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  • 1985-1989  (3,100)
  • 1890-1899
  • 1860-1869
  • Engineering General  (2,473)
  • Physical Chemistry  (627)
  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 26-34 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A set of 4-monosubstituted cyclopentenes, , were synthesized and their relative rates (kX/kH) for bromination and chlorination were determined in methanol, ethanol and acetic acid at 25 °C by competitive method. log(kX/kH) for most of the substituents can be correlated by means of Taft's equation, log(kX/kH) = ρI σI + C. In methanol ρI, Br2 = -2·91, ρI, Cl2 = -0·49, in ethanol ρI, Br2 = -3·07, ρI, Cl2 = -0·70 and in acetic acid ρI, Br2 = -1·64, ρI, Cl2 = -0·65. The presence of C(〈0) is due to a constant steric effect. The deviation of X = H is ascribed to the absence of the steric effect and that of X = CO2Me and CO2Et is accounted for in terms of anchimeric assistance. For chlorination no anchimeric assistance was observed.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 43-50 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The cyclic vinyl ether dihydro-1,4-dioxin is converted to its cyclic hemiacetal hydration product, 2-hydroxy-1,4-dioxane, in aqueous solution by an acid-catalyzed reaction for which kH+ = 1·80 × 10-5 M-1 S-1 at 25°C. This reactivity and the solvent isotope effect kH+/kD+ = 2·2 show that the reaction occurs by rate-determining proton transfer from catalyst to substrate and not by a pre-equilibrium mechanism as recently proposed.2
    Additional Material: 1 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 57-88 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The cation radical vinylcyclobutane (VCB) rearrangement is found to be a reaction of substantial scope, synthetic utility, and exceptional kinetic facility. In conjuction with cation radical cyclobutanation, it constitutes an effective method for net (indirect) Diels-Alder addition to electron rich dienophiles. Reactions can be carried out with either aminium salt or photosensitized electron transfer (PET) initiation and are powerfully facilitated by ionizable substituents such as p-anisyl, phenylthio, and phenoxy at the 2-position of the vinylcyclobutane. The intramolecularity of the reaction is clearly established and in four discrete systems preferred sr (suprafacial/retention) stereochemistry is observed. A theoretical basis for sr stereochemistry in the cation radical VCB rearrangement is advanced. The transition state for the reaction is considered to be similar to that for the direct cation radical Diels-Alder cycloaddition, another cation radical pericyclic reaction which converges on the same product. This model of the VCB rearrangement transition state is used to rationalize the strong rate-retarding effect of a Z-methyl substituent attached to the vinyl group and of a methyl substituent at the 4-position of the vinylcyclobutane ring cis to the vinyl substituent.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 110-116 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The transamination reaction of α-amino acids with glyoxylic acid as catalyzed by copper(II) ions was investigated kinetically in an aqueous medium at pH 5·0 and 30·0°C. L-Phenylalanine transferred its amino group to glyoxylic acid most readily among seven different amino acids used here in the single-walled bilayer vesicle formed with N,N-dihexadecyl-Nα-[6-(trimethylammonio)hexanoyl]-L-histidinamide bromide (N+C5His2C16). Such rate enhancement was found to originate from the cooperative trifunctional catalysis: a coordination effect exercised by copper(II) ions, a general acid-base catalysis by the imidazolyl group of the lipid, and a hydrophobic field effect provided by the bilayer vesicle. Lack of any of the three functions failed to give out significant rate enhancement. As regards correlation between the reactivity and the nature of α-amino acids, the copper(II)-catalyzed transamination was progressively enhanced as hydrophobicity of the α-amino acid was increased in the N+C5His2C16 vesicle.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 1-14 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The mechanism of aromatic nucleophilic substitutions by amines in protic solvents is well established; on the contrary the mechanism/s of the reactions in aprotic solvents is/are still subject of controversy. The present paper describes several systems for which fourth-order kinetics (third-order in amine) were observed. A mechanism is proposed to account for this as well as other observation such as: overall negative energies of activation, quadratic dependence of kA with non-nucleophilic tertiary bases, spectacular effects of hydrogen-bond donor (HBD) and hydrogen-bond acceptor (HBA) catalysts, etc. Other alternative mechanisms are also discussed.
    Additional Material: 5 Ill.
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  • 7
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics and mechanisms of the reactions between 1-phenylethyl benzenesulfonates (1-PEB) with N,N-dimethylanilines are investigated in methanol at 35·0°C. Reactivity and selectivity trends were found to be similar to those for the reactions of 1-PEB with anilines, but the magnitudes of cross interaction constants, ρXZ, between substituents X in the nucleophile and Z in the leaving group were substantially smaller indicating no hydrogen-bond bypass bridge formation in the transition state. However, the magnitude of ρXZ suggested a direct electrostatic interaction between the reaction centers in the nucleophile and leaving group in the frontside nucleophilic attack with a loose transition state structure.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 89-92 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Spectral characteristics of several simple substituted B,B-bis(mesityl)pyrroloboranes are reported which support a theoretical treatment by Bonacic-Koutecky and Michl (J. Am. Chem. Soc. 107, 1765 (1985)) describing the excited states of simple aminoboranes as an example of twisted internal charge transfer. In the aminoboranes the pyrrolo moiety functions as the electron donor group and the empty p-orbital of the boron atom as the acceptor.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 183-186 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The harmonic vibrational frequencies were calculated analytically at the 6-31** level for azetidine using the GAUSSIAN 82 program. The results strongly indicate the presence of several errors in a recent assignment of the fundamentals of azetidine based on a normal coordinate analysis and a revised assignment is suggested. It is concluded that reliable vibrational data for azetidine in the gas phase are needed in order to resolve the remaining ambiguities in the interpretation of the spectra.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 205-213 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Mechanism of the Grignard reactions of aromatic ketones in THF was studied by spectroscopic and kinetic methods. The stable radical intermediates generated in the initial electron transfer from Grignard reagent to ketones are in a state of aggregated dimer of corresponding ion-radical pairs; in which two ketone anion radicals are bridged by a dimer di-cation of Grignard reagent. Subsequent alkyl radical transfer from dimeric Grignard reagent cation moiety to ketone anion radical aggregated each other are promoted by a participation of another neutral Grignard reagent. Proposed mechanism by present authors is able to explain well addition products/reduction products ratios in the Grignard reactions.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 232-242 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Characteristic vector analysis of a set of six physical and empirical parameters of 103 commonly used organic solvents (bp, ∊r, μ, nD, ETN, and δ) gives four vectors describing 95% of the total data variability. Non-hierarchical cluster analysis, applied to our results, leads to ten separate classes of organic solvents.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 103-109 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A preliminary theoretical study of the mechanisms for the reactions of the perchlorofluoroethanes CF2ClCCl3 (1), CF2ClCCl2F (2) and CF3CCl3 (3), with nucleophiles has been carried out by the MNDO method, following the experimentally suggested process shown in Scheme 1. The unlikely chlorophilic attack in the first step of Scheme 1 has been shown to be feasible for 1, 2 and 3 by analysis of the MO interactions. The second step has been found to be affected by the anionic hyperconjugation which stabilizes the anions CF2ClCCl2- (4), CF2ClCClF- (5) and CF3CCl2- (6) and would make reactions (2) (the second step) unfeasible in gas phase, but in solution reaction (2) may still easily occur for 4 and 5.