular components for evaluating stress intensity factors. Specific relationships between nodal displacements and the singular component of stress are presented for the isoparametric element at selected locations within the element. Numerical results for KI and KII in the slant crack problem are presented. The singular components are shown to produce superior results when considering crack opening displacements.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1197-1211 
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    Notes: A compact FORTRAN subroutine for reducing unsymmetric band matrices (in-core solution) is presented. As usual, the zeros inside the band are skipped during the Gauss elimination. However, the theme of the paper is centred on a new approach in applying the above-mentioned band solver to transient problems. The approach results in considerable saving of computational time while also achieving reduction in memory space. This double advantage makes it particularly useful in handling dynamic real world problems. Extension of the use of the algorithm to moving boundary problems is indicated.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1245-1248 
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    Notes: Simplicial finite elements have many symmetries, which are commonly exploited in programs to save computing time and storage. All possible permutations of the interpolation functions of an N-simplex can be expressed in terms of N basic permutation operations. The relevant permutation matrices are given for triangles up to order 20 and tetrahedra up to order 10.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1265-1270 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1297-1311 
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    Notes: Two new finite elements are developed for the Mindlin theory plate bending problem. The formulation is based on the modified Hellinger-Reissner principle with independent transverse shear strains. Numerical examples indicate that, with properly assumed transverse shear strains, these new elements designated as PLAT8 and PLAT8H do not exhibit locking effect even for very thin plates.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1375-1384 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Integration over triangles where the integrand contains a singularity at one of the vertices is considered in this paper. The applications for such problems arise in using the boundary element method. Low order formulae are presented and compared to previous methods where the singularity was not considered.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1401-1411 
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    Notes: An exact expression is derived for the potential due to a uniform source distribution over a triangular domain. This expression, which is valid for arbitrary field points, is important for the numerical solution of electromagnetic field problems. Numerical values of the potential are calculated by using the expression obtained, and are compared with the results derived by numerical integration.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1423-1423 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1425-1427 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1455-1468 
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    Notes: Hybrid stress elements are known to provide accurate results for analyses of plate bending; in particular, for the prediction of moment distribution. The construction of hybrid stiffness matrix requires numerical inversion of a moment matrix, evaluation of some relatively complicated boundary integrals and several matrix transformations. Each of these operations can be time-consuming, and the matrix inversion can result in a loss of numerical accuracy.This paper devises methods to explicitly invert the moment matrices. We find that for triangular elements the inverse is independent of the element shape and is only inversely proportional to its size. We also use a novel set of displacement variables, which greatly simplifies the boundary integration. The displacement variables are chosen in a hierarchical form so that lower order elements can be determined by straightforward reduction of excess terms in a higher order element. Except for the nodal displacements at the vertices, the present approach involves only variables at the midpoints of the sides of an element.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1505-1520 
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    Notes: The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1565-1568 
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    Keywords: Engineering ; Engineering General
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    Notes: The use of warping displacement functions for the torsional stiffness representation of beams with rectangular cross-sections is studied. These functions can directly be employed in the displacement-based formulation of Hermitian and isoparametric three-dimensional beam elements for linear, elastic-plastic or large displacement/large rotation analysis. the results of some studies are given to demonstrate the applicability and use of the proposed functions.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1583-1585 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1601-1611 
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    Notes: A closed solution for dynamic problems with the transform technique is possible for linear behaviour only. Therefore, a strategy for the solution involving nonlinear material behaviour has been developed. Herewith, an iterative equalization is made possible by the repeated transform of the differential equations given through the initial strain method.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1679-1684 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1719-1732 
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    Notes: A two-dimensional linear elastodynamic analysis of crack initiation, fast crack propagation and crack arrest in the DCB specimen is presented. The analysis is performed using the previously developed SMF2D code in its generation mode. The experimentally measured crack tip motion, as well as the specimen's geometry and its material characteristics, serve as input to the simulation. The dynamic stress intensity factor, the dynamic energy release rate and the various distributions of energies are subsequently evaluated. The numerical results are found to be in very good agreement with analytical and experimental findings.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1733-1735 
