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  • 1995-1999  (27)
  • 1985-1989  (648)
  • 1997  (27)
  • 1985  (648)
  • Engineering General  (422)
  • Computational Chemistry and Molecular Modeling  (253)
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  • 1995-1999  (27)
  • 1985-1989  (648)
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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 265-272 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Numerical experiments with a nonlinear (λχ4) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When λ = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (λ 〉 0), a threshold is reached at λ = λc when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of λ. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored. © 1997 John Wiley & Sons, Inc.
    Additional Material: 9 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 279-289 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Testosterone (17β-hydroxy-4-androsten-3-one) was studied by the semiempirical AM1 and PM3 and ab initio STO-3G*, 3-21G*, and 6-31G* methods. The goals were to compare those methods and to know the electronic structure of the hormone. Full geometry optimization was performed, and two crystal conformers (T1 and T2), and experimental dipole moment in solution were used for comparison. One conformer with a dipole moment similar to the solvated conditions was generated. Total energy, entalphies, dipole moments, charges, electrostatic potentials, and highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbital (LUMO) were calculated. Root-mean-square (RMS) index of the theoretical molecules against T1 and T2 showed best results with the 3-21G* and 6-31G* methods, while AM1 gave better energies than PM3. Dipole moments were directed toward the OH group and the botton face of the A ring. The frontier orbitals were located along the C4-C5 π bond, particularly the LUMO was split between C4 and C5, predicting the action of enzymes at C5 yielding to 5α and 5β-reduced androgens. Electrostatic potentials might be also of biological importance since they are coincidental with the dipole-moment orientation. Finally, it is interesting that the solvatedlike conformer, its properties, and the OH group laid between the same group of T1 and T2 and with a total energy between the crystals and the gas phase or in vacuo conditions. This results might also explain the biology of testosterone and use them to model the hormone-receptor interaction. © 1997 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 303-314 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: He I photoelectron (PE) spectra of four carboxylic acids and five esters are measured. Semiempirical and ab initio quantum chemical calculations are used for the interpretation of the spectra. The complex approach which uses empirically established relationships (the dependence of valence electron ionization energies on proton affinities in the gas phase, on the core level ionization energies, and on the structure) was developed. © 1997 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 323-328 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Simple molecular orbital calculations are employed in searching electronic parameters which may characterize the chemical carcinogens. Using frontier orbitals, the carcinogen-DNA bond formation is described as an electron transfer from the highest occupied molecular orbital (HOMO) of DNA to the lowest unoccupied molecular orbital (LUMO) of the carcinogen. Analysis of the DNA bases units shows that the electron donation occurs preferentially at the guanine site. The calculated low LUMO energy of several carcinogens indicate correctly the electrophilic character of these compounds. The difference between the carcinogen and the ultimate carcinogen is analyzed. Epoxides, free radicals, alkylating agents, and other metabolite forms are studied. A reasonable correlation is found between the LUMO energy and the carcinogenic function. © 1997 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1123-1131 
    ISSN: 0020-7608
    Keywords: MD simulations ; liquid surface ; formamide ; molecular orientation ; molecular surface density ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular dynamics simulations of liquid formamide(HCONH2) were carried out using the GROMOS software. The formamide molecule is represented by all of its atoms with all internal degrees of freedom. In contrast to other simulations dealing with bulk properties, this study focuses on the interface liquid-vacuum for the first time. We show that the molecular plane is tilted out of the surface, exposing the HCO group to the vacuum.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1123-1131, 1997
    Additional Material: 9 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1065-1078 
    ISSN: 0020-7608
    Keywords: very precise eigenvalues ; very accurate grid method ; general solution for Schrödinger equations ; rapidly convergent treatment for helium eigenvalues ; superconvergence ; optimization of grids ; treatment of continuum ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An extension to the theory of Schrödinger equations has been made which enables the derivation of eigenvalues from a consideration of a very small part of geometric space. The concomitant unwanted continuum effects have been removed. The theory enables very convergent or “superconvergent” calculations. In the case of the helium ground state, E=-2.90372437703411987 Eh was obtained from 251 terms. The result is comparable to that from the largest variation calculations so far carried out reinforced by extrapolation techniques. The theory is extensible to atoms and molecules irrespectively of the number of electrons or nuclear centers. In these cases, the advantage of “superconvergent” calculations will be more pronounced than in the case of helium.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1065-1078, 1997
    Additional Material: 9 Tab.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 1-11 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Roothaan-Hartree-Fock (RHF) calculations are carried out for the ground states of the atoms from helium to xenon using a minimal basis set of Slater-type functions whose principal quantum numbers are allowed to take variationally optimal noninteger values. The resulting energies are substantially superior to those obtained previously under the usual restriction that principal quantum numbers be positive integers. The energy lowering relative to the single-zeta wave functions of Clementi and co-workers ranges from 0.0066 Eh in He to 11.2 Eh in Xe. Our results are superior to those obtained by Höjer using a minimal basis set of unconventional binomially screened basis functions. Noninteger principal quantum numbers benefit d-orbitals the most; physically realistic negative d-orbital energies are obtained in all cases including those transition-metal atoms for which a conventional single-zeta STF basis leads to positive d-orbital energies. © 1997 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 23-27 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio study on the reaction of the ground state (3D) and the excited state (1D) of Sc+ with methane was performed. Reaction channels on the singlet and triplet potential surface (PES) and the reaction mechanism are examined and discussed. Three regions of the potential surface was studied: the molecular complex, the C(SINGLE BOND)H insertion products, and the transition states for the reaction. Comparisons between singlet and triplet PESs show that the excited state (1D) of Sc+ has more reactivity with methane than does the ground state (3D) due to the spin quantum number conservation with the more stable insertion intermediate. © 1997 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 67-76 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The importance of the hybridization displacement charge (HDC) in describing molecular electrostatic potential (MEP) maps was demonstrated by studying six molecules; pyrazine N-oxide, para-nitropyridine, 5-nitropyrimidine, 3-nitropyridazine, N2, and N2O. It is shown that continuously distributed HDC-corrected Löwdin charges reproduce the MEP features of these molecules, most of which have competing electrophilic sites, in agreement with ab initio results. Further, it is found that for homonuclear diatomic molecules MEP minima can be located properly using HDC-corrected Löwdin (or HDC-corrected Mulliken) continuously distributed charges, but these features cannot be obtained using the conventional Löwdin (or Mulliken) charges. It was shown that the order of molecular electric field (MEF) values near the different electrophilic sites becomes changed when one moves away from the molecules. Thus, pyridine-type nitrogen atoms are the preferred binding sites close to the molecules, while at large distances, effects of oxygen atoms of the NO groups become dominant. © 1997 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 115-124 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some types of atomic vibrations in a chain of the DNA type constructed of G-C pairs were studied. These are the atomic vibrations of the lateral groups of guanine and N(3)H(1)H(2) of cytosine connected by the hydrogen bond h-b-1 and the vibrations of the centers of masses of bases in the direction parallel to bonds h-b-i, i = 1-3. The vibrations mix partially due to the dependence of the energy of the bond h-b-1 on its length and split into two bands because of the interaction between neighboring base pairs. It was shown that the excitation of the bond h-b-1 results in the splitting off of the two local vibrations and in a small deformation of the chain in the vicinity of the pair with the localized hydrogen bond. The law of the dispersion of band vibrations, values of the split-off frequencies, and degree of poly(dG)-poly(dC) chain deformation were determined. © 1997 John Wiley & Sons, Inc.