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 146-160 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The alkaline hydrolysis of several alkylphosphonates and alkylphosphonyl chlorides has been investigated by molecular mechanics calculations (MM2, 1985 version). The difference of the steric energies (ΔE) between tetracoordinate substrate and pentacoordinate transition state of phosphorus compounds represents the activation energy (ΔE≠) in hydrolysis. The change of ΔE for various alkyl groups relative to methyl group (ΔΔER) is suggested as a measure of the steric effect of substituents. Thus the correlation analysis involving log k and ΔΔER of the branched alkyl group gives good results and it is reasonable to anticipate that analogous treatment using ΔΔER for the straight chain alkyl group is not satisfactory owing to the minor contribution of steric effect of the latter. However, the multiple regression analysis of log k with ΔΔER and Taft's σ* provides very good results. As shown by us, for the hydrolytic reactions studied, the proposed ΔΔER is much better than Taft's Es and Charton's ν, the commonly used well-known steric parameters in the chemistry of carbon compounds.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 161-176 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Cyclobutanediyl (2) has been studied in both its singlet and triplet states by ab initio electronic structure theory. The triplet, which is the ground state of the molecule, exists in both C2h and C2v forms which interconvert via a Cs transition state. For the singlet, only a C2h form is found. It passes, via a Cs transition state, onto the C2v surface on which bicyclobutane (3) is the only minimum. The ring-flipping (inversion) process in 3 includes the singlet biradical as an intermediate, and involves a novel, non-least motion path similar to one previously proposed by Gassman. Semiclassical periodic orbit theory indicates that the various minima on both the singlet and triplet surfaces can interconvert via quantum mechanical tunneling.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 169-183 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic behaviour of marine vehicles in extreme sea states is a matter of great concern following some recent and dramatic mishaps. The complex problem of its prediction can be approached from the study, yet of broader scope, of non-linear dynamic systems subjected to stochastic excitations. However, a general non-linear stochastic dynamic theory is not yet available.A new technique, the so-called linearize-and-match method, for predicting the response statistics of non-linear systems, is presented. Essentially, the technique involves the construction of an infinite series of linear systems aimed at the prediction of the response statistical moments of a given order.The linear systems are successively defined by linearizing the original, non-linear system and matching the Volterra functional model response statistics to the desired order. The linear system for predicting second order statistics is shown to coincide with the one obtained using the method of equivalent linearization.Response probability distributions can be constructed from the knowledge of such statistics. Particular attention is devoted to the distribution of maximum entropy and its justification in such underdetermined moment problems.Finally, applications to the roll motion of ships serve to exemplify as well as to assess the accuracy and the versatility of the overall method. Response distributions of maxima so predicted compare very well with digital simulation estimates.
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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 215-230 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a mathematical model is presented, based on the application of an averaging technique, in which the equations governing the behaviour of saturated porous media are integrated (averaged) over the smallest dimension of the domain of the problem (thickness). This results in a two dimensional model, in which the three dimensional nature of the problem is accounted for. In fact, the solution is sought in terms of the mean values over the thickness of the field variables and of the transverse displacement components. For the solution of the resulting governing equations a partitioned procedure is employed, which improves the efficiency of the method. The proposed model is very useful in solving problems in which the spatial nature prevents the applications of two dimensional models.Examples are presented, which illustrate the validity of this approach.
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  • 18
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 233-255 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element analysis was used to study the fracture toughening of a ceramic by a stress induced dilatant transformation of second phase particles. The finite element method was based on a continuum theory which modelled the composite as subcritical material. Transient crack growth was simulated in the finite element mesh by a nodal release technique. The crack's remote tensile opening load was adjusted to maintain the near-tip energy release rate at the level necessary for crack advance. The transformation zone surrounding the crack developed as the crack propagated through the composite. Resistance curves were computed from the analysis; and the results show that during crack advance maximum toughness is achieved before a steady state is reached.The toughening effect of a crack-bridging ductile phase in a brittle material may be predicted if ligament deformation is characterized. A plastically deforming ligament constrained by surrounding elastic matrix material is modelled using finite elements and the relevant toughness enhancement information extracted. Comparison is made to model experiments as well as to toughness measured for technologically important materials. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.
    Additional Material: 21 Ill.
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  • 19
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 323-341 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension-compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0n, φm]s with severed central plies [φ], and of stacking order [02, +45, 02, -45, 0, 90]s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.
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  • 20
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 429-436 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation in the frequency domain for the viscoelastic material behaviour of structural elements. This approach is equally valid for deterministic forces, but also in the case of probabilistic descriptions of those forces. The method takes advantage of readily available experimental data and shows how to introduce them in e.g. finite element formulations.
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  • 21
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 449-452 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 22
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 483-499 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Chebyshev acceleration for a symmetrizable basic iterative method u(n+1) = Gu(n) + k; requires estimates of the extreme eigenvalues m(G) and M(G) of the iteration matrix G. Adaptive procedures are often used in order to obtain good estimates for m(G) and M(G). Some existing adaptive procedures are able to give an estimate of either m(G) or M(G) but not both on any given iteration. In this paper we present an adaptive procedure which can estimate both m(G) and M(G) at the same time and which has other useful properties. Numerical results are given which show the new procedure usually requires fewer iterations than previous procedures.
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  • 23
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 523-546 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three-dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three-dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as pα, where α is 1·4-1·5 for the model problems.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 559-570 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A matrix relationship connecting the Jacobi and the Symmetric Successive Overrelaxation (SSOR) matrices associated with a k-cyclic consistently ordered matrix A is presented. Next the equivalence of the SSOR method and a certain monoparametric k-step one for the solution of the linear algebraic system Ax = b is established. The aforementioned equivalence can be exploited to derive regions of convergence, optimum parameters involved, etc. of the two iterative methods above. This is done by studying the simplest of the two methods that is the monoparametric k-step one. To show how the idea works the case k = 2 is very briefly discussed.
