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  • 1970-1974  (2,181)
  • 1971  (2,181)
  • Polymer and Materials Science  (2,119)
  • Engineering General  (62)
  • 101
    Electronic Resource
    Electronic Resource
    Molecular weights and hydrodynamic properties for homogeneous native DNA, derived from diffusion, sedimentation, and viscosity measurements on polydisperse samplesPresented in part at Symposium, Transportvorgänge in verdünnten Polymerlösungen und ihre Anwendungen, Dresden, April 30, 1969. (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 285-307 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The diffusion, sedimentation, and viscosity behavior of native DNA has been studied as a function of molecular weight absolutely determined by diffusion and sedimentation measurements between 106 and 20 × 106 Daltons. Only data for monodisperse subfractions of the polydisperse DNA samples investigated have been compared. They were derived by means of calculations based on individual sedimentation constant distribution and polymer parameters. The inconstancy of these parameters for the semi-rigid DNA molecules over the range of different sub-fractions of the polydisperse samples has been taken into account. A detailed description of the corresponding mathematical background as well as of the diffusion measurements has been given in the two preceding papers. For the homologous series of monodisperse native DNA molecules, three-parameter equations have been determined representing the s0-[η], s0-M, and [η]-M relations as well as the D0-s0 and D0-M interdependence over the entire molecular weight range of interest. Furthermore a simple equation is given describing the molecular weight dependence of the Mandelkern-Flory-Scheraga parameter β in terms of s0 and [η]. The asymptotic value β∞ has been determined, primarily by measurements at finite molecular weights, to be 2.39 × 106, resulting in β values near 2.50 × 106 at M = 108 Daltons. The hydrodynamic properties of our two calf thymus DNA samples of highest molecular weight proved to be influenced by residual protein interactions resulting in a more compact conformation. Further data are given demonstrating the influence of the individual polydispersity of the investigated samples on diffusion constant and molecular weight averages.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100206
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  • 102
    Electronic Resource
    Electronic Resource
    Potentiometric and circular dichroic measurements of poly(L-glutamic acid) in aqueous solutions of organic and inorganic electrolytes at ambient temperature (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 357-377 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Titration of an aqueous solution of sodium poly-L-glutamate with a strong acid usually produces turbidity and precipitation before the equivalence point is reached. In 1M sodium p-toluenesulfonate and 1M sodium methylcyclohexanesulfonate aggregation was delayed for days to months. In very concentrated tetra-n-butylammonium chloride and bromide the polymeric acid dissolved and could be titrated with NaOH. However, potentiometric titration curves in these solutions did not yield information (by way of plots of apparent pK versus the degree of neutralization) about the helix-to-coil transition of the polymer. It was argued in addition that the apparent pK of a weak polyelectrolyte should not be calculated from titrations in concentrated salt solutions since it is a mixed or composite quantity. It contains not only the effect of the salt on the dissociation of the weak electrolyte but its effect on the activity coefficient of hydrogen ions as well.Circular dichroic spectra were therefore measured a t various degrees of neutralization of poly(L-glutamic acid) in a number of aqueous salt solutions and mixtures of organic solvents with water. It was found that the undissociated polymer in the concentrated methylcyclohexanesulfonate and quaternary ammonium halide solutions had the spectrum of a right-handed α helix. The n → π* band at 222 mμ was used as a measure of the fraction of polymer in the helical conformation. The value of - Δε for the undissociated polyacid in these organic electrolyte solutions was 11.4. By means of this value and a number of assumptions, the fraction of helix (fh) as a function of α, the degree of polyacid neutralization, was calculated for the different solvent mixtures. An empirical equation was used to describe the variation of fh with α, fh = 1/(1 + e-a+bα), in which b represents the degree of cooperativeness of the transition, and a is a measure of the effect of the medium on the onset of the transition. The values of b did not differ very much from one another, suggesting that the cooperativeness of the transition was not sensitive to changes in the medium. On the other hand, the value of a (or its equivalent, the value of α at the halfway point in the transition) was more dependent on the solvent. Comparisons of these results with those of some other workers were made by means of the empirical equation.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100211
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  • 103
    Electronic Resource
    Electronic Resource
    Relation between Mw, Mn and M(swDA), M(swDw) and M(sη) (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 411-416 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100215
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  • 104
    Electronic Resource
    Electronic Resource
    Dielectric relaxation measurements as a tool for studying the kinetics of the helix-coil transition of poly (γ-benzyl L-glutamate) (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 417-419 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100216
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  • 105
    Electronic Resource
    Electronic Resource
    Interaction of proflavine and 9-aminoacridine with DNA at temperatures below and above the melting temperature (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 399-410 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The influence of temperature on the binding of 9-aminoacridine and of proflavine to E. coli DNA in 10-3M NaCl solution has been determined by a spectrophotometric technique. The inadequacy of the expression normally used for the determination of the extent of binding is discussed with reference to measurements at temperatures above which dissociation of the double helix occurs. A method of determining the relative extents of binding to native and denatured DNA at elevated temperatures is described.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100214
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  • 106
    Electronic Resource
    Electronic Resource
    Announcement (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 421-421 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100217
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  • 107
    Electronic Resource
    Electronic Resource
    On the helix-coil equilibrium in two- and three-stranded complexes involving complementary poly- and oligonucleotides (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 423-423 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100218
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  • 108
    Electronic Resource
    Electronic Resource
    Molecular orbital calculations on the conformation of polypeptides and proteins. V. Conformational energy maps and stereochemical rotational states of aliphatic residues (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 491-511 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quantum-mechanical calculations by the PCILO method on the conformation of amino acid residues of proteins have been extended to the valyl, leucyl, and isoleucyl residues. In distinction to the earlier “empirical” computations, the quantum-mechanical results indicate very similar energy contours for the stable conformations of the three residues. Their general outline is also similar to that of the alanyl residue, although reduced by about 25%. Contrary to the “empirical” computations, the present results predict that the region corresponding to the α-helix should be one of great stability for the three residues and in particular for the valyl residue. The quantum-mechanical results are in excellent agreement with the experimental conformations of the aliphatic residues in lysozyme and myoglobin. Their prediction as to the ready availability of the valyl residue in the α-helical conformation agrees moreover with Ptitsyn's statistical evaluation of the participation of this residue in the inner turns of the helical regions in six globular proteins. The maximum conformational space allowed for the aliphatic residues is somewhat smaller than that allowed for the aromatic ones, while the minimum conformational space (region of stability common to all the residues) is similar in both groups.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100306