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  • 11
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 55-65 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We compare geometry configurations, vibrational properties, and electronic structures of (HF)2 in a free state and inside argon atom shells Arn. For the first stage, molecular dynamics calculations for the (HF)2 · Ar62 heterocluster are performed with the help of model potentials HF(SINGLE BOND)HF, Ar(SINGLE BOND)Ar, and Ar(SINGLE BOND)HF. Then, ab initio quantum chemistry analysis is carried out for the smaller systems (HF)2 · Ar15 and (HF)2 · Ar6 when keeping the argon atoms closest to the trapped dimer. We conclude that the hydrogen-bonded complex (HF)2 gains some extra stability inside the argon shells, originating primarily from a decrease of intermolecular distance RFF. Electronic structure calculations are in accord with the changes in dynamical properties, namely, a noticeable increase in the vibrational frequency assigned to the F(SINGLE BOND)F stretching mode (+25 cm-1) and decrease in rms deviations for the corresponding coordinate δFF. In addition to these changes, the argon atoms of the nearest solvent shell donate a small fraction of electron charge which is spent for an increase of population of the antibonding orbital σ*Hf(SINGLE BOND)Ff of the free monomer unit and shift orbital energies primarily of the lone-pair fluorine species. These shifts are greater than the changes due to geometry alterations and the possible inaccuracies of the calculation scheme. © 1997 John Wiley & Sons, Inc.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 245-259 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An efficient expansion method for the evaluation of VB matrix elements is introduced. The overlaps of VB wave functions of N electrons can be treated as algebrants, i.e., generalized determinants, of N × N matrices. An algebrant can be expanded with subalgebrants of lower orders in a successive way. By choosing Rumer spin bases and appropriately arranging the expansion, it is found that the number of unique subalgebrants involved in the expansion increases in a quite moderate way with N. In contrast to the traditional symmetric group approach, which explicitly utilizes all N! representation matrices, the new strategy incorporates the group theoretical factors in a simple way in the successive expansion. As only the unique subalgebrants are further expanded, the computational effort required by the new strategy scales in a very acceptable manner with the increasing number of electrons. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 245-259, 1997
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 261-264 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Characters of irreducible representations (irreps) of the symmetric group corresponding to the two-row Young diagrams, i.e., describing transformation properties of N-electron eigenfunctions of the total spin operators, have been expressed as explicit functions of the number of electrons N and of the total spin quantum number S. The formulas are useful in various areas of theory of many-electron systems, particularly in designing algorithms for evaluation of spectral density moments. © 1997 John Wiley & Sons, Inc.
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 291-296 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The geometries and S-H, S-S, and S-C bond dissociation energies for hydrogen sulfide, hydrogen disulfide, methanethiol, dimethyl disulfide, and dimethyl disulfide were calculated with both ab initio (ROHF and MP2), hybrid (BHandH, BHandHLYP, Becke3LYP and Becke3P86), and nonlocal (BLYP and BP86) density functional theory (DFT) methods. In all studies the 6-31 + G(d) basis set is used. The computed results are compared to the experimentally obtained values, targeting the selection of a suitable ab initio or DFT method for the study of these systems. © 1997 John Wiley & Sons, Inc.
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 297-302 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mechanism and kinetics for the decomposition of β-hydroxypropaldehyde, primary and secondary β-hydroxyketones, were studied by using ab initio RHF/6-31G and RHF/6-31G* methods. The activation barriers of these reactions were refined to be 39.57, 40.10, and 36.80 kcal mol-1 at the MP2/ /RHF/6-31G* level, respectively. The calculated results show that each decomposition is a concerted process with hydrogen transferring and bond breaking via a six-membered cyclic transition state. The thermal rate constants of the decomposition of primary and secondary β-hydroxyketones were obtained by calculating microcanonical probability fluxes through each transition state. It is theoretically confirmed that methyl substitution at the hydroxyl carbon of β-hydroxyketones causes a small enhancement in rates. The theoretical investigations of the mechanism and the rate constants are in agreement with the experimental results. © 1997 John Wiley & Sons, Inc.
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  • 16
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 13-21 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of the anisotropic Heisenberg model is carried out by solving the Bethe ansatz solution of the model numerically as a function of the anisotropy parameter for finite N. A brief introduction to the limit of the infinite chain is presented. The energy for a few special limiting cases of the anisotropy parameter in the Hamiltonian are worked out. Numerical results for finite cycles as well as for the infinite chain are given. Comparison can then be made with the case of finite increasing N. © 1997 John Wiley & Sons, Inc.
