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  • Chemical Engineering  (1,261)
  • Engineering  (920)
  • Wiley-Blackwell  (2,181)
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  • 1990-1994  (1,232)
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  • 1
    Electronic Resource
    Electronic Resource
    Polymer blend containing a thermotropic polyester with long flexible spacer in the main chain (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 22-29 
    Details
    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: Polymer blends of nylon 66 and thermotropic polyester with long flexible spacers in the main chains were prepared by melt mixing. The samples were made as single filaments by passing the polymer blend through a small and round die of a capillary rheometer. Mechanical properties of blends showed that the modulus and strength of nylon 66 could be improved without reduction of extensibility. The morphology of fractured surfaces was observed by a scanning electron microscope (SEM). It showed that the microfibrillar structure of a thermotropic polyester was formed by extensional flow while the spherical and ellipsoidal particles in the nylon 66 (matrix polymer) were produced by shear flow. The polyester particles were occasionally covered with adhering matrix polymer because of good adhesion between these two polymers. They were highly elongated by tensile stress without loss of elongational characteristics of blends. This fact was explained by very good adhesion between the two phases.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300105
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  • 2
    Electronic Resource
    Electronic Resource
    Gelation in thermosets formed by chain addition polymerization (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 83-89 
    Details
    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 physical behavior of the diglycidyl ether of bisphenol A, cured with different concentrations of 2-ethyl-4-methylimidazole, was examined with dynamic mechanical and dielectric analyses, differential scanning calorimetry, and solvent extraction studies, ‘The network formation process was shown to depend strongly on the imidazole concentration’. At high imidazole concentrations, the gel point was characterized by a decrease in sol fraction, the crossover of the dynamic moduli and a rapid increase in viscosity. At low imidazole concentrations, the viscosity remained low until the sol fraction approached zero. For this system, the gel point, which occurred prior to the dynamic moduli crossover, was characterized by comparing the thermal properties of the network with the viscosity and dielectric behavior of the resin system during cure.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300204
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  • 3
    Electronic Resource
    Electronic Resource
    Calculated stresses in dual coated optical fibers (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 108-117 
    Details
    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: We examine several practically important problems, related to the mechanical behavior of dual coated optical fibers: low temperature microbending, evaluation of spring constant due to coating layers, strength of the end portions of fibers clamped in terminal fixtures, and prediction of stresses caused by the misalignment of the openings in the frame and in the terminal fixture. The developed formulas are simple, easy-to-use, and clearly indicate the role of the major factors affecting the mechanical behavior of the fibers. The obtained results can be of help in physical design of dual coated fibers and optical interconnections.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300207
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  • 4
    Electronic Resource
    Electronic Resource
    Energy absorption characteristics of polymeric foams used as cushioning materials (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 129-133 
    Details
    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 “Efficiency of Energy Absorption” (or “Efficiency”) and “Ideality” parameters were evaluated for several plastic foams and were found to be very useful in choosing an appropriate cushion for the protection of a specific product. The maxima in these parameters were found to be in the same range of stresses, when derived from dynamic measurements or from predicted stress-strain curves based on previously proposed “Reference” and “Modified Boltzman Superposition” Models. For the rate independent foams the maxima in these parameters do not change with strain rate and can therefore be derived from slow, constant rate (“static”) experiments. For rate dependent foams however, the maxima from “static” measurements were found to be in a lower range of stresses than those derived from dynamic ones. As a result, slow rate compressive measurements do not predict well the behavior of the foams during impact and the use of the “Reference” and “Modified Boltzman Superposition” Models is required for good predictions. It was found that the suffer PS and PE foams attain maximum Efficiency and Ideality at higher stresses than the more flexible PUR foams.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300210
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  • 5
    Electronic Resource
    Electronic Resource
    Transition mechanism from elastic deformation to plastic flow in poly(methyl methacrylate) (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 96-107 
    Details
    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: Sudden changes of compressive strain-rate on glassy poly(methyl methacrylate) lead to the conclusion that the post-yield state under a constant stress is a state of steady flow in the polymer. Non-linearity between the stress divided by temperature and the logarithm of strain rate for this steady plastic flow can successfully be analyzed using the Eyring equation with structural factors variable depending on stress and temperature. This analysis gives a unique functional relationship between the activation entropy and the activation enthalpy, which agrees fairly well with that for the melt derived from the WLF equation. This agreement provides a direct evidence verifying structural change of the glass into liquid-like structure and enables us to recognize the conformational arrangement as an essential structural parameter controlling molecular mobility. Another experimental relation between the Eyring factors - the activation volume and the activation enthalpy - permits us to estimate the magnitude of an elementary volume for the molecular movement in the melt as a function of temperature. Moreover, the experimental finding of the steady flow in the glassy polymer motivated us to propose a transition mechanism from elastic deformation to plastic flow in which the internal viscosity or the activation volume is introduced as a single parameter representing the transient state of the structure.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300206
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  • 6
    Electronic Resource
    Electronic Resource
    Experimental modeling of solvent-casting thin polymer films (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 118-123 
    Details
    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: An apparatus was designed and assembled to study the solvent removal from solution-cast thin polymer films. The computer interfacing of a thermogravimetric analyzer, spectrophotometer, electronic flowmeters, and control valves for the apparatus enabled the preprogramming of the carrier gas velocity, carrier gas solvent content, and temperature profiles to simulate the environment experienced in large parallel flow industrial driers. The apparatus has also been designed and operated to enable the visual observation of the drying film with an optical microscope. Initial experimental studies conducted with the apparatus involved the effect of temperature on solvent removal. The results indicate that high dryer gas temperatures can apparently cause skinning of the film surface resulting in slower solvent removal rates. The skin formation can be suppressed by higher solvent concentration in the carrier gas. The visual observations revealed the formation of standing waves in the film surface during drying at high gas velocities (〉2OO cm/min). The wave formation at least partially overcomes the effect of skinning by increasing the surface area of the film, and may be the manifestation of flow instabilities involving circulation within the film.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300208
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  • 7
    Electronic Resource
    Electronic Resource
    Ultrasonic processing of thermoplastic foam (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 147-152 
    Details
    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: Ultrasonically induced bubble formation for the production of thermoplastic foam was investigated experimentally and theoretically as a basic study. A general purpose polystyrene and blends of low density polyethylene and polyethylene wax were saturated with nitrogen gas under various pressures and the ultrasonic excitation was applied to the polymer system upon release of gas pressure. The ultrasonic nucleation of bubbles in the polymer matrix was modeled by utilizing the classical nucleation theory. The negative pressure generated by the ultrasonic excitation was considered as the environmental pressure at the moment of nucleation. The experimental results showed that the heterogeneous nucleation must be used for ultrasonic foaming of the viscous fluid and the homogeneous nucleation for the low viscosity fluid. The theoretical analysis also indicated that the ultrasonic nucleation can be applied to the production of thermoplastic foam if the ultrasonic excitation generates large enough negative pressure.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300304