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  • 25
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 637-654 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard implementations of iterative solvers for finite element and finite difference methods frequently use a diagonal (Jacobi) preconditioner, particularly for element-by-element schemes. However, for such methods the actual order of the condition number with respect to mesh size is not reduced by the preconditioner. In the present paper we describe an iterative method where, in addition, the condition number is reduced by an order of magnitude. Moreover, the scheme may also be implemented as an element-by-element method. The method uses a generalized SSOR preconditioner and a wave front or multi-frontal ordering of the mesh nodes. For a general irregular finite element mesh a striped irregular wave front ordering may be used. The performance of the method as well as various iterative acceleration techniques for a parallel computer are examined in the numerical studies.
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. ii 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 27
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 43-73 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a geometrically non-linear formulation (GNL) for the three dimensional curved beam elements using the total Lagrangian approach. The element geometry is constructed using co-ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions. The element displacement field is described using three translations at the element nodes and three rotations about the local axesThe element displacement field has also been described in the literature using Euler parameters, Milenkovic parameters, or Rodriges parameters representing the effects of large rotations.. The GNL three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining non-linear nodal terms in the definition of the element displacement field, and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper non-linear functions representing the effects of nodal rotations. The details of the element properties are presented and discussed. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements. A comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps, large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations. The displacement approximation of these elements is fully compatible with the isoparametric curved shell elements (with large rotations), and since the elements possess offset capability, these elements can also serve as stiffeners for the curved shells.
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 75-93 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The alternative to quadrature, as a procedure for dealing with the integrations required in the direct boundary element method (DBEM), is to carry out the integration analytically and code the results directly. The potential benefits are efficient computer programs; the avoidance of numerical instability; and generally, better accuracy. The technique is developed in this paper.Serious problems arise when Gauss quadrature is employed for the integration of functions which contain, or are close to singularities. A numerical integration approach may fail at the first stage of the analysis, that is, during the assembly of the discrete equations; or it may fail at the subsequent stage of computing domain points near the boundary. The severity of the problem is dependent both on the strength of the singularity, and on geometry. These points are illustrated with examples.
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 127-144 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The successive quadratic programming (SQP) method is used with the finite element method (FEM) to solve frictionless geometrically non-linear contact problems involving large deformations of the elastica in the presence of flat rigid walls. To formulate the SQP problems, the potential energy (PE) is expanded in a Taylor series of second order in displacement increments about a configuration near a contact solution. The SQP problems consist of minimizing the Taylor expansion of the PE subject to the inequality constraints which represent contact. The quadratic programming (QP) method is made part of a Newton-Raphson (NR) search in which the QP corrections are made when a NR step does not satisfy the constraints. A revised simplex method developed by Rusin is used to solve the QP problems. The elastica is modelled with a total Lagrangian FEM developed by Fried. Solutions are obtained for the end loaded buckled elastica in point contact with a rigid wall and for a uniformly loaded elastica in regional contact with a rigid wall. The problems are also solved using a penalty method. The results obtained for the point contact problem are compared to an analytical solution. Calculations were made to obtain numerical information on maximum load step size and the number of inverse operations required for each load step. Cases in which the elastica stiffened substantially as a result of the initiation of contact are also discussed.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 261-277 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basic concept, formulation and numerical application of a fully automatic version of the finite difference method (FDM) on a two-dimensional manifold embedded in three-dimensional Euclidean space are presented. This version of the FDM was developed in order to enable automatic solution of problems formulated in arbitrary curvilinear co-ordinate systems in terms of covariant derivatives (e.g. shell equations).In the classical version of the FDM all operations in the curvilinear co-ordinates (the derivation of base vectors, curvature tensors and so on) have to be performed manually. The goal of the present work was to transfer this job to a computer, in order to minimize the user's effort during the numerical formulation of the physical problem. The relevant version of the fully automatized program FIDAMF, based on the FDM on arbitrary irregular grids,1,2 has been worked out. This code performs automatically all stages of the numerical analysis, starting from the mesh generation and approximation of the shape of the manifold, through computation of necessary objects on this manifold, to the solution of linear or non-linear problems formulated in terms of covariant derivatives.The method has been extended to the analysis of problems in which the co-ordinate system changes during the computation (e.g. the analysis of large deformations in the convectional description). This version of the curvilinear FDM was applied to the analysis of large deformations of hyperelastic membrane shells.The approach and the numerical routines, although used here with the FDM, can be combined with any other approximation method, in particular the finite element method.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 359-368 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct-search optimization strategy, involving pattern-searches, pattern-moves and a simplex algorithm, has been applied to a number of frequency-domain circuit problems. We show that an approximate minimax result can be obtained with our simple approach, which includes using a modified minimax error function. In the examples attempted, the method comes quite close to the accuracy, if not the efficiency, of true minimax optimizers, and yields an accuracy as good as or better than a least-pth (p = 10) gradient optimizer. The method is broadly appropriate wherever it is difficult or inconvenient to calculate the gradients required for conventional minimax optimization.