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 47-53 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The MELD program is employed to evaluate the Slater average potential v(r) felt by an electron at the point r within an atom. The characteristic radius R of the atom is then defined by the classical turning point equation v(R) = -I, where I denotes the first ionization potential of the atom. The atomic radii defined in this way have a close correlation with the van der Waals atomic radii. © 1997 John Wiley & Sons, Inc.
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  • 18
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 77-88 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Highly accurate upper bounds for several 2Pe states of the Li isoelectronic series obtained by extensive Hylleraas-Cl calculations are given. The best value for the 22Pe state (1s2p2) of Li is -5.21373920 au. The evaluation of the occurring integrals is given explicitly. Additionally, we present some expectation values and isotope energies of the Li isoelectronic series. © 1997 John Wiley & Sons, Inc.
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  • 19
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 97-113 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Restricted geometry optimizations at the ab initio SCF level with the 3-21G basis set were employed to investigate the conformation space of flavone acetic acid (FAA) and its related compounds. All the conformations are produced from a conformation which is, according to our previous work, probably the active conformation in terms of antitumor activity shown by these compounds. Detailed studies on FAA were carried out while only brief discussions are made on the analogs. The main results obtained are that (1) FAA is a very flexible molecule, e.g., with the energy barrier up to about 3 kcal mol-1 from the reference conformation, the important torsional angle τ1 can change from 27.0° to 117.0°, τ2 from -168.0° to 2.0°, and τ3 from -50.0° to 30.0°; (2) the hydrogen-bonding effect plays an important role in determining lower-energy conformations; (3) among all the FAA conformations considered, some are active and some are inactive; (4) it seems that the analogs will have similar behavior to FAA when the torsional angle τ3 is restricted to the values which are around the equilibrium values; and (5) the hypothesis put forward previously has been further developed in this work. Now, we postulate that efficient charge transfers will lower the energy and that proper charge transfers will activate the molecule. There are mainly two different types of charge transfer corresponding to two different types of conformation, which are specified in this article. © 1997 John Wiley & Sons, Inc.
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  • 20
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 273-278 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical solutions to the Yukawa-like screened Coulomb nuclear attraction and electron repulsion molecular basic integrals, as well as to the basic integrals required to compute the virial coefficient, over Gaussian basis functions, are derived and cast into a practical closed form, suitable to interface with modern codes for the calculation of molecular electronic structure. © 1997 John Wiley & Sons, Inc.
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  • 21
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1079-1089 
    ISSN: 0020-7608
    Keywords: large-order perturbation theory ; lie algebra ; three-body problem ; symbolic computations ; helium atom ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of o(4, 2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to  +∞ should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit  +∞ is presented for the energies of the helium singlet and triplet ground states.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1079-1089, 1997
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  • 22
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1099-1106 
    ISSN: 0020-7608
    Keywords: metathesis reactions ; bond order ; free valence ; minimum energy path ; nonsynchronization ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A few simple atom-transfer reactions (i.e., Ȧ+X-A→A-X+Ȧ) are studied by quantum mechanical ab initio methods. Emphasis is given to the detailed analysis of density matrices rather than to the energetics. Results reveal that during these reactions a small free valence always develops on the migrating atom at the transition state. The barriers in these reactions arise from the greater extent of bond cleavage in the reactant than that of bond formation in the transition state. Analysis of bond orders estimated from bond lengths using Pauling's relation also leads to the fact that the bond-cleavage process is more advanced than is the bond-formation process in these reactions.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1099-1106, 1997
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  • 23
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 29-45 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The H2 interaction with the Pd dimer and trimer were studied using multiconfigurational self-consistent field (MC-SCF) calculations with the relativistic effective core potential (RECP); the correlation energy correction was included in the extended multireference configuration interaction (MRCI), variational and perturbative to second order. Here, we considered the Pd2 first six states: 3Σ+u, 1Σ+g, 3Πg, 3Δxy, 1Σ+u, and 3Σ+g. For them, the four geometrical approaches included were the side-on H2 toward Pd2, for the hydrogen molecule in and out the Pd dimer plane; the perpendicular end-on H2 toward Pd2; and the perpendicular end-on Pd2 to H2. The Pd2 ground state is 3Σ+u, which only captures H2 in the C2v end-on approach, softly relaxing the H(SINGLE BOND)H bond. The closed-shell 1Σ+g captures the H2 molecule in all the approaches considered: The side-on approach of this state presents deep wells and relaxes the H(SINGLE BOND)H bond, and the end-on approach captures H2 with a relatively longer H(SINGLE BOND)H distance and also a deep well. The 3Πg state was the only one which did not capture H2. For the triangular Pd3 clusters, H2 was approached in the C2v symmetry in and out of the Pd3 plane. In the triangular case, H2 was absorbed in both spin states, with deep wells and relaxing the H(SINGLE BOND)H distance. The linear Pd3 singlet and triplet states capture outside of the Pd3 and break the H(SINGLE BOND)H bond. © 1997 John Wiley & Sons, Inc.
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  • 24
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 89-96 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We presented a calculation of the total and partial decay widths of vibrational predissociation (VP) of the HeI2 molecule for low initial vibrational excitations from the lowest van der Waals (vdW) state with total angular momentum J = 0. A time-dependent golden rule wave-packet method was employed in our numerical calculations for the decay widths. The computed total decay widths, lifetimes, and rates of VP are in fairly good agreement with those extrapolated from the experimental data available. Predicted total decay widths as a function of initial vibrational levels exhibit a highly nonlinear behavior. These results demonstrate that a quantum mechanical decay mode for low vibrational excitation remains as well. The total propagation time needed in the time-dependent golden rule wave-packet calculations is much shorter than is the lifetime of the predissociation of HeI2. It is shown that the final-state interaction between the fragments is important for determining the final rotational-state distribution (partial decay width). We find that the major peak position in the final rotational-state distribution shifts to lower rotational energy levels with increase of the initial vibrational quantum number, which is evidently different from that for higher vibrational levels. This fact can be clearly explained by the dependence of the amount of kinetic energy released to the product degrees of freedom on the initial vibrational state. © 1997 John Wiley & Sons, Inc.