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  • 109
    Electronic Resource
    Electronic Resource
    Experimental thermodynamics of the helix-random coil transition. IV. Influence of the base composition of DNA on the transition enthalpy (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 513-522 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The helix-coil transition of DNA of various base compositions has been followed by measuring the heat capacity and the ultraviolet absorption as a function of temperature through the transition region. The results of these measurements indicate that the transition enthalphy ΔH for a given pH value and salt concentration depends considerably on the base composition of the various DNA samples. The values of the transition enthalpies vary from ΔH = 7.73 kcal/mole base pair (MBP) for 31% GC base pairs to ΔH = 8.52 kcal/MBP for 72% GC base pairs. The results of the heat capacity measurements are discussed in relationship to the theoretical models suggested by various authors. Some peculiarities of the measured heat capacity versus temperature curves are reported. The correlation between these peculiarities and the results of the transcription experiments of DNA is discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100307
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  • 110
    Electronic Resource
    Electronic Resource
    Infrared investigation of poly-L-histidine structure dependent on protonation (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 711-719 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Poly-L-histidine (PLH) films at different degrees of protonation were produced mid subjected to infrared spectroscopic investigation (range 4000-650 cm-1). In addition, the N-deuterated film spectra were plotted. The amide II and III bands show that the peptide group is present in the trans form. The amide I and II bands show that at 0% and 50% protonation the PLH occurs as an α-helix and at 100% protonation as a random coil with some ranges in β structure. At 0% and 50% protonation, no hydration water is bound to the backbone. At 0% protonation all NH groups are linked to each other or to water molecules via hydrogen bonds. At 50% protonation NH+ċN bonds form between the imidazole rings. These protons are present in continuous energy level distribution. Such bonds with tunneling protons are extremely polarizable and between these bonds may act proton dispersion forces. The Cl- ions are bonded to the NH groups of the imidazole groups. The hydration water is bonded to the Cl-- ions and to the NH groups. At 100% protonation, hydration water is bonded also to the CO groups of the backbone. The NH groups of the backbone, like those of the rings, endeavor especially in the dry state to bond to the Cl- ions. This leads to a strong steric constraint of the random coil.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100409
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  • 111
    Electronic Resource
    Electronic Resource
    A cooperative transition between two helical conformations in a linear system: poly-L-proline I ⇌ II. II. Kinetic studies (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 721-737 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The conformational transition between the two helical forms I and II of poly-L-proline serves as an experimental model for the study of the kinetic, behavior of cooperative systems. The slow I ⇌ II conversion after a sudden perturbation of the solvent composition was followed polarimetrically. The dependence of the mean relaxation times on chain length and the degree of conversion was compared with Schwarz's theory. In addition, a description of the entire relaxation curves was possible in three special cases: all-or-nothing, small perturbations of the I ⇌ II equilibrium in long chains, and conversions which start off with molecules completely in one or the other conformational state. The mathematical model on which the theory is based contains only one more adjustable parameter than the equilibrium model, but it adapts to the experimental results surprisingly well. The present kinetic results and equilibrium measurements on this system are described by the same values of those parameters which are common to both models. The found value of the rate constant of the propagation step, i.e. the cis ⇌ trans isomerization of a peptide bond at an existing I-II junction, agrees with the rate of isomerization in N,N-dimethylacetamide reported in the literature. The rate of nucleation is up to 105 times smaller than the rate of propagation.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100410
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  • 112
    Electronic Resource
    Electronic Resource
    Optical rotary dispersion of mucopolysaccharides III. Ultraviolet circular dichroism and conformation al specificity in amide groups (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 739-751 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The circular dichroism of glycosaminoglycans and ganglioside in distilled water are described, showing two bands in the region of amide and carboxyl transitions. The first, negative hand is common to all polymers and the amino sugar derivatives. The characteristics of the second band depend upon polymer structure. Those containing 4-1-linked amino sugars show a second, positive, resolved band about 190 mμ, while those with 3-1-linked amino sugars show a second, negative band less resolved from the first usually ≤185mμ, but clearly centered at 188mμ for dermatan sulfate. Ultraviolet optical absorption from 300 to ∼183 mμ showed inflection regions around 190 mμ for most compounds.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100411
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  • 113
    Electronic Resource
    Electronic Resource
    Stereoselective polymerization of γ-Benzyl Glutamate NCAPaper presented to the joint CIC/ACS Symposium on Kinetics and Mechanism of Stereoregular Polymerizations, Toronto, Canada, May 1970. (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 753-765 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The polymerization of γ-benzyl glutamate NCAs has been investigated. The results indicate that a coil-to-helix transformation is not responsible for the kinetic data. The results were rationalized by assuming formation of polymer aggregates coupled with the stereoselective adsorption of monomer onto growing polymer prior to reaction. From kinetic data a ratio of equilibrium constants for adsorption was determined. Independent data confirmed the assumption that adsorption of monomer onto polymer occurred. Equilibrium constants were evaluated, and their ratio was found to be comparable with that obtained from the kinetic data.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100412
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  • 114
    Electronic Resource
    Electronic Resource
    Hydration of DNA: A neutron scattering study of oriented NaDNA (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 849-863 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A preliminary neutron-scattering study of wet-spun oriented NaDNA samples with various contents of H2O or D2O has been performed to obtain information about the hydration of NaDNA. The preferred orientation was in the direction of the crystallographic c axis. Perpendicular to this direction the samples could be regarded as poly-crystalline. It has been found that the preferred crystallite orientation was also reflected in the water structure. This fact, taken together with the small energy widths of the measured near-elastic peaks indicates that water molecules in the sample are relatively strongly bound to the DNA helix either directly or via other water molecules. Angular distribution measurements of elastically scattered neutrons were performed with the momentum transfer vector directed along and perpendicular to the DNA helix axis. Different Debye-Waller factors were obtained, indicating different water dynamics in the two directions. Comparison between the H2O and D2O measurements suggests that the difference is caused by motions of rotational nature. The shape of the frequency distribution function for the H2O molecules in the NaDNA sample was somewhat similar to that which has been measured in ice.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100509
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  • 115
    Electronic Resource
    Electronic Resource