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    Notes: The solution of a fourth order differential equation, which governs a number of problems in structural mechanics and possibly elsewhere, is considered. It is shown how the use of complex arithmetic can be avoided in the computation.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1739-1740 
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1765-1784 
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    Notes: A powerful new finite boundary concept of seeking field solution, at few selected regions in the solution domain, is introduced. Also a highly economical finite boundary method (FBM) which would greatly reduce the size of the coefficient matrix of the resulting system of simultaneous algebraic equations, requiring lesser computer memory and lesser computing time, is developed. Fluid flow fields governed by the basic elliptic partial differential equations - the Laplace's and the Poisson's equations - in two independent variables are mainly considered. The computational merits of the FBM are shown by solving, as an example, a simple representative flow problem, and the relevant computational finite boundary formulae are given in tabular form. The formulae are numerically derived based on a generalized method presented here. The added feature of the FBM is that it proves to be equally economical even when the solution is sought in the entire flow domain. The problem of steady-state viscous flows governed by the Navier-Stokes equations, the system of two simultaneous partial differential equations - the Poisson's equation and the vorticity transport equation - makes the FBM doubly economical. The possibility of developing an efficient hybrid computational algorithm, for curved problem boundaries, in conjunction with the finite element method, is discussed. The extension of FBM to transient, non-elliptic problems and to three-dimensional problem fields is also indicated. The FBM has been discussed in a more detailed manner so as to clearly bring out the advantages of the new finite boundary concept.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1801-1820 
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    Keywords: Engineering ; Engineering General
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    Notes: A Fourier series solution is presented for a system of first-order partial differential equations which describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. A central step in the method for solving the system of equations is to combine a complementary function with a particular solution of the system in order to satisfy the boundary conditions. The complementary function is the sum of two series. The terms of the first series are products of a Fourier term in one space variable with the solution of an eigenvalue problem in the other space variable. The second series is similar and comes from reversing the roles of the space variables.
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 1855-1871 
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    Notes: A finite element nonlinear shell model has been developed using Reissner's symmetrically loaded shell-of-revolution theory. This model is capable of modelling nonlinear strains, large rotations and nonlinear materials. This paper discusses the limitations of this model by deriving the basic equations and describing the simplifying assumptions used in the theory and the model. Possible extensions of the model are discussed also.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 75-87 
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    Notes: During the propagation of a hydraulically induced fracture in a porous material, fluid leak-off occurs from the fracture to the formation. Conduction and convection of heat also take place, owing to the large difference between the fluid injection temperature and that of the reservoir. The paper describes a quasi-two-dimensional heat transfer model coupled with a filtration model. It is then coupled into different coupled fracture propagation models (two-dimensional and quasi-three-dimensional).The rheological characteristics of the fracturing fluid are temperature-dependent with a sharp breakdown. The fluid diffusion model combines cake growth at the fracture face with two-fluid flow in the formation. Temperature profiles along the fracture and the formation are computed during fracture propagation.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 141-157 
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    Keywords: Engineering ; Engineering General
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    Notes: We have developed a versatile finite element approach to analyse stresses and displacements induced in thermally thinned and thickened geological structures. Material and geometric non-linearities form an important aspect of the finite element simulation. The changes in geometry are incorporated by a multipoint constraint procedure. The method takes into account temperature-dependent variations in rheological properties of the medium, including the presence of a brittle-ductile transition. We illustrate the application of the method for specific geophysical problems associated with the temperature history of the earth's crust at continental margins of the Atlantic type.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 117-128 
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    Notes: A new finite element method is presented. This new method contains several novel features including a streamline upwind formulation for the advection terms and equal order interpolations for all variables: velocities, pressure, temperature and other fluid properties. This new formulation uses an iterative solution method greatly reducing the computer storage requirements. The validity of the new finite element method was tested on both a natural convection problem, a thermally driven cavity, and a forced convection problem, a heated cylinder in cross-flow. The predicted results compared favourably with a benchmark solution for the cavity and an empirical correlation for the cylinder in cross-flow.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. i 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1697-1709 