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  • 25
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    International Journal of Quantum Chemistry 62 (1997), S. 239-244 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We calculate the resonant and antibound state energies for a Morse potential with a centrifugal barrier using Siegert boundary conditions. Starting with a complex wave number k (purely imaginary for bound and antibound states), we integrate numerically from the origin up to a matching point using Numerov's method. The inward integration is performed using the corresponding (first-order) Riccati equation. The complex eigenvalues are found by matching the two logarithmic derivatives. We find narrow shape resonances within the well, above the dissociation limit, and broad resonances above the centrifugal barrier. Antibound states are found even with J = 0. © 1997 John Wiley & Sons, Inc.
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  • 26
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    International Journal of Quantum Chemistry 62 (1997), S. 315-322 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two alternative dehydration reactions C(OH)4 → (HO)2CO + H2O and C(OH)4 + H2O → (HO)2CO + 2H2O are studied by ab initio Becke3LYP/6-311 + G** and MP2/6-31G** methods. Calculated energy and geometry characteristics of intermediates and transition states predict a catalytic effect of one water molecule and the exothermism of the transformations. Relevant HF/6-311 + G**, HF/6-31G**, HF/6-31G, and HF/3-21G calculations were performed for comparison. © 1997 John Wiley & Sons, Inc.
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  • 27
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    International Journal of Quantum Chemistry 63 (1997), S. 1107-1122 
    ISSN: 0020-7608
    Keywords: relativistic pseudopotentials ; heavy atoms ; method of molecular calculation ; electronic structure ; Gaussian approximation ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Gaussian expansions of the generalized relativistic effective core potential (GRECP) components are reported for elements Hg through Rn. The accuracy of the analytical GRECPs is estimated by calculations of atomic transition energies with the numerical one-configurational wave functions in comparison with Dirac-Fock calculations. The results of the corresponding calculations with the RECPs of other groups are also given. An “averaged error” in the reproduction of the transition energies without the change of the occupation number of the 5d-shell is an order of magnitude smaller than that for the RECPs of other groups. As is demonstrated for the transitions with the change of the occupation number of the 5d-shell in mercury, the largest absolute error of the GRECP is only 1.5-2 times smaller than that of the energy-adjusted pseudopotential (PP) or the RECP of Ross et al. with the same space of explicitly treated electrons. However, the dispersion of these errors is 19⋅10-4 au for the energy-adjusted PP, 35⋅10-4 au for the RECP of Ross et al. and only 4⋅10-4 au for the GRECP. One-configurational spin-averaged calculations of the molecular properties for HgH and HgH+ are carried out and compared with the corresponding results of Häussermann et al.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1107-1122, 1997
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  • 28
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 301-315 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element technique for calculating energy release rates is presented. An explicit expression for energy changes due to virtual crack extensions is formulated based on a variation of isoparametric element mappings. Energy release rates are calculated directly from integral expressions evaluated over singular quarter-point isoparametric elements surrounding the crack tip. Since the energy release rates are expressed in variational form, there is no need for the analyst to select a small finite crack extension to simulate a virtual crack extension. The method is shown to produce very accurate solutions even with fairly coarse element meshes. A similar technique for mixed-mode fracture based on mutual potential energy release rates is described.
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  • 29
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 386-386 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 30
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 387-388 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 31
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 32
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 437-449 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper extends the earlier work by the present authors for a single embedded crack in an infinite solid and presents a solution to the problem of multiple coplanar cracks in an infinite medium. An alternating method in conjunction with an analytical solution for a single crack is used to determine the stress intensity factors for interacting multiple coplanar embedded cracks in an infinite body. The alternating method, as implemented here, leads to a highly accurate evaluation of the appropriate stress intensity factors.
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  • 33
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 421-435 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element is developed for the three-dimensional deformation of a circular ring. The derivation is based on ring theory. The unique feature of the element is that it provides for coupling between the in-plane and out-of-plane loads and deflections. The element is derived in terms of polar co-ordinates so that no co-ordinate transformation is needed to assemble the elements. Three ring deflection problems are solved using an assembly of the elements. Two of the solutions are compared with analytical results and one is compared with experimental results. The comparisons verify the theory.
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  • 34
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 543-554 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure to discretize explicit enthalpy formulations for one-dimensional planar phase change problems is derived, which removes numerical oscillations in temperature and phase front position. The technique is based on an enthalpy balance for the control volume containing the phase front in combination with linearized temperature profiles near the phase front. A continuous casting solidification problem and a problem with known analytical solution are applied to demonstrate the effect of the scheme.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 585-600 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generally applicable and simple joint/interface element for three- and two-dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell-to-shell and shell-to-solid interfaces.
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  • 36
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 617-635 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 48 degrees-of-freedom quadrilateral element, including the effect of both material and geometric nonlinearities, is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures. The element surface is described by a variable-order polynomial in curvilinear co-ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co-ordinates. Without being confined to the assumption of axisymmetry, this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones. In the formulation for geometric nonlinearity, the total Lagrangian approach is adopted. Only small strains and small rotations are allowed. In the formulation for plastic deformation, the concept of a layered element model is used. In the inelastic range, the material is assumed to obey the Von Mises yield criterion and the Prandtl-Reuss flow rule. A tangential stiffness formulation is combined with the modified Newton-Raphson iteration method for the solution of nonlinear problems. A systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency.