    Dichroism of TMV in pulsed electric fields (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 865-882 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The linear dichroism induced in a solution of electrically anisotropic molecules by a pulsed electric field has been studied. Equations have been obtained which express the dichroism as a function of dipole moment, excess polarizability, field strength, and the angle α between the dipole moment and the transition moment for the absorption band. These expressions have been related to the experimentally observed difference signal in such a way that when the dichroism is measured as a function of field strength the permanent moment, excess polarizability and angle a can be determined.Experiments have been carried out on tobacco mosaic virus (TMV), which is similar in its properties to the theoretical model. The polarizability anisotropy and rotary diffusion constant for the monomer and dimer of TMV have been obtained from these experiments. In addition to the molecular parameters mentioned above, the saturated electric dichroism of the virus was measured as a function of wave length and the presence of an n-π* transition in the tryptophan spectrum was indicated.Further experiments measuring dichroism as a function of pH demonstrated the general denaturation of the virus at high pH (10-11) but also the existence of a stable fraction which is not fragmented even at the high pH involved.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360100510
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  • 116
    Electronic Resource
    Electronic Resource
    The binding of Mg++ ions to polyadenylate, polyuridylate, and their complexes (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 2459-2490 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The binding of Mg ++ to polyadenylate (poly A), Polyuridylate(poly U), and their complexes, poly (A + U) and poly (A + 2U), was studied by means of a technique in which the dye eriochrome black T is used to measure the concentration of free Mg-. The apparent binding constant KX = [MgN]/[Mg++][N], N = site for Mg++ binding (the phosphate group of the nucleotide), was found to decrease rapidly as the extent of binding increased and, at low extents of binding, as the concentration of Na- increased in poly A, poly (A + U), and poly (A + 2U), and somewhat less so in poly U. Kx is generally in the range 104 〉 KX 〉 102. The cause of these dependences is apparently, primarily, the displacement of Na+ by Mg++ in poly U and poly (A + U) on the basis of the similarity of extents of displacement measured in this work and those measured potentiometrically. \documentclass{article}\pagestyle{empty}\begin{document}$$ \Delta H'{\rm v}.{\rm H}. = - R(\partial {\rm }\ln Kx/\partial 1/T)_\theta,\theta = \frac{{{\rm Mg}N}}{{N_t }} $$\end{document} was calculated and was found to approach zero as the concentration of Na+ increased. In poly U, poly (A + U), and poly (A + 2U) at low ΔH′ v.H. 〉 0, about + 2 kcal/“mole.” In poly A, also at low salt, ΔH′ v.H. ≈ -4 kcal/“mol” for the initial binding of Mg++, and increases to +2 kcal/“mol” at saturation. This enthalpic variation probably accounts for the anticooperativity in the binding of Mg++ not ascribable to the displacement of Na++.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/bip.360101209
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  • 117
    Electronic Resource
    Electronic Resource
    On the conformations of poly-N-methyl-L-alanine (PNMA) in solution (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 2581-2590 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: High-resolution nuclear magnetic resonance spectra at 100 MHz have been obtained on poly-N-methyl-L-alanine in the chloroform-trifluoroacetic acid system under various conditions of solvent composition. Different spectra are observed for the CH3-Cα, Cα-H, and N-CH3 protons. On the basis of conformational analysis an interpretation of the NMR results was attempted.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/bip.360101217
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  • 118
    Electronic Resource
    Electronic Resource
    Evaluation of RNA conformation from circular dichroism and optical rotatory dispersion data (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 2607-2614 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of optical rotatory dispersion and circular dichroism of RNA is described which leads to an estimate of the degree of base pairing. By the use of new standards for the double-helical parts of the molecule, based on data for two-stranded viral RNA species, a good fit between calculated and observed curves can be achieved. Where data are available the results of analyses of optical rotatory dispersion and circular dichroism in general show satisfactory consistency.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/bip.360101220
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  • 119
    Electronic Resource
    Electronic Resource
    The effect of mercuric ion on the DNA-methylene blue complex (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 2625-2628 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360101224
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  • 120
    Electronic Resource
    Electronic Resource
    Electric field effect on poly-alanine and poly-hydroxyproline film conformation (1971)
    New York : Wiley-Blackwell
    Biopolymers 10 (1971), S. 2645-2648 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360101228
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  • 121
    Electronic Resource
    Electronic Resource
    Finite element method applied to the problem of stability of a non-conservative system (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 63-87 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to the stability analysis of structural systems subject to non-conservative forces. The development of the method is general, but the specific application considered here is the stability of thin-walled members subject to follower forces. The method predicts the type of instability, whether it be buckling or flutter. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristic of the finite element formulation.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030110
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  • 122
    Electronic Resource
    Electronic Resource
    Dynamic analysis of structures using the rank force method (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 103-117 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the finite element rank force method for the dynamic analysis of redundant structures is presented. The applied loading consists of discrete and distributed loads. Both forced and free vibrations are considered, the latter yielding latent vectors corresponding to dynamic redundancies.It is shown that the dynamic properties of an element are given by a static flexibility matrix, an inverse mass matrix, a damping parameter and a displacement vector representing the effect of the applied distributed loading.
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    URL: http://dx.doi.org/10.1002/nme.1620030112
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  • 123
    Electronic Resource
    Electronic Resource
    An annular segment finite element for plate bending (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 119-129 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stiffness matrix for a finite element having the planform of an annular segment is derived using the displacement approach. Numerical problems involved in the derivation are discussed and rapid convergence to exact solutions is demonstrated on three sample problems. It is concluded that the new element will be of great value to engineers concerned with the analysis of slabs of bridge decks curved in plan.
    Additional Material: 8 Ill.
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    Stress and deformation analysis of fibrous composite materials by point matching (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 89-101 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The point matching numerical method and its generalization, the method of boundary point least squares, have been successfully applied to numerous boundary value and eigenvalue problems. The present paper demonstrates the application of these techniques to problems in the micromechanics of fibrous composite materials, i.e. determination of elastic moduli and stress concentrations for parallel-fibre materials which are loaded transversely with respect to the fibres. The solution technique utilizes exact solutions of the governing equations of plane elasticity for each component fibre and its surrounding matrix material in a typical repeating section of the composite material. The continuity conditions for stresses and displacements between fibre and matrix and the repeatability conditions at the boundary of the repeating section are satisfied approximately in a pointwise manner. Some special numerical techniques which were found to be particularly useful in applying the point matching method to these problems are delineated. The method is demonstrated for composite materials having circular, elliptical and square fibres in regular, staggered arrays. Numerical results are given which show the accuracy of the method as well as stress concentration and composite elastic moduli data.