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  • 32
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 431-443 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of the recently presented hybrid-Trefftz (HT) p-version elements1 has thus far been restricted to straight-sided polygonal elements. The present paper removes this limitation. Two alternative formulations are studied. In the first one any curvilinear geometry is represented accurately but the rigid body modes are recovered only in the limit as the p-refinement level is increased. In contrast, the second formulation represents the rigid modes exactly while the actual curvilinear geometry is approached with increasing accuracy as the p-refinement level is increased. The practical efficiency of the two alternative approaches is studied and assessed on pertinent examples of thin plates in bending.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 477-478 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 34
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 483-487 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 35
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 533-560 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the formulation and the evaluation of a new three node, nine d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the DKT (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 593-607 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The introduction of composite materials is having a profound effect on the design process. Because these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require a more integrated multidisciplinary design process. Because of the complexity of the design process numerical optimization methods are required.The present paper is focused on a major difficulty associated with the multidisciplinary design optimization process - its enormous computational cost. We consider two approaches for reducing this computational burden: (i)development of efficient methods for cross-sensitivity calculation using perturbation methods; and (ii) the use of approximate numerical optimization procedures. Our efforts are concentrated upon combined aerodynamic-structural optimization. Results are presented for the integrated design of a sailplane wing. The impact of our computational procedures on the computational costs of integrated designs is discussed.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 645-666 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical strategy for the simulation of structural modifications by virtual distortions is proposed. Two cases of structural modification are considered: the first concerns modifications of material distribution, and the second modifications of local constitutive relations (e.g. unilateral constraints for stresses or deformations). A formaulation of the fundamental equations of the simulation method is presented. These equations are applicable to the general structural modification problem of a truss-like structure. Then numerical algorithms which refer to particular applications, such as progressive collapse analysis or the analysis of structures with gaps, are discussed.The versatility of the method is illustrated with a number of examples, and the computational advantages of structural modification by the virtual distortion method are discussed.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 725-726 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 39
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 733-752 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An adjoint approach is presented for the design sensitivity analysis of transient conduction problems. Variations of a general design functional are expressed in explicit form with respect to all design quantities, i.e. material properties, shape, applied thermal loads including convection, and initial conditions. The methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations. Finite element implementation of the method is discussed and an example is provided. Some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed. These involve the application of impulse loadings and Dirac temperature fields in the adjoint loadings.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 801-815 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we compare direct and preconditioned iterative methods for the solution of nonsymmetric, sparse systems of linear algebraic equations. These problems occur in finite difference and finite element simulations of semiconductor devices, and fluid flow problems.We consider five iterative methods that appear to be the most promising for this class of problems: the biconjugate gradient method, the conjugate gradient squared method, the generalized minimal residual method, the generalized conjugate residual method and the method of orthogonal minimization. Each of these methods was tested using similar preconditioning (incomplete LU factorization) on a set of large, sparse matrices arising from finite element simulation of semiconductor devices. Results are shown where we compare the computation time and memory requirements for each of these methods against one another, as well as against a direct method that uses LU factorization to solve these problems.The results of our numerical experiments show that preconditioned iterative methods are a practical alternative to direct methods in the solution of large, sparse systems of equations, and can offer significant savings in storage and CPU time.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 861-877 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of a numerical study of swirling and non-swirling combustor flows with and without density variations are presented. Constant-density arguments are used to justify closure assumptions invoked for the transport equations for turbulent momentum and scalar fluxes, which are written in terms of density-weighted variables. Comparisons are carried out with measurements obtained from three different axisymmetric model combustors. The three experiments cover recirculating flow, swirling flow and variable-density, swirling flow inside model combustors. Together, they offer wide ranging flow conditions to test the validity of the models. Results show that the Reynolds stress/flux models do a credible job of predicting constant-density, swirling and non-swirling combustor flows with passive scalar transport. However, their improvements over algebraic stress/flux models are marginal. The extension of the constant-density models to variable-density flow calculations shows that the models are equally valid for such flows. Therefore, the present results argue well for the adoption of constant-density models for variable-density flows until a successfully validated variable-density model is available.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 37-55 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: With a boundary-fitted curvilinear co-ordinate system, the parabolic approximation is applied to the mildslope equation to describe the wave propagation. Both refraction and diffraction are included in the numerical model. Because the shoreline coincides with one of the curvilinear co-ordinates, the numerical model can be used to compute wave propagations near an irregular shoreline.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 103-112 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 129-144 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A global three dimensional model for numerical weather prediction is described. It uses spheric harmonic basis functions with triangular truncation in the horizontal and a finite element discretization for the vertical. Model experiments are used to compare this model with another version, which uses a finite difference scheme for vertical discretization.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 185-193 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper deals with non-Fickian dispersion of inert solutes in random permeability fields. Attention is focused critically on the statistical characterization of the porous medium which affects pollutant dispersion in groundwater. After a brief account of recent results of stochastic theories of transport in porous media and of the fundamental indications of large-scale field experiments, it is inferred from numerical studies that the particular choice of an analytical form of covariance of log-conductivity has a poor influence on the overall dispersion process. In fact, different covariance structures with the same macroscale (a measure of the distance between two points beyond which the permeability ceases to be correlated) yield very similar dispersion processes. The result has a noteworthy bearing on field studies of pollutant dispersion in groundwater because it underlines the reliability of exponential correlation structures yielding analytical expression for time-varying macrodispersion coefficients.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 231-231 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 47
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1803-1812 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A consistent tangent stiffness matrix for the analysis of non-linear contact problems is presented. The associated element has three or four nodes and establishes contact between three-dimensional structures like solids and shells. It accounts for the non-linear kinematics of large deformation analysis and guarantees a quadratic convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.
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  • 48
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1855-1874 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Two domain-by-domain algorithms, suitable for coarse-grained parallel processing analysis of the transient structural dynamics equation, are investigated for accuracy. The application under specific consideration is the analysis of three-dimensional framed structures subjected to time-varying loading. The domain-by-domain approaches attempt to include the advantageous aspects of both conditionally stable explicit algorithms, which require no simultaneous solution of equations and employ simple communication, and unconditionally stable implicit algorithms, which permit large time steps. The alternating group explicit algorithm is developed for finite element analysis, and its accuracy is investigated for a linear formulation. The group implicit algorithm is extended to non-linear finite element analysis, and its accuracy is investigated for the frame dynamics application. Both algorithms are shown to provide inadequate accuracy for practical time step sizes.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1929-1949 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we propose an original numerical method to get upper and lower bounds for the eigenfrequencies of an elastic structure.This method is based on a ‘static’ formulation for eigenvalue problems built up from a new quotient Rs which is defined on a load space. From Rs properties, upper and lower bounds for the exact eigenfrequencies are proved. The application of the method requires the solution of an eigenvalue problem of finite dimension and the computation of a constant which is characteristic of the discretization subspace. Results of numerical tests are given for the vibration problem of an elastic clamped membrane.