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  • 37
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 683-689 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: As an approximation for the mechanism behind noise emission from a rock drilling rod, the transient damped vibrations of a beam (the drilling rod) in bending and shear is studied. At one end the beam is supported by a distributed damped Winkler-type foundation. In order to determine required transfer function from an applied moment at the other end of the beam, it is divided into two finite elements. Each element is treated as a uniform Rayleigh-Timoshenko beam in an ambient medium. The fast Fourier transform (FFT) technique is utilized. Good agreement between calculated and measured strains is obtained. A single-figure measure which is approximately proportional to the sound power radiated from the vibrating beam is calculated for different damping materials at the supported end. It is found that a relatively high value of the stiffness of the Winkler-type foundation is needed if a significant level of reduction in the sound power radiated from the beam is to be achieved.
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  • 38
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 713-721 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: At present there are many general methods of approximating a possibly nonlinear operator equation by a finite equation system. The most commonly applied methods are the finite element and the finite difference. Numerous papers (e.g. References 9 and 10) have dealt with a comparison of these methods.In Reference 12 the Galerkin finite difference method (GFDM) is developed. The GFDM is a special finite element method designed t o solve nonlinear and possibly coupled partial differential equations numerically. It consists of a finite difference scheme derived from a Galerkin finite element method through the use of special local basis functions and a special grid.In this paper, we are concerned with extending the GFDM to derive ‘normal’ difference schemes. e.g. five-point schemes on two-dimensional domains for a general class of operators, even in nonlinear cases.Using GFDM or the finite element method on two-dimensional regions generally leads to at least 7- or 9-point schemes as well as expensive approximations of the nonlinear terms. Often, numerical integration is necessary. These computational costs are due to the non-orthogonality of the continuous and differentiable local basis functions that are needed in this case.The basic idea of the multi-bases approaches, which are the major concern in this paper11, is to reduce the smoothnessproperties ofthelocal basis functions in favour oftheir orthogonality. Thiscan beachieved with the help of so-called transfer operators which map the non-orthogonal and differentiable basis onto an only bounded but orthogonal basis.
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  • 39
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 777-778 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 40
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 775-776 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 41
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 763-774 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We derive a closed-form expression for the change in the variational indicator of a finite element mesh with respect to perturbations in nodal point co-ordinates. The expression is evaluated very effectively from standard finite element data obtained in one solution, and may be easily programmed as part of a general finite element code. We present the derivation for two- and three-dimensional isoparametric elements used in linear and nonlincar elasticity. The expression has practical applications in the computation of stress intensity factors in fracture mechanics and in the determination of the ‘optimal’ mesh with a given element-node connectivity. We demonstrate both applications by accurately determining the stress intensity factor of a Mode I crack using a finite element mesh which was improved using mesh optimization.
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  • 42
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 825-835 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many plane stress finite elements which can exactly represent rigid-body and constant-strain modes are too stiff in their response to the simple flexural action of a beam. This problem has received considerable interest. In this paper we explore a new interpretation of the problem and show that the poor bending response of the original 4-node plane stress quadrilateral can be quantitatively predicted by an error model.
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  • 43
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    International Journal for Numerical Methods in Engineering 21 (1985) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 44
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1361-1362 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 45
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1345-1359 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Introduced herein is a generalization of Newmark's time marching integration scheme, called the β-m method. Like the SSpj method (introduced in Parts 1 and 2 of this series), the β-m method provides a gcneral single-step scheme applicable to any set of initial value problems. The method is specialized by specifying the method order m along with rn integration parameters, β0, β1, …, βm-1. For a particular choice of m, the integration parameters provide a subfamily of methods which control accuracy and stability, as well as offering options for explicit or implicit algorithms. For the most part, attention is focused on the application to structural dynamic equations. Most well-known methods (e.g. Newmark, Wilson, Houbolt, etc.) are shown to be special cases within the β-m family. Hence, one computationally efficient and surprisingly simple algorithm unifies old and new methods. Stability and accuracy analyses are presented for method orders m = 2, 3 and 4 to determine optimal parameters for implicit and explicit schemes, along with numerical verification.
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  • 46
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1381-1390 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme has been constructed to simulate the imposition of a step in heat transfer at the surface of a multi-layered substrate. The numerical simulation of this process is carried out by applying an extended version of the Keller Box-Scheme to multi-layered diffusion problems. Numerical calculations show that accurate choice of length and time-scales is critical in determining the behaviour of the heat flow through the substrate. Thus, the results from the numerical simulations are of value to the experimentalist, particularly in determining the accurate shape of the response curves which enable experimental apparatus to be designed effectively. The proposed scheme yields heat fluxes as accurately as temperatures, and can be easily adapted to other related applications.
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  • 47
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1521-1533 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple and logical finite element formulation is presented for the analysis of rings and sectors, with Timoshenko effects. The elemental properties are derived from the governing differential equation of motion using the Galerkin method. A quintic polynomial, satisfying the compatibility of derivatives up to second order, has been used for the ring finite element. The interpolating function is the same as for a thin ring. The efficiency of the formulation has been illustrated by the numerical results presented.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1547-1553 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: For about a decade, each and every researcher who used isoparametric quadratic elements to solve fracture mechanics problems employed only incomplete versions of these elements. Although complete formulations of isoparametric elements are almost as available as incomplete ones in general-purpose finite element computer programs, no attempt to use complete formulations has been seen yet. The purpose of this paper is to show how the complete quadratic isoparametric elements can be employed in the field of fracture mechanics.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1709-1727 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented which enables the calculation of the settlement behaviour of circular or general loadings on horizontally layered soils which undergo secondary or ‘creep’ consolidation. The method of analysis involves the use of Hankel or double Fourier transforms to simplify the equations governing the consolidation process. This leads to great savings in the preparation of data and the amount of computer storage needed to solve problems involving three-dimensional loadings since such problems are essentially reduced to that of one spatial dimension: Solutions are then obtained by a ‘forward marching’ process where solutions at a particular time are found from those at a previous time. A method is presented which eliminates the need to store the solutions at all previous time steps, and is therefore very efficient. The theory is illustrated by examples of the behaviour of rectangular and circular loadings on layered soil profiles.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1749-1758 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is described in which global approximations are used to improve the accuracy of the finite element method. The technique is theoretically based on two corollaries to the Lax-Milgram lemma which are presented in this paper. Basically, the technique consists of factoring the unknown function for which an approximation is desired into the product of a global approximation and a second unknown function. Finite element methods are appropriately applied to obtain an approximation to the second unknown function. The approximation to the original function then consists of the product of the specified global approximation and the approximation to the second unknown function. The advantage that finite element methods possess with respect to obtaining banded matrices is preserved in this technique. In addition, numerical examples indicate that the technique's accuracy is as much as a factor of fifty better than the accuracy obtained by directly applying a finite element method to approximate the original function.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1791-1802 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient block overrelaxation algorithm is presented for the solution of the steady-state dam seepage problem. The formulation of Alt is used in conjunction with a finite element method on a fixed mesh to obtain a finite dimensional problem which is then solved by the algorithm. Some similarities of the formulation and the residual flow method of Desai are also discussed. Numerical results are compared with results of other authors.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1938-1939 
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    Keywords: Engineering ; Engineering General
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  • 53
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1925-1934 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Material modelling requirements for accurate stress fields in a nonuniform anisotropic composite are established for all six components of stress at a material point. The gauge section from a conical involute structure tested in an earlier investigation provides the case data for this modelling study. Stress results from a tricubic Hermite finite element model are shown to be in agreement with another computational analysis by Pagano using a Reissner energy formulation. Comparisons are made in the interior and at a corner with high interlaminar stress gradients. The small, but critical, matrix dominated stress components are shown to be very sensitive to modelling material orientation changes within each finite element. Uniform stress accuracy was obtained using distribution functions for material orientation of the same degree as the displacement functions, an isoparametric material geometry model.