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    URL: http://dx.doi.org/10.1002/nme.1620030111
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    Concave programming and piece-wise linear programming (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 131-144 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the mathematical foundations of a technique that has been used extensively in structural optimization.1-6 Two basic problems are considered. The first of these is the concave programming problem which consists of finding the global minimum of ‘piece-wise concave functions’ on ‘piece-wise concave sets’. Since any function can be approximated by a piece-wise concave function, this method could in principle be used to find the global minimum in non-convex optimization problems. The second one is the piece-wise linear programming problem in which the objective function is convex and piece-wise linear. The iterative method outlined for handling this problem is shown to be much more efficient than the standard simplex method of linear programming.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030114
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    A frontal solution program for finite element analysisB. M. Irons, ‘A frontal solution program for finite element analysis’, Int. J. num. Meth. Engng, 2, 5-32 (1970). (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 149-149 
    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.1620030116
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    Editorial notice (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 154-154 
    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.1620030202
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  • 128
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    Reduced integration technique in general analysis of plates and shells (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 275-290 
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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 plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced.In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations.The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030211
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    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    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.1620030301
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    Discussion of paperS. Gallof and B. Kaplan, ‘Numerical solution and utilization of Green's functions,’ Int. J. num. Meth. Engng, 1, 169-175 (1969). by S. Gallof and B. Kaplan (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 295-296 
    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.1620030214
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  • 131
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    A static and dynamic finite element shell analysis with experimental verification (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 299-315 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A system of finite element shell analysis codes, called SABOR/DRASTIC, is used to analyse a complex two-layered shell of revolution under static and dynamic asymmetric loads. The dynamic analysis is compared with experimentally measured response. In this linear elastic analysis, emphasis is placed on the inherent flexibility of the finite element method in modelling the complex structural geometry of a given test specimen. Static studies, which involve variations in important shell parameters, and dynamic studies, which provide a successful correlation with experiment, are used to illustrate both the detail and the generality with which shell analyses may now be performed with confidence.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030302
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    On the calculation of consistent stress distributions in finite element approximations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 317-325 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory of conjugate approximations1 is used to obtain consistent approximations of stress fields in finite element approximations based on displacement assumptions. These consistent stresses are continuous across interelement boundaries and involve less mean error than those computed by the conventional approach.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030303
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  • 133
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    Generation of two- and three-dimensional finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 327-347 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many of the known finite elements are based on a variational procedure in a functional basis of monomials. The present paper attempts to formulate completely a finite element procedure which is non-variational on a functional basis which is left to the choice of the user.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030304
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    Discussion of paperSuryanarayan Patnaik and Pasala Dayaratnam, ‘Behaviour and design of pin connected structures’, Int. J. num. Meth. Engng, 2, 579-595 (1970). by Suryanarayan Patnaik and Pasala Dayaratnam (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 443-444 
    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.1620030312
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    Network-topological formulation of analysis and design of rigid-plastic framed structures (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 425-441 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified network-topological approach to the formulation and solution of the analysis and minimum weight design of rigid-plastic structural systems is presented. It is shown that both analysis and design can be formulated using network concepts, but that, in contrast to elastic networks, the formulation results in a mathematical programming problem. Formulations based both on the static and kinematic theorems of plasticity are presented, and it is shown that duality guarantees that the two types of formulation yield identical results. The problem is first formulated on the basis of a simple definition of yielding, and is then generalized to the case where yielding is defined in terms of a yield surface.
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    Non-linear structural analysis by dynamic relaxation (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 463-483 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dynamic relaxation, an iterative method for use with digital computers, is described and is shown to be suitable for the solution of a system of linear equations and in particular for such problems derived from structural frame analysis. It is further shown that the method may be modified to include non-linear equations relating to these problems.Some specific examples of linear and non-linear solutions are given and comparisons are made with another computer method which performs the same tasks.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030403
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    A finite-deflection analysis of shallow arches by the discrete element methodThis paper is Crown copyright and is reproduced here with the permission of the Controller, Her Majesty's Stationery Office. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 529-552 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discrete element displacement method is used to analyse the finite-deflection behaviour of shallow arches. The arches are idealized as assemblies of shallow curved elements and the necessary properties of the displacement patterns in these elements are discussed. Numerical solutions of the geometrically non-linear problem are obtained by directly minimizing the total potential energy of the system.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030408
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    Global-local finite element (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 565-574 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element procedures usually require more degrees of freedom for a specified accuracy than does a classical Ritz procedure if suitable coordinate functions are available. This paper develops a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods. This hybrid method preserves much of the flexibility of the finite element method while increasing the solution accuracy for a specified system order. The method is illustrated by examination of a beam and a plate vibration problem.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030410
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    A simple algorithm for the stiffness matrix of triangular plate bending elementsThe authors are indebted to the referees for many comments and suggestions. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 553-563 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For a hierarchy of polynomials on the triangle there is derived an algorithm for computing the stiffness matrix of the plate bending element. The algorithm is easy to program and means a considerable saving of the computing time. The same approach can be used for any elliptic equation with constant coefficients.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030409
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  • 140
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    Improved numerical integration of thick shell finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 575-586 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadratic thick shell element derived from a three-dimensional isoparametric element was first introduced by Ahmad and co-workers in 1968. This element was noted, however, to be relatively inefficient in representing bending deformations in thin shell or thin plate applications. The present paper outlines a selective integration scheme for evaluating the stiffness matrix of the element, in which each component of the strain energy is evaluated separately using a different Gaussian integration grid for each contribution. By this procedure, the excessive bending stiffness of the element, which results from the use of me quadratic interpolation functions, is avoided.The improved performance of this element, as compared with the original thick shell element, is demonstrated by analyses of a variety of thin and thick shell problems. Editors' note: A similar development was outlined by O. C. Zienkiewicz and co-workers in lnt. J. num. Meth. Engng, 3, 275-290 (1971). Some important details differ between the two papers which are thus complementary.
    Additional Material: 14 Ill.