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  • 8
    Electronic Resource
    Electronic Resource
    Rheology-morphology relationships in nylon 6/liquid-crystalline polymer blends (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 7-12 
    Details
    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: Extrusion measurements have been carried out on blends of nylon 6 and a liquid-crystalline copolyesteramide (LCP). The flow curves at low temperature show a behavior similar to that of pure LCP with a rapid rise of the viscosity at low shear rates. At high shear rates the viscosity is lower than that for each of the two components. This minimum has been attributed to the lack of interactions between the two phases and to the formation of fibrils of the LCP phase. The SEM analysis shows, indeed, that fibrils of the LCP phase are produced in the convergent flow at the inlet of the capillary at high shear rates. These fibrils are lost during the flow in the long capillary.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300103
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  • 9
    Electronic Resource
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    Rheological properties of a liquid crystalline copolyester (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 124-128 
    Details
    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: Rheological studies of an experimental liquid crystalline (LC) copolyester were carried out using a capillary rheometer and a cone and plate rheometer. Rheological characteristics of the polymer in the nematic state were observed. The nematic melt was found to be pseudoplastic and the degree of pseudoplasticity varied with shear rate. Melt viscosity was found to decrease with shear rate. Negative die swelling was observed at the exit of the capillary rheometer at temperatures marginally above the solid-nematic transition temperature of the polymer and was also found to be a function of shear rate. The dynamic mechanical properties of the polymer were studied as a function of temperature. The activation energies of flow and of dynamic mechanical deformation were calculated.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/pen.760300209
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  • 10
    Electronic Resource
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    Enhancing adhesion by ion beam-induced atomic mixing at the interface between copper film and polyimide substrate (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 137-141 
    Details
    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: Ion beam mixing was used to improve the adhesion between deposited Cu film (400 Å) and polyimide (PI) substrate. Ar+ ion with the energy levels between 180 and 200 keV, and the dose between 1014 to 4 × 1016 ions/cm2 were used. The surface analyses were carried out by Rutherford Backscattering Spectroscopy (SEM). RBS analysis, using 2 MeV He+ ions, showed mixing of Cu and FI and the mixing depended on the Ar+ energy and dose. The X-ray study showed a very broad halo for deposited Cu film but the (111) peak appeared after the Ar+ implantation and the peak increased with Ar+ ion dose. Optical micrographs showed that Cu film formed circular bubbles after many thermal cycles when adhesion was poor and fracture cracks when adhesion was good.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/pen.760300302
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  • 11
    Electronic Resource
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    Measures of mixing in laminar flow (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 153-161 
    Details
    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 general domain in which this work resides is that of mixing in creeping flows. Mixing, in this context, refers to the stretch of an interfacial line, or area in a strain field. The advancement of mixing technology is applied to the design of continuous mixers used in polymer processing. The geometric designs included single screw extruders, static motionless mixers, and co- and counter-rotating twin screw extruders. The co-rotating twin screw extruder was chosen to be studied in detail since it enjoys wide applications and, for which, little understanding of the contribution to mixing in the different screw geometries is known. In order to evaluate the rate of mixing for the non-uniform strain history flows, the method for measuring mixing had to be reexamined and broadened. An automated method has been developed which incorporates a digital camera and a computer to analyze the cross-sections of interest. Two measures of mixing - the correlation function and the distribution function - are developed to describe mixing in these regimes. These measures are applied successfully to the mixer geometries revealing subtle differences as to the nature of mixing in each.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300305
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  • 12
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    Rotary injection reaction injection molding (RI-RIM). Part II: Interfacial segregation of release systems (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 175-186 
    Details
    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: This paper describes the shear imposed interfacial segregation of release systems for the facilitated attenuation of polyurethane (PU) adhesion to metal coun-terfaces using a RI-RIM system. It is shown that the migration rate of the dispersed release additives due to a shear imposed stress in the resin fluid is much greater than that arising from Fickian diffusion, thereby removing a vital constraint from conventional practice. The novel rotary injection RIM system is presented to simulate the on-line injection and shear induced interfacial segregation in model PU/abherent systems. A wide range of recipes comprising single (liquids or solids) and multicomponent (liquid-liquid and solid-liquid) release materials were injected into the polymerizing resin mixture to provide cohesively weak and friable “particle” boundary layer assemblies at the PU/metal interface. An instrumented Blister Test was employed to evaluate the quality of the molded interfaces in terms of adhesion and the concentration distribution of the injected species in the final cured moldings was determined through high pressure liquid chromatography (HPLC). A comparison of the results on the shear modified and the compounded interfaces confirm an accentuated lateral migration of the additives to the interface resulting in an appreciable diminution in the adhesion of the system. Finally, transport models are suggested to account for the observed augmented transport.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/pen.760300307
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  • 13
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    Masthead (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990) 
    Details
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760300401
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  • 14
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    Mechanical properties and behavior of open cell foams used as cushioning materialsFirst part appeared in Polymer Engineering & science, Jan. 1990, 30, 129. (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 197-201 
    Details
    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: It is the purpose of the present publication to show that most of the phenomenological viscoelastic theories developed for bulk polymers can be readily adapted to plastic foams in order to evaluate their mechanical properties. In addition it will be demonstrated how the mechanical properties of open cell plastic foams can be predicted from a few simple compression and relaxation experiments.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/pen.760300402
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  • 15
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    The plane-strain essential work of fracture as a measure of the fracture toughness of ductile polymers (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 211-218 
    Details
    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: We have extended the essential work of fracture technique to allow for the determination of the plane-strain essential work of fracture. The new technique is to measure the specific work of fracture as a function of ligament length in deeply double edge notched samples. This type of data is then experimentally corrected to remove the plastic work of fracture and leave only the essential work of fracture as a function of ligament length. By extrapolating the essential work of fracture to zero-ligament length, we claim to be measuring the plane-strain essential work of fracture. This new technique was applied to two rubber toughened nylons and to a series of polyethylenes. The plane-strain essential work of fracture was found to be independent of thickness. Where comparison can be made to J-integral testing, the plane-strain essential work of fracture was similar to the critical J-integral, JIc.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/pen.760300404
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  • 16