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1965-1967 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1971-1975 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2041-2058 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems. The basic idea is to generate such an information at the expense of only one more ‘virtual load case’ in the sensitivity analysis part of the finite element code. To achieve this goal a primal-dual approach is employed, that can also be interpreted as a sequential quadratic programming method.Another objective is to relate the proposed method to the well known family of approximation concepts techniques, where the primary optimization problem is transformed into a sequence of non-linear explicit subproblems. When restricted to diagonal second derivatives, the new approach can be viewed as a recursive convex programming method, similar to the ‘Convex Linearization’ method (CONLIN), and to its recent generalization, the ‘Method of Moving Asymptotes’ (MMA).This new method has been successfully tested on simple problems that can be solved in closed form, as well as on sizing optimization of trusses. In all cases the method converges faster than CONLIN, MMA or other approximation techniques based on reciprocal variables.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2203-2218 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The aim is to build up and test a numerical method to calculate the velocity of stationary two-dimensional flows. Both inviscid and viscous fluids are considered. They act in the unbounded domain surrounding a given profile and a stream function is introduced. A variational procedure, adapted to unbounded domains, reduces the problem to solving a finite sequence of hormonic equations, posed in bounded domains. Some profiles are tested using a finite element method.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2223-2238 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper, a Mindlin plate element is formulated based on the Hellinger-Reissner principle and the γ-technique. The stiffness consists of a constant stress (one-point quadrature) matrix and a stabilization matrix. The stabilization matrix is compared with those previously proposed. In addition, the element uses a projection to modify the nodal displacements so that the patch test is satisfied. The projection matrix is based on a mode decomposition. Several numerical cases are presented, and it is shown that the mode decomposition projection is necessary both for satisfaction of the patch test and convergence.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2307-2321 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method for the time domain identification of modal parameters of a vibrating structure using Z-transformation sequences is presented in this paper.This identification proceeds using the Z-transfer function of a vibrating structure from which an auto-regressive and moving-average (ARMA) model of the vibrating structure is derived. From this ARMA model and time domain data, the modal parameters can be identified. The time domain data can be obtained from single point or multiple shaker excitation modal testing. To demonstrate the application and efficiency of the method, a test on a simulated cantilever beam is presented.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2361-2381 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The dynamic behaviour of a saggy suspension cable under a moving load was investigated. First of all, the updated Lagrangian formulation and the finite element method were used to derive the property matrices of a saggy suspension cable in order to define the discretized equations of motion. Then, the Jacobi method was applied to the determination of the natural frequencies and the mode shapes of the suspended cable. The moving-load-induced dynamic responses of the saggy suspended cable were obtained by using the Newmark direct integration method incorporated with the Newton-Raphson iteration technique. The influence of some pertinent factors, such as speed of moving load, ratio of axial rigidity to total cable weight (AE/0m̄g0L) and ratio of moving load mass to total cable mass, is the key point of the dynamic analysis.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 211-236 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An a posteriori error estimator is presented which allows a good pointwise evaluation of the error in predicted stresses and can easily be implemented in existing FE codes. Although this estimator has especially been developed for and tested on p-version Hybrid-Trefftz (HT) elements, it is anticipated that it can also be applied to conventional conforming p-version elements. The practical efficiency of the estimator is illustrated through the solution of various plate bending problems by using the HT p-version Kirchhoff plate elements.2
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 245-260 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A numerical model is developed for computing two-dimensional circulation in coastal regions dominated by large tidal flat motion. This model is based on the shallow water momentum and continuity equations being operated upon by the Galerkin finite element method. The particular advantage of the model lies in its ability to accommodate a changing domain boundary. This is accomplished by adopting finite elements that change shape so as to consistently move with the water's edge. Application of the model to the Kuwait Bay is described, and the associated results on circulation are given.
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  • 59
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 315-329 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Electrostatic charging inside a tank is analysed numerically using the boundary integral method. The electrostatic charge is transmitted to the tank through a charged liquid. Profiles for the charge density and potential are obtained in the tank during the filling operation. The analysis is based on the equation governing the transport of charge and Poisson's equation. The results are characterized by two dimensionless parameters, the dimensionless Debye length given by the Debye length divided by the height of the tank, and the number Pe defined as a Peclet number. The results show where the maximum charge density and potential occur and give a prediction of when during the filling operation a hazardous situation may occur.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 385-414 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9-node shell element. The stabilization procedure can be justified based on the Hellinger-Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co-ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9-node element. Example problems show good accuracy and an almost optimal rate of convergence.
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  • 61
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2695-2707 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of ‘non-Delaunay’ line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified.An efficient algorithm is proposed for the construction of Delaunay triangulations over non-convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. In the mesh generation process, the Delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle. In contrast to convex domains, intersection between the proposed triangle and the domain boundary has to be checked; this can be simply done by considering only the ‘non-Delaunay’ segments on the generation front.Through the study of numerous examples of various characteristics, it is found that high-quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.
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  • 62
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2713-2714 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 63
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2715-2760 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this paper,1 the conceptual framework of a rate variational least squares formulation of a continuously deforming mixed-variable finite element method was presented for solving a single evolution equation. In Part II2 a system of ordinary differential equations with respect to time was derived for solving a system of three coupled evolution equations by the deforming grid mixed-variable least squares rate variational finite element method. The system of evolution equations describes the coupled heat flow, fluid flow and trace species transport in porous media under conditions when the flow velocities and constituent phase transitions induce sharp fronts in the solution domain. In this paper, we present the method we have adopted to integrate with respect to time the resulting spatially discretized system of non-linear ordinary differential equations. Next, we present computational results obtained using the code in which this deforming mixed finite element method was implemented. Because several features of the formulation are novel and have not been previously attempted, the problems were selected to exercise these features with the objective of demonstrating that the formulation is correct and that the numerical procedures adopted converge to the correct solutions.
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  • 64
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2839-2853 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Zienkiewicz-Zhu error estimator is shown to be effective in problems of plate flexure. When used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed, very fast adaptive convergence for results of specified accuracy is achieved.
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  • 65
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2889-2906 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The construction of changing sequences of irregular and nested triangulations, based on the use of conforming refinement/derefinement algorithms for triangulations, is presented and discussed. This strategy is particularly appropriate to combine adaptivity and full multigrid algorithms for dealing with moving fronts or fluid dynamics problems. It is shown that the quality of all the triangulations iteratively generated depends only on the geometric characteristics of the initial grid. A data structure suitable to create, manage and modify series of nested triangulations as well as the main features of the DEREF prototype package are described, and numerical examples are given.
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  • 66
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2923-2941 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified presentation of some popular continuation procedures used in the non-linear finite element analysis of structural mechanics is introduced. An extension of the elliptical constraint equation proposed by Crisfield is given. It is shown that in the proposed procedure real roots can always be obtained in solving the iterative change of the load parameter. Updated weighting factors are introduced in the constraint equation in order to get better convergence characteristics in the case when localized deformations occur. For bifurcation points a modification of Rheinboldt's branching procedure is presented. Post critical response after limit and bifurcation points is determined in some numerical examples.
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  • 67
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2191-2202 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note reports numerical experiments on the efficiency of simple error estimates derived earlier1 applied to incompressible mixed or related penalty type formulations. The rate of convergence and performance of various mixed elements is compared. Numerical results from a driven cavity and an incompressible elastic problem demonstrate that the T6B1/3D and T6/3C elements give a faster rate of convergence than the T6/1D element. However, in the case of a plane extrusion analysis (stronger singularity), the rate of convergence for the T6B1/3D element drops and is inferior to that of the T6/1D, while the T6/3C element still proves superior to the other two elements.