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    Notes: A new functional which forms the basis of an improved hybrid element formulation is proposed. The variables for the functional include stresses, strains and displacements, and the displacements and stresses are further decomposed into two parts respectively. The proposed new formulation appears to be particularly suitable for improving conforming models.Based on this formulation, a new four-node plane hybrid element Qcs6 can be developed, and the conforming element Q4 and the non-conforming Wilson element Q64 and modified Wilson element Qm6 can also be derived directly by this hybrid approach. It should be noted that more accurate stresses can be obtained from this element which utilizes the concept of two stress components.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1721-1739 
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    Notes: The method of space-time finite elements enables the simple solution of quite new problems. It is possible to assume the arbitrary partition of the structure area in each moment of integration of the motion equation. Instability is caused by a too large time step and too great changes of joint locations in successive time steps. A changeable spatial partition is useful in contact dynamic problems, in the case of a travelling support, generally in problems with movable edges. In this paper a stability problem is described and some investigations for chosen types of non-rectangular space-time finite elements are carried out. Linear and surface elements which in time space gain an additional time dimension are presented. Some numerical examples prove the efficiency of the described method under determined limitations.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 659-661 
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    International Journal for Numerical Methods in Engineering 24 (1987) 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 679-687 
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    Notes: It is shown how the various norms of the coefficient matrix of a set of finite difference equations can, in many cases, be employed in an easy, straightforward fashion to find sufficient conditions for stability in situations involving non-periodic boundary conditions and variable coefficients. With the aid of the easily computed norms, particularly the infinite norm, one does not have to rely on the necessary condition provided by the spectral radius, which has been the main basis of criticism of the matrix method in the past.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 711-724 
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    Notes: Exactly integrated isoparametric plane stress elements behave poorly in flexure. The 4-noded element ‘locks’, with errors that progress indefinitely as element aspect ratio increases. Reduced integration of the shear strain energy eliminates this locking entirely. The 8-noded element does not lock, but improves in performance with reduced integration of shear strain energy. Both elements, with their original shape functions, show severe shear stress oscillations in flexure. In this paper we attribute these oscillations to the lack of ‘consistency’ of shear strain fields derived directly from independent field-variable interpolations. We derive error models for specific tractable examples which can confirm the accuracy of this conceptual scheme through digital computation using the finite element models. A field-consistent redistribution strategy for the shear strain field is offered as an elegant procedure to free the elements of spurious oscillations and give a ‘lock’-free performance.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 927-944 
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    Notes: Having established the non-uniqueness, in general, of quadratic-linear functionals in elasticity, the investigative work on this topic is reviewed, whence it is noted that there is no existing formal approach for the identification of either the causes of singular solutions or suitable remedial measures that might ensure their elimination. A comparison of the weighted averages obtained from the single field and Reissner's principles is then used to identify a higher order uniqueness criterion for the latter. A detailed consideration of the application of the new condition to the arch equations demonstrates how and why singular solutions can be obtained, and thence how suitable forms of remedial action can often be identified. Finally, several other classes of problem are briefly investigated in order to show how the criterion can be used to explain the full range of known behaviour of the mixed methods.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 2036-2036 
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    International Journal for Numerical Methods in Engineering 24 (1987) 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 2057-2070 
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    Notes: An officient preconditioned conjugate gradient (PCG) technique and a computational procedure are presented for the analysis of symmetric anisotropic structures. The technique is based on selecting the preconditioning matrix as the orthotropic part of the global stiffness matrix of the structure, with all the nonorthotropic terms set equal to zero. This particular choice of the preconditioning matrix results in reducing the size of the analysis model of the anisotropic structure to that of the corresponding orthotropic structure. The similarities between the proposed PCG technique and a reduction technique previously presented by the authors are identified and exploited to generate from the PCG technique direct measures for the sensitivity of the different response quantities to the non-orthotropic (anisotropic) material coefficients of the structure. The effectiveness of the PCG technique is demonstrated by means of a numerical example of an anisotropic cylindrical panel.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1232-1232 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1233-1250 
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    Notes: A system of algorithms is presented for the computer simulation of confined unsteady flows of a compressible fluid. The methods are valid for a wide range of time scales and are applied to simulate wind tunnel acoustics, flow over a ramp and flow past aircraft cavities.
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