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    Liquid crystal polymer-carbon fiber composites. Molecular orientation (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 228-234 
    Details
    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 objective of this work has been to study composite systems in which carbon fibers are dispersed in a liquid crystal polymer matrix. The fundamental point of interest here has been the interfacial response that fiber surfaces can potentially induce in self-ordering polymers. The matrix material used was a thermotropic liquid crystal polyester synthesized in our laboratory from the monomers p-acetoxybenzoic acid, diacetoxyhydroquinone, and pimelic acid. The aromatic-aliphatic polymer was characterized by NMR as a chemically disordered polymer of the three structural units which exhibits a nematic phase at temperatures above 150°C. Breadline proton NMR above the solid to liquid crystal transition was used to measure the rate of magnetic alignment of molecules in the matrix and polarized optical microscopy was used to analyze interfacial zones in composite samples. Fiber surfaces were found to influence the orientation and orientational dynamics of a liquid crystal polymer matrix. This was revealed by enhanced rates of magnetic orientation in the polymer melt when carbon fibers are dispersed in the medium. Fiber surfaces were also found to stabilize nematic ordering of the polymer as the melt was heated towards complete isotropization. The phenomena discovered here may originate in the development of zones around fibers with a common molecular orientation anchored by the carbon surface.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/pen.760300406
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  • 17
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    Impact fracture toughness tests on polymers (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 241-248 
    Details
    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 series of impact tests are described in which the plane strain fracture toughness, Kc1, of five different polymers is measured using a three point bend specimen at striker speeds up to 5m/s. At low speeds Kc1 is determined using the maximum load and a static analysis, but at speeds greater than 1 m/s the dynamic effects render the load signal unusable. For the higher speeds the fracture is timed using contact and crack propagation gages and the analysis is performed using the striker displacement at fracture. A dynamic analysis is used to convert this measurement to the true specimen displacement and Kc1 is determined from this. The apparent downward trends in the Kc1 results obtained, especially at speeds above 3m/s, are discussed.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/pen.760300408
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  • 18
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    Masthead (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200101
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  • 19
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    Numerically efficient procedures for dynamic contact problems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1-14 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of dynamic contact (elastic impact) problems is complicated by the changing nature of the contact area. If a finite element approach is used, the system matrices vary with the contact area. If the problem is properly formulated, such changes are rank one. Rank one changes produce easily determinable changes in the LDLT decompositions of the system matrices. This renders a class of dynamic contact problems soluble with the same accuracy and computational effort as is associated with the solution of any dynamic problem using finite element procedures. Consideration of an example problem involving the impact of spring-mass systems confirms this claim.
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    URL: http://dx.doi.org/10.1002/nme.1620200102
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  • 20
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    A Taylor-Galerkin method for convective transport problems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 101-119 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions. To produce accurate temporal differencing, the method employs forward-time Taylor series expansions including time derivatives of second- and third-order which are evaluated from the governing partial differential equation. This yields a generalized time-discretized equation which is successively discretized in space by means of the standard Bubnov-Galerkin finite element method. The technique is illustrated first in one space dimension. With linear elements and Euler, leap-frog and Crank-Nicolson time stepping, several interesting relations with standard Galerkin and recently developed Petrov-Galerkin methods emerge and the new Taylor-Galerkin schemes are found to exhibit particularly high phase-accuracy with minimal numerical damping. The method is successively extended to deal with variable coefficient problems and multi-dimensional situations.
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    URL: http://dx.doi.org/10.1002/nme.1620200108
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  • 21
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    A note on symmetry considerations in the transient response of unsymmetrically laminated anisotropic plates (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 175-181 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620200113
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  • 22
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    Asymmetric bending of axisymmetric shells (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 169-173 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A two-noded, straight element with one-point quadrature is introduced for the unsymmetrical bending of orthotropic axisymmetric shells. The numerical results indicate that the present simple element performs accurately for both thick and thin shell applications.
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    A comment on the effectiveness of uniform finite element refinements (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 187-194 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical results using uniform h-refinement approaches to the solution of a pair of elasticity problems with singularities are presented and compared to recently published results based on the uniform p-refinement approaches.
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    Numerical solutions to some free surface flows through nonhomogeneous media (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 143-167 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Steady-state, free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique. The problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel. These ponds and channels may have variable shaped bottoms. Since the Baiocchi transformation was used to define a new dependent variable, the form of the permeability function was restricted to a product of functions of the independent variables. Herein the permeability was chosen to be a function of the depth only. For certain forms of this function, namely those having negative gradients, part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory. The governing differential equation, which holds in the sense of distributions, is derived for a fixed solution domain and a simple algorithm (a finite difference successive over-relaxation scheme with projection) is given to obtain the solution to these free surface problems. Numerous comparisons are made with published results. Rigorous mathematical justification of the methods used herein can be found in the references cited.
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    Announcements (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 195-195 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200201
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    Chebyshev filtering Lanczos' process in the subspace iteration method (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 182-186 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Bathe's basic algorithm of subspace iteration for the solution of the symmetric eigenvalue problem is improved by including a Chebyshev filtering mechanism. To obtain satisfactory convergence for the largest eigenvalues, a shifting strategy is adopted. The shift factor is approximately computed by the Lanczos process.
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    Deflection of thick beams of multimodular materials (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 479-503 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A transfer-matrix analysis is presented for determining the static behaviour of thick beams of ‘multimodular materials’ (i.e. materials which have different elastic behaviour in tension and compression, with nonlinear stress-strain curves approximated as piecewise linear, with four or more segments). To validate the transfer-matrix method results, a closed-form solution is also presented for cases in which the neutral-surface location is constant along the beam axis. Numerical results for axial displacement, transverse deflection, bending slope, bending moment, transverse shear, axial force and location of neutral surface are presented for multimodular and bimodular models of unidirectional aramid cordrubber. The transfer-matrix method results agree very well with the closed-form solutions.