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    An introduction to applied probability and random processes, J. B. Thomas, Wiley, New York, 1971. No. of pages: 350. Price: £6·15 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-592 
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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.1620030415
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    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    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.1620030101
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  • 143
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    Erratum (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 1-2 
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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.1620030102
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    Editorial (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 3-3 
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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.1620030103
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  • 145
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    The finite difference and localized Ritz methods (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 155-160 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The conventional central finite difference equations for the plane stress extension of flat plates are derived as a localized Ritz process. A dual differential-variational discretization of this type enables common classification of the finite difference and finite element methods. Also, it provides alternative methods of establishing sufficiency conditions and relative rates of convergence for discrete systems derived from a localized Ritz process, and the existence of solution bounds for discrete systems derived using difference procedures.
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    URL: http://dx.doi.org/10.1002/nme.1620030203
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    Finite element formulation of general electrothermoelasticity problems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 161-179 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of consistent discrete models, via the concept of finite elements, of linear and non-linear electrothermomechanical behaviour of continuous bodies. In the development, general energy balances are utilized to derive equations governing electromagnetic fields over an element and coupled equations of motion and heat conduction of a typical element of the continuum. These equations make it possible to study a general class of field problems involving arbitrary geometries and boundary conditions. Sample problems are included.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030204
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    Axial wave propagation in membrane shells of revolution (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 181-198 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic finite element technique, which is referred to in the literature as ‘computer-analysis’, is applied to wave propagation problems occurring in finite and semi-infinite linearly elastic membranes of revolution. Both semi-infinite and finite versions of cylindrical and conical membranes are considered, and a finite membrane having a meridional curve which is parabolic is solved. The source of excitation is generally a constant velocity motion of one end of the membranes, but the results for a stress-pulse input at one end of a semi-infinite cylindrical membrane are also given. The results for the finite membranes are new, and the results for the semi-infinite problems are discussed with respect to previously published results. The two-dimensional state of stress in the membrane requires careful ordering of the calculations, and the boundary conditions for finite membranes are shown to follow logically from this ordering of the calculations. The difference in the solutions resulting from prescribing an axial or a tangential velocity excitation at the end of a conical membrane is presented, and the mesh size necessary for convergence to the solution is indicated. The graphs of the results clearly indicate regions in space and time where the membrane model should be replaced by the shell formulation to represent a realistic structure. The technique is shown to be self-contained and independent of any formal method such as the method of characteristics.
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    URL: http://dx.doi.org/10.1002/nme.1620030205
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    Dynamic programming and the solution of the biharmonic equation (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 199-213 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton-Jacobi-Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.
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    URL: http://dx.doi.org/10.1002/nme.1620030206
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    Non-linear programming for the plastic analysis of local deformations in shell structures (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 215-232 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load-deflection behaviour of these structures after the application of the yield-point load in order to predict the appearance of any snapping action.The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non-linear programming routine.The results of this analysis are correlated with a non-dimensional boss size parameter p and compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.
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    URL: http://dx.doi.org/10.1002/nme.1620030207
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  • 150
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    Trigonometric function representations for rectangular plate bending elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 261-273 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study of bending of plates for small deformations by applying the finite element method is presented in this paper.A new class of displacement functions has been developed for rectangular bending elements. For the first time a method is proposed for the derivation of displacement functions in which trigonometric expressions that had apparently failed to yield satisfactory results in earlier attempts can be used along with polynomial terms.The derivation leads to conforming type of displacement functions which satisfy the convergence criterion. The approach also demonstrates how many more new displacement functions can be found.
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    URL: http://dx.doi.org/10.1002/nme.1620030210
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    A steepest gradient method for optimum structural design (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 249-259 
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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 a search procedure for finding the unconstrained maximum or minimum of a function of many independent variables. If this function represents the volume, cost, stiffness, etc. of a structure and each of the independent variables is associated with a parameter governing the geometry of the structure then designs of optimum geometry may be made in certain cases with the assistance of this search procedure. The procedure consists of steepest gradient calculations used in conjunction with a reverse Fibonacci location process. A ridge-following technique is included to speed convergence in addition to localized exploration in the region of an optimum.The search procedure has been programmed for computer use and an outline of its structural design applications is presented together with an example of its efficiency in a specific case.
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    URL: http://dx.doi.org/10.1002/nme.1620030209
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  • 152
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    Quadrature rules for brick based finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 293-294 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030213
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  • 153
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    A note on accuracy and convergence of finite element approximations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 291-292 
    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.1620030212
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  • 154
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    Recent advances in matrix methods of structural analysis and design, edited by R. H. Gallagher, J. T. Oden and Y. Yamada, University of Alabama Press, Alabama, 1971. No. of pages: 904. Price: $32.50 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 446-446 
    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.1620030315
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    Discussion of paperR. S. Barsoum and R. H. Gallagher, ‘Finite element analysis of torsional and torsional-flexural stability problems’, Int. J. num. Meth. Engng, 2, 335-352 (1970). by R. S. Barsoum and R. H. Gallagher (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 444-445 
    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.1620030313
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  • 156
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    Announcements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 447-448 
    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.1620030316
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  • 157
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    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    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.1620030401
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  • 158
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    The elasto-plastic indentation of a half-space by a rigid sphere (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 451-462 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Using the finite element method, a detailed study of the deformations and stresses produced in an elastic-perfectly plastic half-space indented by a rigid sphere was done. The analysis covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold. Experimental results available in the literature are in good agreement with the analysis. In solving repeatedly the large number of linear equations involved in the solution of the problem, it was found profitable, in order to save computer time, to modify the direct elimination method. This technique is described in some details in the paper.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030402
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  • 159
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    A note on convergence of finite element solutions (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 485-493 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of nodal displacements obtained by the finite element method is investigated for special element patterns in plane elasticity with the aid of the differential equation derived from the equilibrium condition at each node. The convergence of strains is also discussed. It is shown that averaging is an effective tool for obtaining approximations to strain for some kinds of mesh arrangement. It is also shown that the approach becomes inaccurate along force boundaries.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030404