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  • 68
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2239-2255 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Timoshenko's and Vlasov's beam theories are combined to produce a C0 finite element formulation for arbitrary cross section thin-walled beams. Section properties are generated using a curvilinear co-ordinate system to describe the cross section dimensions. The element includes both shear and warping deformations caused by the bending moments and the bimoment. A Gauss quadrature order is employed which exactly integrates the bending and warping stiffness matrices and provides a reduced integration order for the shear stiffness matrices. Numerical results are presented for a channel section cantilever beam. The influence of shear deformation is investigated and the calculated results are shown to be in excellent agreement with the classical solutions.
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  • 69
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 929-942 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The virtual crack extension technique is a very efficient and accurate approach to fracture mechanics calculations in the numerical analysis of bodies containing cracks using the finite element method. A few variations of the technique have been described in the literature, and have been extensively used in linear elastic fracture mechanics, where good validation has frequently been available with accepted alternative solutions for standard tests. However, for non-linear materials extra complications arise in the technique, particularly in describing material response in a compatible manner. It is shown that, using few assumptions, a very competitive virtual crack extension technique based, on a direct minimization of potential energy is available for elastic non-linear elastic materials. Such materials can be closely approximated to elastic-plastic behaviour for monotonically increasing loads including mechanical, thermal and body force forms. The technique is described and demonstrated via examples to be in good agreement with alternative fracture parameter evaluations when evaluated in the same computer system, BERSAFE.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 979-979 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 71
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 71-85 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study of linear monochromatic wave propagation is presented, based on a theory of potentials. The usual Berkhoff equation has been extended by the addition of partially pervious solid boundary effects and the bed friction.The problem has been solved by a hybrid finite element method including the effect of singular local elements such as the end of breakwaters or wharfs. This numerical method confirms the interest in quadratic Lagrangian finite elements.The comparisons with analytical solutions and existing numerical results show the validity of the method. Some original examples also prove the good performance of the proposed computation method.As an example, the study of the erosion of the beach of Calvi Bay in Corsica, France is presented. The phenomenon had started already in 1960, but the problem began to be very severe four years ago, after the implementation of a new harbour in 1982 and buildings, hotels, restaurants, and a main sewer on the beach. To consider the impact of these constructions and other factors like waves, currents and geomorphological aspects, the studies were divided into four parts: sedimentological, currents, wave propagation and geomorphological.This paper will describe the results of a complete two years study on the site, from February 1986 to December 1987.Findings show that the erosion process is due to the rise of the relative sea level with, as a catalyst, tourist behaviour and the implementation of the new constructions.
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  • 72
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 153-167 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Jacket structures have many sub-sea appurtenances attached to them. For example, a typical jacket structure has hundreds of sacrificial anodes attached to its members. The fluid loading of these structures is calculated using Morison's formula. The force coefficients used in the equation are based on experiments carried out, for the most part, on single cylinders in laboratories in ideal flow. There are very few experimental data available for the fluid loading of cylinders with appurtenances. Moreover, it is not possible to calculate theoretically the loading on such configurations in flows of practical interest using approaches such as the finite element method. However, appurtenances can contribute significantly to the overall loading on a structure. This paper presents the preliminary theoretical work that has been carried out as part of a programme to establish a rational method for estimating the fluid loading on tubular members with appurtenances.
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  • 73
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    International Journal for Numerical Methods in Engineering 27 (1989) 
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    Keywords: Engineering ; Engineering General
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  • 74
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2943-2946 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 75
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 331-358 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite strip method is applied to the non-linear analysis of plate structures. Large deflection effects are included via first order non-linearities in the strain-displacement relations, and material non-linearities are included via the von Mises yield criterion and associated flow rule. The virtual work equations are integrated numerically using Gauss quadrature, and the resulting non-linear equations are solved by Newton-Raphson iteration. Numerical results are presented for many applications including uniformly loaded rectangular and I beams, and square plates with either simply supported or clamped ends (or edges). The results are compared with known results from analytical and/or finite element analyses. Finally, a uniformly loaded stiffened panel is analysed and the results are compared with finite element results. In all cases, the results indicate that a single bending mode in the strip direction is sufficient to yield engineering accuracy for design purposes.
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  • 76
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    International Journal for Numerical Methods in Engineering 28 (1989), S. ii 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 77
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2257-2273 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A multi-domain method of solving three-dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt r $\end{document} displacement and \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt r $\end{document} traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt r $\end{document} term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, II and III are obtained directly from crack-front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny-shaped crack.
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  • 78
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2339-2360 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structural analysis often involves the solution of a sparse system of linear equations using matrix factorization. For structural reanalysis problems, the system of equations is progressively changing and matrix factorization is required at each iteration step. In this paper, we study the problem of updating the structure of sparse matrix factors using an ordered-tree model. The ordered-tree model provides the information needed to symbolically compute the non-zero structure of the matrix factor of a sparse matrix. Furthermore, for matrix factor modification problems, this tree model can be used to determine the numerically modified entries in the matrix factor. Examples for modification of a structure and h-adaptive refinement of a finite element model are given to illustrate the potential application of the procedures developed in this study.