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    An 8-node brick finite element (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 523-528 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An 8-node brick element based on the assumed stress hybrid formulation is described. With three additional stress fields, the element stiffness matrix now has the required rank of 18, and the ‘bending’ response is exact with rectangular elements. Surprisingly, the 2 × 2 × 2 Gauss rule suffices for all numerical integrations, to satisfy the constant stress patch test.
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    An assumed stress hybrid curvilinear triangular finite element for plate bending (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 529-548 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An assumed stress hybrid curvilinear triangular finite element is described which is based upon the Kirchhoff theory of plate bending. The derivation extends the assumed stress hybrid technique to curvilinear boundaries where the twelve connectors are related to those of an equilibrium rectilinear element and to Semiloof. The solution process demands only first derivatives of the shape functions.The element is subjected to various patch tests for constant bending, e.g. where the central element is in close approximation to a circle. All tests are passed for stress couples and vertex displacements, but values of the remaining connectors do not resemble exact results. Patch tests for rigid-body movements are passed exactly in every respect.
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    Numerical solution of a parabolic system with coupled nonlinear boundary conditions (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 505-514 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A numerical technique has been developed to solve a system that consists of m linear parabolic differential equations with coupled nonlinear boundary conditions. Such a system may represent chemical reactions, chemical lasers and diffusion problems. An implicit finite difference scheme is adopted to discretize the problem, and the resulting system of equations is solved by a novel technique that is a modification of the cyclic odd-even reduction and factorization (CORF) algorithm. At each time level, the system of equations is first reduced to m nonlinear algebraic equations that involve only the m unknown grid points on the nonlinear boundary. Newton's method is used to determine these m unknowns, and the corresponding Jacobian matrix can be computed and updated easily. After convergence is achieved, the remaining unknowns are solved directly. The efficiency of this technique is illustrated by the numerical computations of two examples previously solved by the cubic spline Galerkin method.
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    The maximum principle for bilinear elements (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 549-553 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: It is demonstrated that finite element discretizations may not, in general, satisfy the maximum principle; and sufficient conditions are presented to guarantee that solutions based on bilinear elements do satisfy the maximum principle.
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    On the efficiency and accuracy of the boundary element method and the finite element method (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 515-522 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper. This comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods.
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    Economy and convergence of notch stress analysis using boundary and finite element methods (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 565-572 
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    Notes: The BEM is shown to be superior to FEM with respect to economy (man hour and data processing) and convergence (with increasing number of boundary nodes) in the elasic notch stress analysis of compact components.
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    A note on discontinuous numerical solutions of the kinematic wave motion (1984)
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 555-563 
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    Notes: This note discusses the numerical solution of the kinematic wave equation under those conditions when the solution contains a discontinuous shock. A finite element solution is described in which shocks are represented by discrete nodal discontinuities. The implementation of the method follows conventional finite element practice over the shockless regions of the solution domain which are coupled by frontal constraints. The basis of the method and examples of its application to the solution of the kinematic wave equation in one and two dimensions are presented.
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    Formulation methods of geometric and material nonlinearity problems (1984)
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 887-914 
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    Notes: A concise survey of formulation methods of geometric and material nonlinearity problems is given. Differences between existing formulations in the literature are discussed. A consistent Lagrangian and updated Lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration. Differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. Specific forms of constitutive equations for elastic and elastoplastic materials are presented. Some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent. Sample numerical examples intended for checking some particular points in the formulation are presented.
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    Two high-order numerical methods for solving boundary-value nonlinear ordinary differential equations (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 845-849 
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    Keywords: Engineering ; Engineering General
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    Notes: Two numerical methods for solving two-point boundary-value problems associated with systems of first-order nonlinear ordinary differential equations are described. The first method, which is based on Lobatto quadrature, requires four internal function evaluations for each subinterval. It does not need derivatives and is of order h7, where h is the space chop. The second method, which is similar to the first but is based on Lobatto-Hermite quadrature, makes the additional use of derivatives to achieve O(h9) accuracy. Results of computational experiments comparing these methods with other known methods are given.
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    Optimization for vibration isolation (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 915-929 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An almost linear optimization problem of importance in vibration isolation has been identified and algorithms were developed to minimize the forced vibrational response of structural systems. The constraints can be either displacements or accelerations. These algorithms have been studied for transient response, frequency response and stationary random using the direct dynamic solution. Multiple response points and loading conditions may be used.
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    A robust incomplete Choleski-conjugate gradient algorithm (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 949-966 
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    Notes: When applied to large sparse sets of simultaneous equations, classical iterative methods may yield very poor convergence rates. This paper gives an incomplete Choleski-conjugate gradient algorithm (ICCG) which has reliably good convergence rates at the expense of computing and using at each iteration an incomplete Choleski factor of the coefficient matrix. The method is applicable to any problems in which the coefficient matrix is symmetric positive definite and is likely to be advantageous with respect to elimination when it is not possible to represent the equations in a dense band form.
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    Efficient linear and nonlinear heat conduction with a quadrilateral element (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 931-948 
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    Keywords: Engineering ; Engineering General
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    Notes: A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
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    Implementation of an improved bisection algorithm in buckling problems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 979-979 
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    Keywords: Engineering ; Engineering General
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    Physical property algorithms. J. F. Stelzer, Karl Thiemig AG, Publ. 1984. ISBN 3-521-06144-2. (pbk.) No. of pages: 501. Price: 68 D.M. (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 980-980 
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    Keywords: Engineering ; Engineering General
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    Double noding technique for mixed mode crack propagation studies (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 967-977 
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    Keywords: Engineering ; Engineering General
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    Notes: A simple dynamic finite element algorithm for analysing a propagating mixed mode crack tip is presented. A double noding technique, which can be easily incorporated into existing dynamic finite element codes, is used together with a corrected Ĵ integral to extract modes I and II dynamic stress intensity factors of a propagating crack. The utility of the procedure is demonstrated by analysing test problems involving a mode I central crack propagating in a plate subjected to uniaxial tension, a stationary slanted central crack in a plate subjected to uniaxial inpact loading and an extending slanted-edge crack in plate subjected to uniaxial tension.