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  • 160
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    A refined curved element for thin shells of revolution (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 495-508 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A refined axisymmetric curved finite element for the analysis of thin elastic-plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co-ordinates for the assumed in-plane and out-of-plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in-plane stress-resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic-plastic solutions has also been observed.Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030405
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  • 161
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    Numerical methods for evaluation of equilibrium composition of ideal gases (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 509-517 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper considers methods of solution of the relevant equations based on the Newton-Raphson process. Expressions are derived for calculation with both good and very poor initial guesses and for calculation of pressure, volume and temperature during an equilibrium process. A method of programming the calculations is outlined. Variations and modifications to suit specific situations are discussed.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030406
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  • 162
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    An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co-ordinates (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 519-528 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi-linear co-ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co-ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three-dimensional tetrahedral elements is indicated.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030407
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  • 163
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    Incremental displacement in non-linear analysis (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 587-588 
    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.1620030412
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  • 164
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    An introduction to APL, W. Prager, Allyn and Bacon, Boston, 1971. No. of pages: 134 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-591 
    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.1620030414
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  • 165
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    Letters to the editor (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 588-591 
    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.1620030413
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  • 166
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    Vibration analysis of rotating cantilever plates (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 233-248 
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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 technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components - one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in-plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in-plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030208
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  • 167
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    Numerical control, olesten, Wiley-Interscience, New York, 1970. No. of pages: 645. Price: £9.50 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 445-446 
    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.1620030314
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  • 168
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    The numerical solution of non-linear consolidation problems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 5-11 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It has long been recognized that permeability, compressibility and viscosity vary during the consolidation of soil. However, the introduction of these variations into consolidation theory leads to formidable difficulties due to their rendering the equations highly non-linear. Numerical methods are given herein which enable the governing equation to be solved for a variety of different non-linear laws.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030104
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  • 169
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    Application of the simultaneous iteration method to undamped vibration problems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 13-24 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030105
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  • 170
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    An economical method for determining the smallest eigenvalues of large linear systems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 25-33 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general eigenvalue problem Ax = λBx as arising from vibration problems tackled by the finite element method is often solved by the economization method in which the two matrices are reduced to a more manageable size and approximate answers are obtained.This paper analyses the method in a more mathematical way than previous accounts and leads to a definition of the optimum set of variables to be retained during the reduction. An extension to the method is suggested which allows the approximate eigenvalue to be improved and bounds are obtained on the eigenvalues of the full problem before reduction.An estimate is made of the calculation involved in the method and it is concluded, by reference to examples, that the extended method leads to a more efficient algorithm.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030106
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  • 171
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    Solution of the compressible flow equations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 35-43 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is described for solving the compressible flow equations in subsonic flow. The general quasi-linear equation ∇.g∇v = 0 is considered with g a function of ∇v. ∇v, and iterations of the form ∇.gn∇vn+1 = 0 are analysed, where g0 is suitably chosen and gn defined from vn for n≥1. This approach is applied to the compressible flow equations in terms of a velocity potential ø: monotonic convergence is predicted and at each iteration the error is multiplied by a factor less than the square of the greatest Mach number in the solution.Reliable convergence has been obtained in practice solving the linear equation for øn+1 by a finite difference method. The alternative of working in terms of the stream function ψ is discussed, and also discretization by the finite element method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030107
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  • 172
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    The piecewise-linear analysis of two connecting structures including the effect of clearance at the connections (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 45-51 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of analysis is presented for two structures which have connections with clearance. It is assumed that the behaviour of the structures is described, by the movement of discrete nodes and that as the load on the structure changes, clearances open or close between corresponding nodes on the structures; each time this occurs the stiffness of the combined structure changes because its configuration has changed. Between these changes, the structure will behave linearly and the overall behaviour can be described as piecewise linear. Applications include diesel engine crankshafts with bearing clearances and the wrap-around problem in pin-and-eye connections.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030108
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  • 173
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    Non-axial-symmetric thermal stresses in circular discs or cylinders (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 53-61 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution is presented for the computation of the transient thermoelastic stresses in a hollow cylinder with temperature boundary conditions given as a circumferential variation of surface heat transfer coefficient. The temperature distribution is solved explicitly. The problem is set up using the Airy stress function which leads to the biharmonic equation. This approach requires the satisfaction of three Michell integrals at the inner boundary in order to ensure single-valued displacements and rotation. An iterative method is described in which these integrals are all simultaneously satisfied and thus provide the necessary non-zero boundary conditions for the solution of the biharmonic equation which is rapidly solved by Gaussian elimination. Results are presented for the general case where the temperature is a function of r and θ. The computer program is checked by assuming a constant value of the surface heat transfer coefficients. In this case a closed form solution is obtained.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030109
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  • 174
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    Note on dynamic relaxation (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 145-147 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Dynamic Relaxation (DR) method of solving a set of simultaneous linear equations requires an estimate of the spectral radius of the matrix. Dividing each equation by the corresponding row sum of moduli of the elements of the matrix gives a convenient upper bound of unity to this. This note shows that the DR method then gives a faster asymptotic rate of the convergence than the degenerate Chebyshev method which it closely resembles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030115
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  • 175
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    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    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.1620030201
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  • 176
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    Process analysis by statistical methods, D. M. Himmelblau, Wiley, New York, 1968. No. of pages: 460. Price: £8·75; $19.95 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 151-151 
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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.1620030117
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  • 177