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  • 54
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2013-2025 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An effective technique is presented for recovering surface tractions and distributed reaction forces from finite element displacement solutions of structural mechanics problems. Nodal values of surface tractions and assumed trial functions are used to represent the distribution of surface stresses. Equations obtained from the familiar Galerkin formulation are used to compute the nodal traction values. The method is demonstrated to be efficient and highly accurate, even in the presence of jump conditions or singularities. Extensions of the method are possible for recovering secondary solution variables in non-structural finite element applications.
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  • 55
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1941-1955 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper compares the performance of the SS22 and SS23 (References 1 and 2) single step algorithms for the numerical solution of the second-order structural dynamic equation and a related new algorithm SS32B applied to the equivalent first-order system, with sine and step forcing functions. Various aspects of stability relevant to these equations are discussed.
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  • 56
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1957-1969 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for obtaining difference equations from differential equations which has previously been applied to ordinary differential equations is here applied to the time-dependent heat conduction equation as a representative example of parabolic partial differential equations. Explicit difference equations are derived which are stable for all values of αΔt/Δ2 and are also accurate. Implicit-algorithms with improved accuracy are also derived. Problems in cartesian and cylindrical co-ordinates are treated.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2128-2129 
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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 21 (1985), S. 2157-2168 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a method which makes it possible to apply the idea of iterated defect correction to finite difference methods for the numerical treatment of partial differential equations. The method yields numerical approximations of very high accuracy for the solution, while the corresponding algebraic systems of equations still have ‘reasonable’ size.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2201-2219 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A higher-order shear deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, Vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three-dimensional elasticity theory.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2289-2302 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Bernoulli-Euler theory and Bessel functions are used to obtain explicit expressions for the exact dynamic stiffnesses for axial, torsional and flexural vibrations of any beam which is tapered such that A varies as yn and GJ and I both vary as y(n + 2), where A, GJ and I have their usual meanings; y = (cx/L) + 1; c is a constant such that c 〉 - 1; L is the length of the beam; and x is the distance from one end of the beam. Numerical checks give better than seven-figure agreement with the stiffnesses obtained by extrapolation from stepped beams with 400 and 500 uniform elements. A procedure is given for calculating the number of natural frequencies exceeded by any trial frequency when the ends of the member are clamped. This enables an existing algorithm to be used to obtain the natural frequencies of structures which contain tapered members.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2305-2306 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 62
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    International Journal for Numerical Methods in Engineering 21 (1985) 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 21 (1985), S. i 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1-11 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: ‘Dynamic’ or ‘viscous’ relaxation procedures have not gained much popularity in finite element analysis in which the direct (Gaussian elimination) solution dominates. Reasons for this are various - the most important being the rather slow convergence generally achieved for such procedures. However, it is possible to accelerate this quite dramatically and a method of doing so is shown in this paper. With the use of such acceleration and the inherent advantages of greatly reduced storage requirements and simplicity of programming, relaxation procedures promise an exciting possibility for the solution of large two- and three-dimensional problems in both linear and nonlinear ranges.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 13-18 
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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 21 (1985), S. 37-63 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structural reanalysis problems, such as in nonlinear finite element analysis or optimum design, involve progressive changes in the global stiffness matrix and its matrix factors. Although many studies have been devoted to the subject of matrix factor modification, most investigations have dealt with the problem separately from sparse matrix methods. This paper introduces a graph-theoretic model for the forward solution procedure which is applicable for identifying the modified entries of the matrix factors due to changes in the original matrix. Applications of this graph-theoretic model to existing refactorization methods are presented. The relation between substructuring and sparse matrix ordering strategies, and their effects on reanalysis are discussed. Modification of a sparse matrix associated with an n × n finite element grid ordered by the nested dissection scheme is analysed.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 19-36 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the design of thin turbomachinery blades with specified whirl velocities across the blade span. The numerical scheme involves iteration between the directs solution of a finite-volume method developed earlier on by Soulis1 and a design solution.The finite-volume method, which is a combination of finite elements and finite differences, solves the three-dimensional, inviscid, steady arid potential flow through turbomachinery blade rows in the incompressible, compressible and transonic flow range. In the design step, the whirl velocity distribution is specified across the blade span (Dirichlet boundary condition). The design procedure yields a new set of co-ordinates for the blade geometry which are used in the next iteration of the direct solution. However, in the present analysis only thin turbomachinery blades are designed, although a fully three-dimensional numerical method is used (the whirl velocity components of the flow field are averaged over the blade suction and pressure surface).The numerical method has been used to design free-vortex thin turbomachinery blades. Results show that the new numerical procedure is a comparatively economic and reliable method for designing thin turbomachinery blades. It may form the baseline for complete three-dimensional turbomachinery blade designs.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 65-88 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution procedure for the analysis of planar and axisymmetric-contact- problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure are the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 89-104 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Relations between displacement models using reduced integration and hybrid mixed models based on the Hellinger-Reissner and the Herrmann principles have been investigated. Five different isoparametric elements are considered for the case of plane stress, plane strain and plate bending elasticity problems.It is proved that the following relations hold for both models, provided the number of terms of a polynomial expressing the stress or strain component in the formulation of the mixed models is equal to the number of integration points of the reduced integration. If the stiffness matrix of the mixed model is evaluated by the identical integration rule with the reduced integration, the stiffness matrices of both models are identical. Thus, both models are equivalent, if the stiffness matrix of the mixed model is integrated exactly by the identical integration rule with the reduced integration.The displacement models using uniform reduced integration and selective reduced integration are equivalent to the mixed models based on the Hellinger-Reissner and the Herrmann principles except for the 6-node element, respectively.