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    Conference diary (1984)
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1370-1371 
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    Keywords: Engineering ; Engineering General
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    Numerical formulation for a higher order plane finite dynamic element (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1407-1414 
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    Keywords: Engineering ; Engineering General
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    Notes: The paper describes the development of an eight-node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices. Numerical test results of free vibration analyses are presented in detail for the newly developed eight-node element and also the corresponding four-node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures. Such results indicate a superior pattern of solution convergence of the presently developed dynamic element.
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    An iterative approach for the evaluation of delamination stresses in laminated composites (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1415-1431 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational strategy for the evaluation of delamination stresses in multilayered fibre-reinforced composites is presented. The approach uses special inter-laminar shear elements and an iterative procedure in the calculation of out-of-plane stresses. Both regular and singular elements for the free edge are presented. The solutions are carried on by switching between direct matrix solution methods of small systems of equations and an iterative conjugate gradient method. The proposed discretization avoids ill-conditioning problems, modelling difficulties and large computational cost associated with three-dimensional analysis of delamination of holes, cut-outs, joints and areas of complex stress states.
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    A consistent and accurate procedure for obtaining difference equations from differential equations (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1433-1441 
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    Keywords: Engineering ; Engineering General
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    Notes: A general, consistent and accurate procedure for obtaining difference equations from differential equations is presented and illustrated by several examples. The procedure is an extension of the integral method and incorporates what is known of the solution to the differential equation in the formation of the corresponding difference equation. For the same accuracy, large increases in grid size over that obtained by standard Taylor's series approximations are possible. Both boundary-value and initial-value problems are treated.
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    An improved isoparametric transformation for finite element analysis (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1443-1459 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The standard isoparametric transformation for finite element analysis is shown to be only a special case of a more general transformation which allows for flexibility in locating side and interior element nodes. Side nodes positioned at the same relative distance from corner nodes in both local and global space, and interior nodes positioned such that they do not affect the Jacobian of the co-ordinate transformation, provide improved accuracy over nodes positioned locally without regard for the global configuration. This concept is demonstrated in the context of two-dimensional quadratic quadrilateral isoparametrics, but is also applicable to higher orders and dimensions. In the test cases examined, the new formulation provides a reduction in error of up to three orders of magnitude and also provides accurate solutions for nodal placements which are not allowed using the standard transformations.
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    An improved explicit finite element method for tidal flow (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1461-1475 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A weighting function by which the mass matrix is made to be diagonal is deduced on the two-dimensional simplex element. Adopting the weighted residual method with the deduced weighting function for spatial domain and the two-step Lax-Wendroff method for time differentiation, the two-dimensinoal tidal flow in a model basin is calculated by means of the explicit finite element method. The water mass transport integrated over one tidal period at some cross-sections of the basin is also estimated, in order to verify the water mass conservation. It is found that the water mass is nearly conserved in the present method, although the usual lumped mass matrix technique fails to conserve.The present explicit finite element method with the conservative form of governing equations is also investigated and the water mass conservation is found to be a little more improved in this case than in the case of non-conservative forms. Application to a real bay indicates that the method with the conservative form of equations could be used for the estimation of tidal residual flow.
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    Incremental elastoplastic stiffness matrix for materials obeying the principal stress yield criterion (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1477-1489 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work, the plastic stress-strain relation and the incremental elastoplastic stiffness matrix for materials obeying the principal stress yield criterion are derived in the context of the associated theory of plasticity. Particular attention is paid to the treatment of the singularity conditions associated with this yield criterion.
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    The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1491-1506 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is demonstrated that the residual in a compatible (displacement) finite element solution can be partitioned into local self-equilibrating systems on each element. An a posteriori error analysis is then based on a complementary approach and examples indicate that the guaranteed upper bound on the energy of the error is preserved.
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    Numerical laplace transformation and inversion in the analysis of physical systems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1507-1519 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper develops a new discrete transform pair which economizes on the number of samples of F(s) and f(t) compared with the standard pair. Whereas the standard pair used uniform sampling along the Bromwich contour, the new method allows a progressive increase in the sampling interval, thereby reducing the number of samples required to meet a specified bandwidth requirement. In the case of the computation of transient responses of physical systems, a reduction by a factor of 10 is not unrealistic. The new transform pair is based on the generalization of fundamental sampling principles. In particular, this leads to an integration contour different from the Bromwich contour.
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    A note on ‘a two-step approach to finite element ordering’ (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1553-1554 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200815
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    Partitioned rational Runge Kutta for parabolic systems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1581-1597 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new family of coupled time integration operators of different orders is developed. It permits different time integration operators to be used simultaneously in various regions of the model. This approach has the advantage of applying a very accurate time integrator, such as Runge Kutta method of order two to four, to the local nonlinear region of interest and a simple time integrator, such as the implicit-explicit or mixed time implicit-explicit method of order one, for the remaining region. The computer implementation aspects, stability analysis as well as the numerical evaluations of these new methods are presented. This is another attractive addition to the repertoire of time integration methods.
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    A finite element analysis of metal-forming problems with an elastic-viscoplastic material model (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1613-1628 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for elastoviscoplasticity problems in the presence of large strains and deformations is presented in this paper. The formulation is capable of using any of a class of combined creep-plasticity constitutive models with state variables for the description of material behaviour. The specific problem considered is plane strain extrusion using the constitutive model originally proposed by Hart. Numerical results are presented for sample problems and the important effects of extrusion speed and friction (at the die-workpiece interface) on the residual stresses in an extruded sample are investigated. The computer program developed here is quite general and can be modified to solve problems for other manufacturing processes like rolling, sheet forming, etc.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620200906
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    A direct search package for unconstrained minimization (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1643-1660 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new direct search package is presented. Typical test functions solved establish the robustness and efficiency of the package. The most significant features of the package are that it works satisfactorily even in single precision and requires much less memory. It needs only the function values and the unidimensional search is totally dispensed with. Methods such as different descent techniques, the RMS procedure, the co-ordinate movement technique and the gallop-canter equalization scheme form the sequence of strategies.