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  • 79
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2423-2449 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a general boundary element method (BEM) for two- and three-dimensional quasistatic poroelasticity is discussed in detail. The new formulation, for the complete Biot consolidation theory, operates directly in the time domain and requires only boundary discretization. As a result, the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses, particularly those which involve extensive or infinite domains.The presentation includes the definition of the two key ingredients for the BEM, namely, the fundamental solutions and a reciprocal theorem. Then, once the boundary integral equations are derived, the focus shifts to an overview of the general purpose numerical implementation. This implementation includes higher-order conforming elements, self-adaptive integration and multi-region capability. Finally, several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for consolidation analysis.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2451-2463 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modelling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modelling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2569-2581 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: At corners or edges in the boundary of the domain of a potential problem the local normal gradient of potential is double-valued. When Dirichlet boundary conditions are specified there are thus two unknowns at a single nodal point, and the sets of equations resulting from the usual BIE discretization are rendered indeterminate. We discuss here earlier approaches to the resolving of this problem, and describe a further approach which appears to offer some advantages. Both normal gradients can be approximated directly from local potential boundary conditions, showing the problem indeed to be formally overdetermined. This ability is discarded, in favour of yielding a robust and well-conditioned relationship between the two gradients. This, in conjunction with the BIE analysis, permits solutions of considerable accuracy to be found, including the gradients at such corner nodes. Illustrative calculations are presented for rectilinear and curvilinear domains. These show that, even with as few elements as there are corners, and thus one and a half times as many unknowns as there are nodal points, good approximations to the gradients can be obtained. The need for progressively finer discretization as a corner is approached is thus much reduced.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2710-2711 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2711-2711 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2777-2793 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress-stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.The conventional formulation requires a 2 × 2 × 2 or 2 × 2 × 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through-thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 × 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present formulation is an order-of-magnitude economical compared to the conventional scheme.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2829-2838 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the prevention of snow loading on an overhead conductor caused by the mechanism of cylindrical-sleeve growth. The eccentric snow loading on the windward side of the conductor, having finite torsional stiffness, causes the conductor to rotate and a theoretical study of how this rotation can be controlled on attaching counterweights along the span of the conductor is presented. In the absence of counterweights, the non-linear rotation equation is solved analytically in terms of elliptic functions, simulating ice loading by a uniform torque density; for large torque density an asymptotic solution is obtained using matched asymptotic expansions. In the rotation equation the counterweights producing torque at discrete points are incorporated as delta functions which enable the discontinuity in the twisting couple at such locations to be accounted for by means of an integral moment balance. A simple algorithm is then presented for integrating the equation of rotation as an initial value problem which can deal with any distribution of counterweights along the span of the conductor. Illustrative numerical results are presented for zero, one, two, three and four counterweights per span; in the absence of counterweights analytical and numerical solutions are in exact agreement.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 2907-2922 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for assembling blocks of global equations in FE programs is presented. The method has been implemented in SAP IV, the well-known FE program.The new assembling process consists of two phases. First, for each pair of blocks, the numbers of active elements are determined in ascending order. Then, from the sequential file containing element matrices, active records only are read and processed, the non-active ones being skipped.The most important features of the new method as compared to the method previously used are the following: (i) it saves up to 2/3 of the CPU-time for assembling, (ii) the amount of data on an auxiliary file is negligible, (iii) it does not require any additional high speed storage, (iv) it can be directly applied in any FE program with blocks using the constant bandwidth row storage scheme, (v) after some modifications it can be applied also in FE programs with blocks using the skyline column storage scheme.The full source code in FORTRAN IV is given in Appendix II.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1299-1316 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The preconditioned conjugate gradient (CG) method is becoming accepted as a powerful tool for solving the linear systems of equations resulting from the application of the finite element method. Applications of the non-linear algorithm are mainly confined to the diagonally scaled CG. In this study the coupling of preconditioning techniques with non-linear versions of the conjugate gradient and quasi-Newton methods creates a set of conjugate- and secant-Newton methods for the solution of non-linear problems. The preconditioning matrices used to improve the ellipticity of the problem and to reduce the computer storage requirements are obtained by the application of the partial preconditioning and the partial elimination techniques. Both techniques use a drop-off parameter ψ to control the computer storage demands of the method, making it more versatile for any computer hardware environment. Consideration is given to the development of a highly effective stability test for the line search minimization routine, which computes accurate values without much effort. This results in a beneficiary effect not only on the convergence properties of the methods but on their efficiency as well.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1371-1387 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented. The shape functions in the radial direction comprise the first two terms of the asymptotic expansions of Hankel functions. The integrals with infinite limit for calculating the coefficient matrix have been worked out. Numerical tests on the diffraction by a surface-piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder. Other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element. A computer program, WALOAD, has been developed for computing the wave forces on fixed two and three dimensional bodies.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1521-1537 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged.For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load-deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (KI = KIC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.
    Additional Material: 14 Ill.
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  • 90
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1599-1618 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method based on the virtual work principle to determine the steady state response of frams in free or forced periodic vibration is introduced. The axial and flexural deformations are coupled by mean of the induced axial force along the element. The spatial discretization of the deformations is achieved by the usual finite element method and the time discretization by Fourier coefficients of the nodal displacements. No unconventional element matrices are needed. After applying the harmonic balance method, a set of non-linear algebraic equations of the Fourier coefficients is obtained. These equations are solved by the Newtonian iteration method in terms of the Fourier coefficient increments. Nodal damping can easily be included by a diagonal damping matrix. The direct numerical determination of the Fourier coefficient increments is difficult owing to the presence of peaks, loops and discontinuities of slope along the amplitude-frequency response curves. Parametric construction of the response curves using the phase difference between the response and excitation is recommended to provide more points during the rapid change of the phase (i.e. at resonance). For undamped natural vibration, the method of selective coefficients adopted.Numerical examples on the Duffing equation, a hinged-hinged beam, a clamped-hinged beam, a ring and a frame are given. For reasonably accurate results, it is shown that the number of finite elements must be sufficient to predict at least the linear mode at the frequency of interest and the number of harmones considered must satisfy the conditions of completeness and balanceability, which are discussed in detail.
    Additional Material: 11 Ill.
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  • 91
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1703-1713 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a 3-D boundary element method (BEM) for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations, ‘Part-through’ elliptic cracks in an elastic plate with traction-free surfaces are analysed and the stress intensity factor (SIF) values along the crack front are found to compare favourably with widely accepted numerically obtained SIF results by Raju and Newman.1
    Additional Material: 9 Ill.
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  • 92
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    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 93
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    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 15-25 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Solvolysis of 2-X-2-phenylpropane (1-X) in 25 vol% acetonitrile in water at 25°C produces 2-hydroxy-2-phenylpropane (1-OH) and 2-phenylpropene (3). The carbocationic intermediate discriminates between different nucleophiles; azide anion, acetate anion, and methanol are more efficient nucleophiles than water, kN3/kH2O = 42 kOAc/kH2O = 3, and kMeOH/kH2O = 2·9 (ratio of second-order rate constants). The fraction of the elimination product 3 increases with increasing basicity of the leaving group X as well as by addition of general bases. The Brønsted parameter for this catalysis is small, β = 0·13, with substituted acetate anions. The kinetic deuterium isotope effect for the dehydronation of the intermediate has been measured (assuming the reaction from intermediate to alcohol is insensitive to isotopic substitution) employing the hexadeuterated substrate d6-1-X as k3H/k3d6 = 3·5 ± 0·2 for the chloride 1-Cl with acetate anion, and, without added base, 3·1 ± 0·2 for the acetate 1-OAc, and 3·1 ± 0·2 for the p-nitrobnzoate 1-PNB, respectively, and ∼5 for the protonated methyl ether 1-OMeH+. The variation in isotope effect with change in leaving group is discussed in terms of elimination from contact ion pairs and ‘free’ carbocation. The overall kinetic isotope effect for the solvolysis was found to be kobsH/kobsd6 = 1·31 (1-OMeH+), 1·38 (1-OAc), 1·40 (1-PNB), and 5·7 (1-OH2+). These isotope effects consist of the isotope effect k12H/k12d6 for the formation of the substitution product 1-OH and k13H/k13d6 for production of the olefin 3. It is concluded that the latter isotope effect is enlarged owing to a branched mechanism in which the deprotonation of the carbocationic intermediate competes with formation of the substitution product. As large an isotope effect as k13H/k13d6 ∼6·5 has been measured for 1-OMeH+.