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 105-114 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new three-noded triangular element for plate bending is described. The element is based on an earlier stress-smoothed triangular element due to Razzaque,1 but extra internal ‘bubble’ functions are included to make it more flexible. The accuracy of the new element is compared with that of a number of other high-performance triangular elements. It is concluded that the present element and that due to Hansen, Bergan and Syvertsen2 are the two most accurate triangular thin plate elements currently available. The extra lines of FORTRAN required to convert Razzaque's shape function subroutine to that for the new element are given, thus making the new element easy to implement in any general-purpose finite element program.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 115-129 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A vector boundary integral equation (BIE) formulation and numerical solution procedure is presented for problems of three-dimensional elastic wave radiation and scattering from arbitrarily shaped obstacles. The formulation is explicitly in terms of surface traction and displacement, rather than wave potentials, and the BIE on which numerical work is based is written in a form entirely free of Cauchy principal value integrals. Indeed, the subsequent computational process, based on quadratic isoparametric boundary elements, renders all integrals free of singularities, so that ordinary Gaussian quadrature may be used. Numerical examples include scattering from spherical surfaces and radiation from a cube.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 163-168 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A fully discrete stability and accuracy analysis of some algorithms for the one-dimensional heat equation is presented. Results illustrate that 2-pass explicit schemes which simultaneously employ lumped and coupled capacity matrices are capable of improved performance over the standard 1-pass explicit scheme.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 169-182 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A general matrix operator is established for solving linear boundary value problems in slip-line field theory. The operator will enable a wider class of problems to be solved than were previously possible with the matrix slip-line field technique. As an illustration, a range of solutions are generated involving the previously intractable Coulomb friction boundary condition.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 193-193 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 193-193 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 194-195 
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    International Journal for Numerical Methods in Engineering 21 (1985) 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 229-238 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 197-209 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Exact expressions are presented for the potentials, at an arbitrary point in space, due to two quadratic distributions in a triangular disc. These expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions. It is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here, together with an expression for the potential corresponding to a linear distribution. This latter expression was presented in an earlier paper.1 Numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 211-228 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Use of the Green function, for the solution of boundary-value problems, frequently results in singular integral equations. Algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method (BEM). They are based upon the use of appropriately weighted Gaussian quadrature formulae, together with numerical geometrical transformations of the region of integration. The use of high-order subdomain expansion functions, for interpolation over nonplanar elements, allows boundary curvature to be accommodated. In particular, the handling of Green functions with logarithmic and r-1 behaviour are detailed. Volume integrals, with r-2 singularity, are outlined. Operations are performed on a simplex, thus resulting in generality and ease of automation. This scheme has been incorporated into boundary element method software and successfully applied to a variety of problems.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 239-265 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper reports a new explicit and conditionally stable finite difference equation for heat conduction. It predicts results with an accuracy comparable with or better than that obtainable by other methods. Stability of operation can be extended to any desired degree by subdividing the basic time step and increasing the number of nodes. Some existing difference equations are special cases of the new equation reported in this paper. The new solution has been tested by calculating the response of a slab to transient and progressive waves whose analytical solutions are known.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1577-1581 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An efficient method for solving algebraic equations is given. The linear equations are solved only once and iterations are performed on the non linear equations. If an initial approximation to a desired root is available, then it is utilized in the solution process. Results of some computational experiments are given.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2221-2236 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem treated is the integration of singular functions which arise in three-dimensional isoparametric formulations of boundary integral equations. A Taylor expansion in the local parametric co-ordinates is developed for the singular integrand, so allowing singular terms to be integrated in closed form, even for curved surface elements. The remainder integral obtained by subtracting out the worst singularities is integrated by repeated Gaussian quadrature.Two groups of tests are presented. First, the accuracy of the integrations has been checked for plane parallelograms (for which exact solutions have been developed) and for curved elements on a sphere. Secondly, results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems; zonal surface harmonics on a sphere and the capacitance of an ellipsoid. The agreement obtained with few degrees-of-freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2273-2287 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A software system for the automated computer simulation of two-dimensional elastostatic problems by the finite element method is described. This system consists of two parts, automated mesh generation and automated stress analysis. The mesh generation is based on a method in which equilateral triangles are generated successively in the unmeshed region. Automated mesh refinement is carried out in the latter part of the simulation process. The stress analysis is based on the assumed stress hybrid method and the successive over relaxation method. The computer program developed for this paper can generate a succession of increasingly refined triangular meshes until a certain mesh convergence criterion is achieved. The mesh convergence criterion is based on a comparison of nodal stresses in successive analyses until all the stress differences are within a specified tolerance.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 267-283 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a previous paper1, design sensitivity analysis of static response of structural systems when general boundary conditions are imposed during the analysis phase was developed and presented. This paper presents methods for design sensitivity analysis of dynamic response of structural systems when general boundary conditions are imposed during the analysis phase: Eigenvalue as well as transient response problems are discussed. Design sensitivity expression for eigenvalue constraints is derived. For the transient problem, point-wise as well as the integral-type constraint functions are treated. Advantages of these design sensitivity analysis procedures for the dynamic problem are the same as for the static problem. Namely, they are compatible with any existing finite element analysis computer code. Also, they can handle general boundary conditions that are design independent or dependent. Three simple examples are presented to show use of the procedures. Based on these applications, general-purpose numerical procedures can be developed and incorporated into existing computer codes.