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    Numerical evaluation of the quarter-point crack tip element (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1629-1641 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper attempts to answer two commonly raised questions during the preparation of a finite element mesh, for the linear elastic fracture analysis of cracked structure: how to set up the finite element mesh around the crack tip, and what level of accuracy is to be expected from such a modelling.Two test problems, with known analytical expressions for their stress intensity factors, are analysed by the finite element method using the isoparametric quadratic singular element. The modified parameters were the order of integration, aspect ratio, number of elements surrounding the crack tip, use of transition elements, the singular element length over the total crack length, the symmetry of the mesh around the crack tip. Based on these analyses, a data base is created and various plots produced. The results are interpreted, the accuracy evaluated and recommendations drawn.Contrary to previous reports, it is found that the computed stress intensity factor (SIF) remains within engineering accuracy (10 per cent) throughout a large range of l/a (singular element length over crack length) for problems with a uniform non-singular stress distribution ahead of the crack tip (i.e. double edge notch), and l/a should be less than 0·1 for problems with a non-singular stress gradient (i.e three-point bend). Also, it is found that the best results are achieved by using at least four singular elements around the crack tip, with their internal angles around 45 degrees, and a reduced (2 × 2) numerical integration.
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    Structural design sensitivity analysis with general boundary conditions: Static problem (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1661-1670 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents and analyses methods for design sensitivity analysis of static response for structural systems when general boundary conditions are used during the analysis phase. The design sensitivity analysis methods where the boundary conditions are used to reduce the equilibrium equation have been presented earlier. In such procedures, the reduced stiffness matrix is non-singular. This fact is used to show differentiability of the displacement vector. When reduction procedures are not used, the global structural stiffness matrix may be singular. In such a case, differentiability of the displacement vector may be questionable. However, it is shown that the displacement vector is still differentiable. Several forms of the structural design sensitivity equations are presented. Although these equations are derived with Lagrange multiplier treatment of general boundary conditions, it is shown that they are applicable with any treatment of general boundary conditions. For example, they can also be used with co-ordinate reduction schemes. Therefore, design sensitivity analysis can be carried out with any existing finite element analysis computer code. Moreover, the procedures presented can be used to calculate sensitivity of a force of constraint can that is desired. The formulations are kept quite general such that design dependent boundary conditions can be routinely treated. An example is used to illustrate the procedures.
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    An efficient zooming method for finite element analysis (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1671-1683 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an efficient, exact zooming technique is developed which employs static condensation and exact structural reanalysis methods. For a multiple level of zooming such that the successive level of zooming is contained within the prior levels of zoom, repeated application of static condensation will reduce the system to one that is associated only with the degrees-of-freedom (dof) of the original model. Then, application of an exact static reanalysis technique permits the displacements at the dof of the original model that are contained in the final zoomed portion of the structure to be obtained first. Next, the response external to the zoom, as well as the response of additional dof within various levels of zooming, can be computed. With the triangular factor of the stiffness matrix of the original system available, this approach involves only the solution of a system of equations of small order. The proposed method is demonstrated by a numerical example.
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    The numerical treatment of laplace transforms: I. The Koizumi inversion method (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1697-1702 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An inversion formula based on expansion in a Fourier sine series, proposed by Koizumi in 1935, is examined. It is found to give results of moderate accuracy with relatively little work.
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    Rational approach for assumed stress finite elements (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1685-1695 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.
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    On the computational significance of the strain space formulation of plasticity theory (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1703-1709 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The strain space and traditional stress space formulations of plasticity theory are compared. We show how plasticity theory has been implemented numerically to solve static and dynamic problems, and conclude that the numerical loading criteria that have been used for two decades are identical to the strain space loading criteria proposed by Naghdi and co-workers.
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    Animating structure plots: Experiments with a PERQ (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1729-1733 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A PERQ single user computer can be used to animate structure plots, which is of great assistance when interpreting the results from finite element programs. Excellent appreciation may be obtained of a structure oscillating in complicated natural modes. The technique is also useful for studying deformations due to static forces.
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    Finite element criteria for some shells (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1711-1728 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Simple solutions are extracted from the exact compatibility equations of inextensional bending for a special class of shell shapes, and it is speculated that these solutions provide useful criteria towards evaluating finite elements for these and closely related shapes. Curved finite elements of a quadratic parametric representation, which do not belong to the special class, are then studied. By using a series of exact inextensional bending displacements, it is concluded from numerical evidence that the criteria apply to finite element shapes in this representation when they are shallow, as is usually the case in practice. Criteria for homogeneous membrane actions follow from Gol'denveizer's static-geometric analogue.
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    A partial-boundary element approach to the elastic torsion problem of a prismatic beam with a cracked rectangular cross-section (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1745-1749 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Using the partial-boundary element approach, in which only a part of the boundary in problem is discretized, the elastic torsion problem of a prismatic beam of a cracked rectangular cross-section has been solved in this brief paper, together with a numerical example to show the accuracy and versatility of the approach.
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    An effective finite element approach for calculation of potential distribution in a multi-dielectric cable (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1751-1755 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The radial symmetry of the cable results in circular finite elements to evaluate the potential distribution in a multi-dielectric cable. Owing to this, a two dimensional analysis used in conjunction with triangular finite elements is reduced to one-dimensional analysis. This method therefore suggests an alternative proposal to calculate the potential distribution in a multi-dielectric cable with better accuracy.
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    Comment on the paper: ‘An implementation of the boundary element method for zoned media with stress discountinuities’ (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1756-1756 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Linear analysis of frameworks, T. R. Graves Smith, Ellis Horwood Series in Engineering Science, 1983. No. of pages: 451 (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1757-1757 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Mechanics of continuous media, S. C. Hunter, Ellis Horwood, Chichester, 1983. Price: £32.50 (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1757-1758 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620200920
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    Announcements (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1758-1759 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201001
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    Use of minimum surface theory to aid finite element contour plotting (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1791-1796 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Contour plots of finite element solutions, especially for derivatives, often are discarded due to poor plotting algorithms. This note shows how a smoothing scheme based on a minimum surface theory can significantly improve the quality of the graphical results. The scheme proposed is compared with many other smoothing schemes, including least squares, on a simple problem.