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    An equation solver of very large capacity (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 379-388 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A very simple equation solver of very large capacity is developed. The method described here does not require a very large in-core memory; however, a fast random access device like a magnetic disk drive is required.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030307
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  • 178
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    A numerical solution of axisymmetric problems in elastodynamicsThis research was supported by the Research Foundation of the State University of New York. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 361-377 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The equations governing the axisymmetric dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first-order partial differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary value problems in elastodynamics is presented. Two examples are considered.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030306
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  • 179
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    The solution of structural equilibrium equations by the conjugate gradient method with particular reference to plane stress analysis (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 349-360 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer program is described for the analysis of plates in extension using the equivalent plane-framework idealization. The conjugate gradient method is adopted to solve the resulting large number of simultaneous equations. Performance figures are quoted for the program when used on an ICL KDF9 machine with a restriction of 18K on the available core store. The method is generally shown to provide a satisfactory solution to a heavy computational task and thus permits the solution of very large structural systems on a small computer.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030305
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  • 180
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    A powerful hybrid method in finite element analysis (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 389-403 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An important limitation of finite element analysis, namely, the need for a large number of small elements in regions of finite or infinite stress concentrations and the difficulties of convergence in such cases, is well known. Rao1 suggested a possibility of overcoming this by developing hybrid techniques combining continuum and finite element concepts. In such techniques, each region of stress concentration is covered by one large ‘primary element’ whose description includes term(s) identifying the type and order of concentration, while the remaining structure is split into a few ‘secondary elements’ which are conventional finite elements. In this paper a procedure incorporating this concept is developed and its effectiveness is clearly demonstrated by successful application to two important examples, one of them with stress singularities. The concept, in fact, can be applied equally well to other two- and three-dimensional problems of continua with discontinuities and concentrations.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030308
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  • 181
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    Linear programming methods of displacement analysis in elastic-plastic frames (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 415-423 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The analysis is aimed at determination of displacements in elastic-perfectly plastic frames, in the case of monotonically increasing loads. Spread of partial plasticity from hinges and change of geometry on the conditions of equilibrium are not included. Extremum energy principles and linear programming methods are employed to solve the problem. Both the kinematic and the static formulations of the problem are presented. The mathematical models of the formulations constitute a dual pair of linear programming problems.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030310
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  • 182
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    Use of optimization methods to solve heat convection problems with unknown wall boundary conditions (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 405-413 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In convection heat transfer problems, it is convenient to solve the governing differential equations by using straightforward marching techniques for numerical integration. However, the boundary layer equations in these heat transfer problems are not of the initial value type even though they are parabolic equations. Consequently marching techniques are not successful until correct initial values are known. A means of determining these initial values is presented herein. Selected optimization methods are utilized in conjunction with marching integration techniques to solve third- and fourth-order ordinary differential equations which have three unknown initial boundary conditions. Two optimization methods, one deterministic and the other non-deterministic in nature, are used both independently and in combination as determined by the particular circumstances. Two applications are used to demonstrate the technique and comparison is made with existing solutions.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030309
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  • 183
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    Lamellar and interlamellar structure in melt-crystallized polyethylene. II. Lamellar spacing, interlamellar thickness, interlamellar density, and stacking disorder (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 85-114 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Measurements of the small-angle scattering power and the degree of crystallinity in melt-crystallized high-density polyethylene have been used to evaluate the “amorphous” density in situ by the relation, \documentclass{article}\pagestyle{empty}\begin{document}$ (2\pi/V)\int_0^\infty {S\tilde g} (S)dS = (\rho_{\rm c} - \rho_{\rm a})^2 \upsilon_{{\rm er}} (1 - \upsilon_{{\rm er}}) $\end{document} where V is the irradiated volume and ḡ(S) is the “slit-smeared” absolute intensity. The amorphous density is a function of sample history and is always higher than the extrapolated melt density. After slit-height correction, and within the experimental error, the ratio of the two observed long periods is 2:1 at all temperatures (25--126°C). The lamellar thickness and the average interlamellar spacing are obtained from the degree of crystallinity and the first corrected long period. At increasing temperatures between 25°C and 110°C, the lamellae become thinner while the interlamellar zone expands by almost half. Over this range the changes are reversible with temperature. Above 110°C, both the lamellae and the interlamellar region expand with temperature. The thickening is partially reversible upon recooling. Other results obtained include measurements of stacking disorder and of microstructural changes with crystallization temperature and with time at ambient temperature.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090107
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  • 184
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    Electronic Resource
    Planar organosilicon polymers (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 143-160 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Work on two sheet organosilicon polymers, one derived from the mineral chrysotile and the other from the mineral apophyllite, is described. This work provides direct evidence that both these polymers are composed of sheets. In addition, it shows that in the chrysotile-derived polymer the sheets curl into scrolls, and that in the apophyllite-derived polymer the sheets are essentially flat.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090110
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  • 185
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    Electronic Resource
    Viscoelastic behavior of low molecular weight polystyrene (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 209-243 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The shear creep and creep recovery behavior of narrow molecular weight distribution polystyrene samples of low molecular weight, 1.1 × 103, 3.4 × 103, and 1.57 × 104 are reported as a function of temperature, near and above the glass temperature. Time-temperature equivalence for the total creep compliance is found to be nonapplicable, and in fact the steady-state recoverable compliance, Je, is a strong function of temperature. The time-scale shift factors for the recoverable compliance are analyzed in the light of free volume theory. Viscosity data are presented for samples with molecular weights between 1.1 × 103 and 6.0 × 105. The temperature dependence of the characteristic time constant ηJe can be explained in terms of free volume concepts whereas that of viscosity η cannot. Effects of residual molecular weight heterogeneity are demonstrated.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090202
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  • 186
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    Scattering of light by deformed three-dimensional spherulites (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 295-311 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A theoretical calculation of the Hv light-scattering patterns for deformed three-dimensional spherulites is presented. Affine deformation is assumed. The optic axis of the scattering element is allowed to lie at an arbitrary angle ß to the radius which is permitted to change in the course of the deformation in a manner that may depend upon the angular location in the spherulite. The consequences of twisting of the optic axis about the spherulite radius are also explored.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090206
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  • 187
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    Adsorption of polydimethylsiloxanes from solution on glass (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 331-343 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The adsorption of polydimethylsiloxane polymers from solution on glass has been studied. The amount of polymer adsorbed depends markedly on the solvent because of specific solvent - surface interactions. The presence of silanol groups in the polymer, particularly as endgroups, markedly increases the amount of polymer adsorbed. Large differences are shown between the adsorption of the commercially available, and fully trimethylsilylated polydimethylsiloxanes of narrow molecular weight distribut on. Possible adsorption mechanisms are discussed.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090208
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  • 188
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    Composition equation for block copolymers (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 383-384 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090214
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  • 189