    Additional Material: 2 Ill.
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  • 94
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: IR spectroscopy is presented as a convenient means to monitor the formation of acyl (and alkyl) cations from corresponding acid chlorides, with Lewis acids at low temperature in the solid state. Phenylacetyl chloride is co-deposited (under vacuum at -173°C with antimony pentafluoride on a KBr window), as in the ‘molecular beam’ method of cation generation. The initial IR spectrum of the deposition shows (in addition to starting materials) that a small amount of phenylacetyl cation (2274 cm-1) has been formed. Warming the solid matrix to -123°C Promotes the smooth conversion of acid chloride to acyl cation. Ultraviolet irradiation (through quartz windows) at -123°C to -73°C facilitates this conversion but does not result in the loss of carbon monoxide from the acyl cation to form benzyl cation. When benzyl chloride is used in place of phenylacetyl chloride, there is no noticeable difference between IR spectra taken before and after warming and/or photolysis of the solid deposition.
    Additional Material: 1 Ill.
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  • 95
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 93-102 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Organocerium(III) reagents reacted with α,β-unsaturated carbonyl compounds to give 1, 2-addition products (allylic alcohols) in good to high yields. The reaction was studied from a mechanistic point of view by the use of (E)- and (Z)-1-(4′-methoxyphenyl)-3-phenyl-2-propen-1-ones and 4,4-ethylenedioxy-2,6-dimethyl-2,5-cyclohexadienone as the probe compounds. A polar pathway was suggested for the reaction with the former enones. On the other hand, the operability of single electron transfer processes was demonstrated in the reaction with the latter probe compound.
    Additional Material: 1 Ill.
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  • 96
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Bis(1,2-diaryl-1,2-ethylenedithiolato)metal(0) complexes (1; metal = Ni, Pd, and Pt) react with quadricyclane (Q) to give selectively 1:1 adducts which are identical with the adducts between 1 and norbornadiene (NBD). In the adducts, two sulfur atoms of the different dithiolato ligands are added to one of the double bonds of NBD. The reactions of 1 with Q are 103-104 times faster than those with NBD. The more electropositive dithiolatometal complexes react faster with Q and NBD. The adducts are dissociated to the free dithiolatometal complexes and NBD by UV-irradiation (254-436 nm). Upon irradiation with 254 nm light, the photodissociation occurs before the decomposition of the dithiolatometal complexes.
    Additional Material: 8 Ill.
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  • 97
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 117-130 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Gas phase ion/molecule reactions have been used to probe the structure of ions obtained by electron impact upon 1-(diphenylmethylene)cyclopropane and 2,2-diphenyl-1-methylenecyclopropane. The resulting ions of molecular composition C16H14 (m/z 206+) were reacted with charge transfer reagents (6·9 〈 IP 〈 8·8eV), giving evidence for the presence of isomeric ions with different reactivities. The less reactive ion is identified as a trimethylenemethane species (TMM+) in which one cyclopropane bond is broken; the more reactive ions are assigned as vertical ions in which the cyclopropane ring is unaffected. The vertical ions have recombination energies of 8·44 ± 0·05eV, whereas TMM+ has one of 7·41±0·05eV. The TMM+ fraction is not constant; it increases with increasing IP of the reagent. This is attributed to a reagent-catalyzed isomerization of the vertical ion to TMM+. In addition, the reagent ions are observed to undergo a unique reaction with the neutral methylenecyclopropane derivatives: electron transfer and ring opening to yield TMM+. These findings limit the application of the customary equilibrium measurements as a method to determine the substrate IP.
    Additional Material: 7 Ill.
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  • 98
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 177-182 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 4-O2NC6H4OCH2CH2NHPh undergoes clean base-catalyzed Smiles photorearrangement to 4-O2NC6H4N(Ph)CH2CH2OH in dimethyl sulfoxide-water (25:75). A linear plot of φ-1 vs [OH-]-1 indicated that the limiting quantum yield at high [OH-] is 0·12 and that uncatalyzed photorearrangement does not occur. Rate constants for the deprotonation step were determined for a variety of bases having conjugate acid pKa values in the range 5-10. When plotted according to the Brønsted Catalysis Law, these data gave a non-linear plot approaching slopes of zero and unity above and below a pKa of 6-7. This indicates that the proton-donating intermediate in this photo-Smiles rearrangement is the zwitterion diradical (pKa ≈ 7) rather than the Meisenheimer complex (pKa ≈ 2).
    Additional Material: 2 Ill.
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  • 99
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 225-231 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The gas-phase pyrazole elimination of N-alkyl pyrazoles has been studied using MNDO semi-empirical molecular orbital (MO) theory with complete geometry optimization of all stationary points. We found that the activation energies (Ea) of the concerted processes are around 80 kcal/mol, 25 Kcal/mol higher than experimental values. But the differences in Ea between compounds with different substituents are in good agreement with the experimental ones.
    Additional Material: 4 Ill.
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  • 100
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 255-262 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The photostimulated reaction of neopentyl halides with different nucleophiles by the SRN1 mechanism of nucleophilic substitution has been studied. Neopentyl halides do not react with carbon nucleophiles, diethylphosphite, diphenylphosphonite and azide ions, but they react with arsenide and selenide ions. The photostimulated reaction of neopentyl bromide with diphenylarsenide ions gave only the straightforward substitution product neopentyldiphenylarsine. On the other hand, the photostimulated reaction of bromobenzene with dineopentyl arsenide ions gave three arsines: dineopentylphenylarsine, neopentyldiphenylarsine and triphenylarsine. Neopentyl chloride reacts under irradiation with diphenylphosphide ions giving good yields of the substitution product.
    Additional Material: 1 Tab.
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