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    An automated design scheme: Weight minimization of a single hulled ship compartment (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1763-1790 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the stages of development of an optimum structural design scheme. Any attempt to generate the optimum scantlings of a structure of even moderate complexity usually poses nonlinear programming problems for which there exist no universally accepted solution method. The structure considered here is a complete compartment of a single-hulled ship acted upon by multiple load cases. The elastic responses under four different load types are obtained by a quasi finite element analysis routine developed specifically for this purpose. Sequential linear programming (SLP) with appropriate artifices to achieve rapid convergence has been successfully employed as an optimization routine to minimize the object function, which in this case was the total weight of the major structural members. The test problem has 490 basic degrees-of-freedom, 21 free design variables and more than 100 mixed constraints, the majority of which are nonlinear implicit stress functions. The method is then applied to a number of cases representative of small warship designs. Suggestions for future extensions and general conclusions are included at the end of the paper.
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    Transformation of dependent variable in the finite element solution of some phase change problems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1815-1821 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The approach of Cermak and Zlamal1 for solving quasilinear parabolic equations is modified and improved. The modified approach leads to a normal system of ODE, which may be solved with a standard program. The numerical solution of a specially selected example is compared with the exact solution. The method is applied on a system of quasilinear parabolic equations, which describes a real process - crystallization of a metal ingot.
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    The design of a variable-step integrator for the simulation of gas transmission networks (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1797-1813 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The simulation of a large-scale gas transmission network involves the numerical solution of a large system of initial valued, stiff algebraic/differential equations. Rapid changes in the solution are present due to the disturbances generated by the varying consumer demand and the operation of network controlling devices such as compressors. This paper discusses the design of an efficient variable-step integrator for the solution of the problem. Two sets of strategies are presented for implementing the variable-step integrator; one for the implicit numerical method such as the diagonally implicit Runge-Kutta methods, and the other for the linearly implicit Rosenbrock-type method. The performance of the numerical methods implemented are compared with the British Gas simulation program PAN on a number of large, realistic transmission networks.
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    Optimal shape remodelling of linearly elastic plates using finite element methods (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1823-1840 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The optimality conditions for the optimal shape remodelling of linearly elastic plates are obtained by introducing the total variation of a function defined on a variable domain, although the variation of a function has been taken on a fixed domain in most literature on calculus of variations. Using these optimality conditions, a solution scheme involving an iterative algorithm is proposed, together with several numerical examples.
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    A statically determinate truss model for thin shells: Two-surface analysis (bending theory) (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1863-1884 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a simple scheme for analysing shells subject to the Kirchhoff-Love hypothesis. The method combines a previously developed, statically determinate truss model with the static-geometric analogy of elastic thin shell theory. In this way, both in-plane and flexural mid-surface actions are obtained by simply repeating the elementary computations performed on an essentially ‘membrane’ truss.
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    A statically determinate truss model for thin shells: One-surface analysis (membrane hypothesis) (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1841-1861 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the modelling of open shells, such as those used in roof construction, by means of a single-layered, pin-jointed truss. The latter exhibits several advantages over existing framework models, such as, for example, statical determinacy and the capacity to cope with arbitrary material constants. In the present article, the truss model is developed for and applied to the numerical analysis of shells subject to the membrane hypothesis. However, the same statically determinate model forms the basis for a computational scheme for analysing shells according to the more formal, statically indeterminate bending theory; the latter application of the truss model will be presented in a subsequent paper.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201007
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    Galerkin finite element methods for parabolic problems, in lecture notes in mathematics, Vidar Thomée, Springer, Berlin, 1984 (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1951-1952 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201015
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    Fundamlntals of soil dynamics, B. M. Das, Elsevier Science Publishing Co., New York, 1983. No. of pages: 399. Price: $32.50 (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1952-1952 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201016
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    Conference diary (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1957-1958 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201018
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    Announcements (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1953-1956 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201017
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    Masthead (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201101
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    Substructure condensation using modified decomposition (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1959-1964 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for static condensation is presented. This method utilizes Choleski decomposition with some modification to obtain the effective stiffness matrix and the effective load vector. A comparison between this modified decomposition method and the usual matrix decomposition method shows that the former is more efficient than the latter.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201102
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    Automatic three-dimensional mesh generation by the modified-octree technique (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1965-1990 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approach for the fully automatic generation of three-dimensional finite element meshes is presented. The method is specifically designed for use with solid modelling systems which provide a complete and unique definition of the geometry of a part. The method follows from the basic concepts of the octree encoding technique with specific modifications made to produce valid, user controllable finite element meshes. Example problems are included to demonstrate the technique.
    Additional Material: 24 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201103
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    A combination of the finite element and singular-integral equation methods for the solution of the generally cracked body (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 2065-2075 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method which combines the finite element technique and the singular-integral equation method is presented. The association of the two methods is obtained with the help of Schwarz's alternating method (SAM). The method was applied with satisfactory results to the solution of a series of problems of a circular arc crack lying inside a finite thin plate for various lengths of the circular arc and for various dimensions of the rectangular cracked sheet.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201109
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    Masthead (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201201
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    A new 48 d.o.f. quadrilateral shell element with variable-order polynomial and rational B-spline geometries with rigid body modes (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 2121-2141 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 48 degrees-of-freedom (d.o.f.) quadrilateral thin elastic shell finite element using variable-order polynomial functions, B-spline functions and rational B-spline functions to model the shell surface is developed. This development may allow the stiffness formulation of the shell element to be linked to the geometry data bases created by computer aided design systems. The displacement functions are that of bicubic Hermitian polynomials. The displacement functions and d.o.f. are expressed and investigated in both the curvilinear and Cartesian forms. The cuivilinear form is simpler and can provide the proper solution for a certain class of shell problems. For certain highly curved shells such as bellows, however, the curvilinear form fails to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the high order displacement functions. It is suggested in this study that such difficulty can be circumvented and the rigid body modes can be properly included if a Cartesian form is used for displacement functions. The strain-displacement equations are expressed in curvilinear co-ordinates. Thus, the Cartesian displacement functions require a transformation to curvilinear displacement at each numerical integration point. Examples include a pinched cylinder, a translational shell under central load, a uniformly loaded hypar shell, a pressurized ovel shell, a semi-toroidal bellows and a U-shaped bellows. For the first four examples, geometric modellings consist of polynomials of second-order (subparametric), third-order (isoparametric), and fourth and fifth-order (both superparametric) as well as B-spline functions of fourth- and fifth-order. The geometries of the pinched cylinder, the semi-toroidal bellows, and the U-shaped bellows were modelled exactly using rational B-spline functions. All the results obtained are in good agreement with alternative existing solutions.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201114
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    A finite element method for contact problems related to fracture mechanics (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 2175-2195 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for contact problems in crack mechanics is developed on the basis of the penalty function method. The method is successfully applied to three important problems in fracture mechanics: a crack propagated from a pin hole, a two-point supported specimen with an edge crack loaded by a stamp, and a thick plate with a through-wall crack under bending force.