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 317-328 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A geometrically nonlinear formulation for a 48 degrees-of-freedom (d.o.f.) quadrilateral shell element is presented. Each of the three displacement functions of u, v and w is based on the bicubic Hermitian polynomial. The surface of the element is modelled using linearized ratronal B-spline functions which may be linked to the geometric data bases generated by the computer-aided design system. The displacement functions and the 48 d.o.f. are expressed in both curvilinear and Cartesian forms, whereas the strain-displacement equations are expressed in curvilinear co-ordinates. The use of Cartesian displacement functions and degrees-of-freedom allow for the proper representation of the six rigid body motions even for the element with nonzero Gaussian curvature, such as a bellows. Two examples are demonstrated: snap-through buckling of a spherical cap and large deflection of a semi-toroidal bellows shell. Results compare well with alternative solutions.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 361-365 
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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 21 (1985), S. 367-383 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 385-385 
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  • 90
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 487-507 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper reviews the derivation procedure of conventional stress-based elements and then shows how the procedure can be simplified by using degrees-of-freedom which are amplitudes of the boundary loading modes (‘mode-amplitude technique’). This gives one class of element based on stress assumptions and uses only one virtual principle. The natural formulation of hierarchical stress elements is shown.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 529-541 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The finite prism technique introduced by Zienkiewicz and Too4 is extended to include 12-node prism elements and, more importantly, a novel offset beam element. The use of 12-node prism elements enables parabolic strain distributions to be simulated, this being useful for structures which have strongly tapered cross-sections. The offset beam element is used to simulate flexure and torsion of a beam whose centroid is offset from the main structure. The element is specified completely at the nodes of adjacent prism elements and so is not really an ‘element’ in the usual sense.The analysis is applied to thin and thick plates and to shells, with and without edge beams. It is shown to be more versatile than the finite strip method and it requires smaller computer resources than the finite element method. Experimental verification of the analysis is obtained by comparison with measurements for a double-T bridge deck tested by Loo14.
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 93
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 583-584 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 94
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 601-616 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The displacement of a slightly compressible liquid by another in a porous medium has been modelled. This problem, which involves a moving boundary, has been numerically solved for the one-dimensional case by using the Galerkin method. State and parameter estimation have been carried out using the extended Kalman filter.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 95
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 663-670 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three boundary integral equations for the solution of an important class of elastic slab problems are considered. Some numerical examples are examined in order to illustrate the application of the integral equations to particular boundary-value problems.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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  • 96
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 837-851 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Orthogonal curvilinear co-ordinates represent the logical choice for description of the middle surface of the majority of shells in engineering practice. By means of orthogonalization of originally skew parameter lines at integration points for shell analysis by the finite element method (FEM), the remaining minority can be treated without having to resort to skew curvilinear co-ordinates. Therefore, it does not seem to be worth while to extend existing computer codes for shell analysis by the FEM, restricted to orthogonal curvilinear co-ordinates, to general curvilinear co-ordinates. Depending on the structure of such a code, this extension may require a substantial amount of recoding. (However, it is advisable to consider general curvilinear co-ordinates if a new computer code for shell analysis by the FEM, based on thin- or thick-shell theory, is written).Based on these considerations, the concept of ‘discrete orthogonalization of parameter lines’ has been developed. It is presented in this paper and applied to the analysis of a hyperbolic paraboloid groined vault subjected to dead load. In the numerical investigation it is demonstrated that treating skew parameter lines incorrectly as orthogonal has a significant effect on the results for the displacements and the internal forces.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 97
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 909-928 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non-physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 98
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 801-824 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mixed finite element procedures with triangular and quadrilateral elements are evaluated and applied for nonlinear elastic and elastic-plastic analysis of some engineering problems. The elastic-plastic analysis involves implementation of von Mises, Drucker-Prager and Cap models. A number of special techniques such as symbolic programming, utilization of dihedral symmetry and the frontal solution are used to achieve computational economy. The procedure is also adopted for simulation of construction sequences in geomechanics such as excavation involving stress-free surface. The proposed procedures are evaluated and verified with respect to closed-form solutions, other finite element (displacement) procedures and field observations.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
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  • 99
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 899-908 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Non-Newtonian fluid motion generated by a vertical porous hot plate in the presence of a transverse magnetic field is studied when viscous and ohmic dissipations are significant. When the temperature of the plate is very large, a general differential approximation for the radiative flux enables the asymptotic flow, valid far away from the tips of the plate, to reduce to a set of nonlinear and coupled ordinary differential equations. The solutions of these differential equations are studied for both small and large values of the absorption coefficient. The temperature, velocity and magnetic field distributions are discussed quantitatively. A primary conclusion of the analysis is that the distributions of temperature, velocity and magnetic field are much larger for a fluid with a large absorption coefficient than for a fluid with a small absorption coefficient.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 100
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 929-939 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A body-fitted curvilinear co-ordinate system is used to solve the equations of two-dimensional incompressible laminar flow over bluff obstructions by finite differences. Arbitrary conditions at the corner are removed by this method. Results for a backward-facing step are in reasonable agreement with those obtained with conventional mesh systems, and the differences are explained. A treatment of a channel expansion, in comparison with empirical data, is also included. The capability of the present method to handle arbitrary two-dimensional geometries is stressed and demonstrated, using a triangle and a semi-circle as examples.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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