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    Long-chain branching in low-density polyethylene (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 421-430 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A method is given for the analysis of long-chain branching in polymers by using combined GPC and intrinsic viscosity measurements. A computer program was written to evaluate branching indices by a tabular, iterative method. The method was applied to the evaluation of long-chain branching in low-density polyethylene.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090303
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  • 190
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    Side-chain relaxation in stereoregular poly(isobutyl methacrylate) (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 431-435 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effects of stereoregularity on the low-temperature relaxation processes were studied by dynamic mechanical measurements on isotactic and syndiotactic polyisobutyl methacrylates (iso-PiBMA and syn-PiBMA). The α, β, and γ relaxation processes were observed in both stereoregular forms. Both the α, and β loss peaks were at lower temperatures for iso-PiBMA than for syn-PiBMA. The γ loss peak was observed at about -155°C at 30 Hz for both forms, and the apparent activation energy of this process was same for both samples within experimental error (6.7 ± 0.5 kcal/mole). It was reduced from these results that the α and β processes are both considerably influenced by the isotactic configuration but the γ process is not.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090304
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  • 191
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    Polyphenylenes (1971)
    Hoboken, NJ : Wiley-Blackwell
    Journal of Polymer Science: Macromolecular Reviews 5 (1971), S. 385-430 
    Details
    ISSN: 0076-2083
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.230050105
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  • 192
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    Stereochemistry of poly(vinyl alcohol) (1971)
    Hoboken, NJ : Wiley-Blackwell
    Journal of Polymer Science: Macromolecular Reviews 5 (1971), S. 431-540 
    Details
    ISSN: 0076-2083
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Additional Material: 41 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.230050106
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  • 193
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    Studies on formaldehyde condensation resins. XIII. Gelation of acetoguanamine-formaldehyde resin (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 15-26 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The gelation reaction of acetoguanamine with formaldehyde was investigated in the light of the gelation theory for tetrafunctional amino resins described in the previous paper. The gel time and extents of reaction of formaldehyde, amino groups, and imino groups varied with the molar ratio in the feed, but values of K (the ratio of the rate constant for condensation to that for addition) and k (the ratio of the rate constant for addition of the imino group to that of the amino group) were nearly constant. When the catalyst concentration was increased, the gel time, extents of reaction of each functional group, and the values of K and k varied; in particular K increased markedly. From the results of varying the molar ratio and concentration of acidic catalyst, it was found that the number of methylol groups per molecule of acetoguanamine at the gel point was influenced by the reaction conditions but the number of methylene linkages per molecular of acetoguanamine was nearly constant at about 0.6, regardless of reaction conditions. The number-average molecular weights up to the gel point varied with the reaction conditions, but at the gel point they were all nearly constant at about 385.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090102
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  • 194
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    Electronic Resource
    Ultraviolet photoelectric effects in polyethylene (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 543-555 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Photocurrents developed in polyethylene in the wavelength range 360-180 nm have been measured. The action spectra show features which can be related to the corresponding features in the absorption spectrum, and in addition there is electron injection from the metal electrode at a wavelength determined by the electrode material. The time dependence of the response indicates that a long-lived space charge is formed in the material.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090312
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  • 195
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    Electronic Resource
    Photocurrents in simple polymer systems. II (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 569-576 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Large photocurrents have been observed in films of some simple polymers (containing no π-orbitals), of which poly(vinyl fluoride) is a typical example. Not only are the currents large (up to 10-5 A/cm2) but also they are capable of being excited by light in the visible wavelength region where absorption by the polymer is too low to be detectable. The results indicate that the effects are electronic, rather than ionic, in nature.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090314
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  • 196
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    Some probability relations in multicomponent copolymers (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 577-584 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: It was previously shown that for a stationary random copolymer of A, B, and C, we have in general p(AB) + p(AC) = p(BA) + p(CA), etc., in place of p(AB) = p(BA) which is valid for a stationary binary copolymer. Here, p(AB) for example, is the probability that a randomly picked pair of consecutive comonomers in the polymer consists of an A followed by a B. For a stationary ternary copolymer produced by a first-order Markovian addition mechanism, we show that PABPBCPCA/PACPCBPBA = k, where k is a constant characteristic of a particular set of three monomers but independent of its composition. Here, PAB is the conditional probability of finding a monomer of B given that its immediate predecessor is an A. We further show that if the individual rate constants of the monomer additions involved take a special form such as used in the Alfrey-Price Q-e scheme, then we have k = 1 irrespective of the kinds of monomers, and in addition we have p(AB) = p(BA), p(AC) = p(CA), etc. Thus, although these latter results were previously proposed by Ham as an alternative basis to supplant the Q-e scheme, they may rather be regarded as mathematical consequences of special assumptions adopted for the form of the individual rate constants. For a stationary random copolymer of four components A, B, C, and D, we have p(AB) + p(AC) + p(AD) = p(BA) + p(CA) + p(DA), etc., in general. For a first-order Markovian four-component copolymer, we show that there are seven different combinations of the conditional probabilities that are constants (k1, k2,…, k1) independent of the monomer composition. Again, if we assume the same special form for the rate constants involved, we find that all the seven constants k1, k2, …, k7 reduce to unity and p(XY) = p(YX) for X,Y, = A, B, C, D.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090401
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  • 197
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    Laser-Raman spectra of vinyl chloride-vinylidene chloride copolymers (1971)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 717-729 
    Details
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Several copolymers as well as homopolymers of vinylidene chloride and vinyl chloride have been examined by Raman spectroscopy. Probabilities of concentrations of monomer sequences have been calculated from known reactivity ratios. Surface scattering intensities at some frequencies were found to be linearly proportional to specific microstructure concentrations. Normalization of scattering intensities was accomplished using the intensity of the CH2 asymmetric stretching mode at 2926 cm-1, which is common to all samples examined. Good correlation was found for the concentrations of comonomer sequences {B}, {BB}, {BBB}, {AA} and {AAAA} in which A denotes vinylidene chloride and B vinyl chloride.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1971.160090411
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  • 198
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    Comments on “an analytical solution to tung's axial dispersion equation. Applications in gel permeation chromatography” (1971)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 15 (1971), S. 247-250 
    Details
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    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
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/app.1971.070150121
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  • 199
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    Permeability of polyethylene film to organic vapors (1971)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 15 (1971), S. 327-339 
    Details
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    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 permeabilities of polyethylene film to vapors of 19 organic compounds at temperatures of 21°C, 38°C, and 49°C were measured by a sorption method. The film was formed into a pouch, which was filled with silica gel, sealed, and suspended in a saturated atmosphere. The permeability was calculated from the steady-state rate of the gain in weight. The permeability data were correlated with the Hildebrand solubility parameters of the organic substances.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/app.1971.070150207
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  • 200
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    Flow of viscous fluid through a circular aperture (1971)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 15 (1971), S. 369-379 
    Details
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    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 creeping flow of a highly viscous incompressible fluid through a circular aperture located in an infinitely wide horizontal plate is analyzed by solving Navier-Stokes equations without inertia terms. Solutions for vertical and radial velocities as well as pressure have been obtained in terms of integral equations with an undetermined Kernal function. This function has been evaluated by assuming several different velocity distributions at the aperture, and the corresponding pressure drop for each case has been calculated. The results show that the pressure loss for a given flow rate goes through a minimum as the assumed velocity profile changes from flat to parabolic. Based on the minimum energy dissipation theorem of Helmholtz, the most appropriate velocity distribution is discussed. Experimental data obtained using sharp-edged orifices are compared with theoretical predictions.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/app.1971.070150210
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