    Additional Material: 24 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201203
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    A total lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part I. Two-dimensional problems: Shell and plate structures (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 2253-2281 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co-ordinate system, based on the shell principal curvature directions, for the evaluation of strains and stresses. A series of examples of nonlinear analysis of shell and plate structures is given.
    Additional Material: 20 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201208
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    Solution of the partial eigenproblem by iterative methods (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 2283-2301 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A combined iterative method is formulated for the partial solution of the eigenproblem Ax = λBx that arises from the application of the finite element method. The method is a combination of the conjugate gradient (CG) method and the symmetric successive co-ordinate overrelaxation (SSCOR) method. Both of these methods belong to the same family of iterative methods which retain their vectorial form and approach the solution by seeking stationary points of the Rayleigh quotient. The formulation consists in splitting a characteristic matrix into the sum of two matrices, one of which corresponds to the SSCOR matrix, and then accelerating the associated iteration using the CG. The behaviour of the method is illustrated for five test cases and comparisons are made with other iterative methods. The influence of the relaxation parameter ω on the computational efficiency of the methods is also studied.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620201209
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    A unified set of single step algorithms. Part 2: Theory (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 2303-2309 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Part 1 of this paper1 presents a very general single step algorithm SSpj for the numerical integration of first and second order time dependent differential equations. In Part 2 we present and discuss results of the accuracy and stability analysis for SS11, SS21, SS31, SS22 and SS32. There is also a detailed comparison of SS22 and the Newmark algorithm.
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620201210
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    Textbook of dynamics (second edition), F. Chorlton, Ellis Horwood, Chichester, 1983 (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 2325-2325 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620201212
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    A new class of transitional blended finite elements for the analysis of solid structuresPresented at the SIAM 30th Anniversary Meeting, Stanford University, 19-23 July 1982. (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 241-253 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620200205
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    Non-iterative solution of a tridiagonal-type matrix coupled by diagonal submatrices (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 297-304 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A non-iterative method is presented for solving a system of algebraic equations forming a banded matrix with each diagonal submatrix being tridiagonal and all other submatrices being diagonal. A recursion relation is assumed between successive elements of the solution vector. This relation is determined by equating a linearly combined form of it with the original set of equations also being linearly combined. The solution vector is determined by back-substitution of elements in the recursion relation. Since the method takes advantage of the banded structure of the matrix, it is more efficient than the conventional methods. A FORTRAN program that incorporates the present method is included.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620200208
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    Shells of revolution with local deviations (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 305-313 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element model that is suitable for the analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of shell elements: rotational, general and transitional. The rotational shell elements, which are most efficient, are used in the region where the shell is axisymmetric. The general shell elements, which can simulate almost any shell geometry, are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis.The form of the global stiffness matrix is somewhat unique in the new model. Non-zero terms are not confined to a narrow band along the diagonal, but occur throughout the matrix. This is due to the following: (1) two different types of nodes, ring nodes and point nodes, are combined in a single analysis; and (2) a locally non-axisymmetric geometry creates a coupling of the Fourier harmonic coefficients of the rotational elements. Yet, the matrix still contains many scattered zero terms that should be considered for numerical efficiency. In this paper an efficient solution procedure that is effective for this situation is developed. The steps include the use of a substructuring technique and separate partial harmonic analysis. A numerical example is presented and compared with existing solutions to demonstrate the capabilities and the efficiency of the new model.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620200209
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    A two-dimensional analysis of the wave equation model for finite element tidal computations (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 369-383 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200214
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    Ritz finite element approach to nonlinear vibrations of beams (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 353-367 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Ritz finite element approach is used here to study the large amplitude free flexural vibrations of beams with immovable ends. The formulation is based on Lagrange's equation of motion with the definition of the time function at an instant corresponding to the point of reversal. The element displacement vector is chosen as a combination of inplane and transverse displacements. The nonlinear stiffness is written as a combination of the bending-membrane interaction and bending stiffness. The solution for nonlinear equations is sought by using an algorithm - the direct iteration technique - suitably modified for eigenvalue problems. Convergence is checked using the displacement norms on eigen-modes, and frequency norms for eigenvalues.The nonlinear frequencies, and modeshapes for transverse and longitudinal displacements, are determined for the simply-supported, clamped-clamped and simply-supported-clamped beams. Results are presented in the form of tables. In almost all the cases the nonlinear frequency values are found to be the lower bound like the earlier Galerkin finite element method.
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    URL: http://dx.doi.org/10.1002/nme.1620200213
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    Scalar potentials in multiply connected regions (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 665-680 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm, for use on a digital computer, is explained for cutting multiply connected regions in three-dimensional space. The algorithm is suitable for complex electromagnetic field problems where a magnetic scalar potential, affected by current loops, is to be calculated in a multiply connected region. Problems in fluid dynamics with vorticity affecting a scalar potential, could also be attacked with this algorithm. Since finite element methods are ubiquitous in field calculations, the cuts of the space constructed by the algorithm should ideally correspond to the given discretization; this can be arranged by an application of the Lebesgue Covering Theorem, for which a second algorithm is provided.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620200406
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    Finite element approach to propagation in elliptical and parabolic waveguides (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 681-688 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the application of the finite element method to the solution of propagation problems in elliptical and parabolic waveguides. Mode classification in empty waveguides is discussed, followed by extensions of the method to problems where metallic ridges lie along either major or minor axes.
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    URL: http://dx.doi.org/10.1002/nme.1620200407
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